Estimating Global Input Relevance and Enforcing Sparse Representations with a Scalable Spectral Neural Network Approach

TL;DR

This paper introduces a scalable spectral neural network method that automatically estimates input feature relevance and enforces sparse representations, enhancing model interpretability without extra computational overhead.

Contribution

It presents a novel spectral re-parametrization technique that ranks input features by importance during training and promotes sparsity for better explainability.

Findings

Eigenvalues effectively measure feature relevance.

The method outperforms existing techniques on synthetic and real data.

Enforces sparse input representations automatically.

Abstract

In machine learning practice it is often useful to identify relevant input features. Isolating key input elements, ranked according their respective degree of relevance, can help to elaborate on the process of decision making. Here, we propose a novel method to estimate the relative importance of the input components for a Deep Neural Network. This is achieved by leveraging on a spectral re-parametrization of the optimization process. Eigenvalues associated to input nodes provide in fact a robust proxy to gauge the relevance of the supplied entry features. Notably, the spectral features ranking is performed automatically, as a byproduct of the network training, with no additional processing to be carried out. Moreover, by leveraging on the regularization of the eigenvalues, it is possible to enforce solutions making use of a minimum subset of the input components, increasing the explainability of the model and providing sparse input representations. The technique is compared to the most common methods in the literature and is successfully challenged against both synthetic and real data.