An Operator Theoretic Approach for Analyzing Sequence Neural Networks

TL;DR

This paper introduces an operator theoretic framework based on Koopman theory to analyze trained neural networks globally, revealing semantic features and inner mechanisms through eigenanalysis.

Contribution

It presents a novel Koopman analysis method for neural networks, enabling global insight into their dynamics and interpretability.

Findings

Eigenvectors highlight sentiment-related n-grams.

Eigenvectors capture salient ECG features.

Eigenvalues relate to network behavior stability.

Abstract

Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze trained neural networks using an operator theoretic approach which is rooted in Koopman theory, the Koopman Analysis of Neural Networks (KANN). Key to our method is the Koopman operator, which is a linear object that globally represents the dominant behavior of the network dynamics. The linearity of the Koopman operator facilitates analysis via its eigenvectors and eigenvalues. Our method reveals that the latter eigendecomposition holds semantic information related to the neural network inner workings. For instance, the eigenvectors highlight positive and negative n-grams in the sentiments analysis task; similarly, the eigenvectors capture the salient features of healthy heart beat signals in the ECG classification problem.