An Operator Theoretic Approach for Analyzing Sequence Neural Networks
This provides a novel method for interpreting neural networks, which is a fundamental challenge in machine learning, though it appears incremental as it builds on existing Koopman theory.
The authors tackled the problem of analyzing deep neural networks by proposing an operator theoretic approach based on Koopman theory, which globally represents network dynamics with a linear operator and reveals semantic information through eigendecomposition, as demonstrated in sentiment analysis and ECG classification tasks.
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.