Is network fragmentation a useful complexity measure?

TL;DR

This paper investigates the phenomenon of network fragmentation in deep neural networks, exploring its potential as a complexity measure to predict generalization performance and revealing new insights about its behavior in representations and training.

Contribution

The study introduces a fragmentation-based complexity measure that correlates with generalization and uncovers new properties of fragmentation in hidden representations and training dynamics.

Findings

Fragmentation occurs in input and hidden representations.

Fragmentation trends align with validation error during training.

Fragmentation is not solely caused by increased weight norms.

Abstract

It has been observed that the input space of deep neural network classifiers can exhibit `fragmentation', where the model function rapidly changes class as the input space is traversed. The severity of this fragmentation tends to follow the double descent curve, achieving a maximum at the interpolation regime. We study this phenomenon in the context of image classification and ask whether fragmentation could be predictive of generalization performance. Using a fragmentation-based complexity measure, we show this to be possible by achieving good performance on the PGDL (Predicting Generalization in Deep Learning) benchmark. In addition, we report on new observations related to fragmentation, namely (i) fragmentation is not limited to the input space but occurs in the hidden representations as well, (ii) fragmentation follows the trends in the validation error throughout training, and (iii) fragmentation is not a direct result of increased weight norms. Together, this indicates that fragmentation is a phenomenon worth investigating further when studying the generalization ability of deep neural networks.