Graph Structure of Neural Networks
Xiaolan Xu, Robin Wen, Yue Weng, Beizhen Chang
We develop a new way of representing a neural network as a graph, which we call relational graph. Our key insight is to focus on message exchange, rather than just on directed data flow. As a simple example, for a fixedwidth fully-connected layer, we can represent one input channel and one output channel together as a single node, and an edge in the relational graph represents the message exchange between the two nodes (Figure 1(a)).
(1) Clustering Coefficient
(2) Average Path Length
Experimental Setup (Section 4 in the paper)
Major Conclusions (Section 5 in the paper)
(1) graph structure of neural networks matters;
(2) a “sweet spot” of relational graphs lead to neural networks with significantly improved predictive performance;
(3) neural network’s performance is approximately a smooth function of the clustering coefficient and average path length of its relational graph;
(4) our findings are consistent across many different tasks and datasets;
(5) top architectures can be identified efficiently;
(6) well-performing neural networks have graph structure surprisingly similar to those of real biological neural networks.