Graph Structure of Neural Networks

TL;DR

This paper explores how the graph structure of neural networks influences their predictive performance, revealing a 'sweet spot' in relational graph properties that improves accuracy and aligns with biological neural networks.

Contribution

The paper introduces a novel relational graph representation of neural networks and demonstrates how specific graph properties correlate with performance improvements.

Findings

A 'sweet spot' in relational graph structure enhances neural network performance.

Performance correlates with clustering coefficient and path length of the graph.

High-performing networks have graph structures similar to biological neural networks.

Abstract

Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its predictive performance. Here we systematically investigate how does the graph structure of neural networks affect their predictive performance. To this end, we develop a novel graph-based representation of neural networks called relational graph, where layers of neural network computation correspond to rounds of message exchange along the graph structure. Using this representation we show that: (1) a "sweet spot" of relational graphs leads to neural networks with significantly improved predictive performance; (2) neural network's performance is approximately a smooth function of the clustering coefficient and average path length of its relational graph; (3) our findings are consistent across many different tasks and datasets; (4) the sweet spot can be identified efficiently; (5) top-performing neural networks have graph structure surprisingly similar to those of real biological neural networks. Our work opens new directions for the design of neural architectures and the understanding on neural networks in general.