Assessing Neural Network Representations During Training Using Noise-Resilient Diffusion Spectral Entropy

TL;DR

This paper introduces diffusion spectral entropy and mutual information as noise-resistant measures to analyze neural network representations during training, revealing insights into learning dynamics and aiding in model initialization and performance prediction.

Contribution

It proposes novel diffusion spectral measures for neural representations that are robust to noise and high-dimensionality, improving analysis of training processes and model performance.

Findings

DSE increases during training, indicating growing intrinsic complexity.

DSMI with class labels increases during generalization but stagnates during overfitting.

DSE and DSMI can predict downstream accuracy and guide network initialization.

Abstract

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.