Graph Structure of 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 graphbased 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) topperforming 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 DOI:
 10.48550/arXiv.2007.06559
 arXiv:
 arXiv:2007.06559
 Bibcode:
 2020arXiv200706559Y
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Computer Vision and Pattern Recognition;
 Computer Science  Social and Information Networks;
 Statistics  Machine Learning
 EPrint:
 ICML 2020, with opensource code