Emergence of Network Motifs in Deep Neural Networks

TL;DR

This paper demonstrates that network science tools can analyze the emergence of functional motifs in artificial neural networks, revealing how initialization and learning dynamics shape network topology.

Contribution

It introduces the application of network motif analysis to deep neural networks, showing how initialization schemes influence motif development during learning.

Findings

Learning dynamics shape network topology significantly.

Initialization schemes bias the emergence of motifs.

Motifs in neural networks resemble those in biological systems.

Abstract

Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called "network motifs". In this article we show that network science tools can be successfully applied also to the study of artificial neural networks operating according to self-organizing (learning) principles. In particular, we study the emergence of network motifs in multi-layer perceptrons, whose initial connectivity is defined as a stack of fully-connected, bipartite graphs. Our simulations show that the final network topology is primarily shaped by learning dynamics, but can be strongly biased by choosing appropriate weight initialization schemes. Overall, our results suggest that non-trivial initialization strategies can make learning more effective by promoting the development of useful network motifs, which are often surprisingly consistent with those observed in general transduction networks.