Characterizing Learning Dynamics of Deep Neural Networks via Complex Networks

TL;DR

This paper applies Complex Network Theory to analyze the learning dynamics of Deep Neural Networks, introducing new metrics that reveal distinct behaviors of accurate versus under-trained models.

Contribution

It introduces novel CNT-based metrics for DNNs, enabling detailed analysis of learning dynamics and distinguishing network accuracy levels.

Findings

Accurate networks exhibit significantly different node and layer fluctuation patterns.

The proposed metrics can differentiate between low and high accuracy models.

Efficient implementation of CNT metrics for various neural network architectures.

Abstract

In this paper, we interpret Deep Neural Networks with Complex Network Theory. Complex Network Theory (CNT) represents Deep Neural Networks (DNNs) as directed weighted graphs to study them as dynamical systems. We efficiently adapt CNT measures to examine the evolution of the learning process of DNNs with different initializations and architectures: we introduce metrics for nodes/neurons and layers, namely Nodes Strength and Layers Fluctuation. Our framework distills trends in the learning dynamics and separates low from high accurate networks. We characterize populations of neural networks (ensemble analysis) and single instances (individual analysis). We tackle standard problems of image recognition, for which we show that specific learning dynamics are indistinguishable when analysed through the solely Link-Weights analysis. Further, Nodes Strength and Layers Fluctuations make unprecedented behaviours emerge: accurate networks, when compared to under-trained models, show substantially divergent distributions with the greater extremity of deviations. On top of this study, we provide an efficient implementation of the CNT metrics for both Convolutional and Fully Connected Networks, to fasten the research in this direction.