Structure and performance of fully connected neural networks: Emerging complex network properties

Abstract

Understanding the behavior of Artificial Neural Networks is one of the main topics in the field recently, as black-box approaches have become usual since the widespread of deep learning. Such high-dimensional models may manifest instabilities and weird properties that resemble complex systems. Therefore, we propose Complex Network (CN) techniques to analyze the structure and performance of fully connected neural networks. For that, we build a dataset with 4 thousand models (varying the initialization seed) and their respective CN properties. This is the first work to explore the CN properties of an ample number of fully connected networks accounting for the variance caused by random weight initialization. The networks are trained in a supervised classification setup considering four vision benchmarks and then approached as a weighted and undirected graph of neurons and synapses (learned weights). Results show that neuronal centrality is highly correlated to network classification performance. We also propose the concept of Bag-Of-Neurons (BoN), a CN-based approach for finding topological signatures linking similar neurons. Results suggest that six neuronal types emerge in such networks, independently of the target domain, and are distributed differently according to classification accuracy. We also tackle specific CN properties related to performance, such as higher subgraph centrality on lower-performing models. Our findings suggest that CN properties play a critical role in the performance of fully connected neural networks, with topological patterns emerging independently on a wide range of models.