Estimating global input relevance and enforcing sparse representations with a scalable spectral neural network approach

In machine learning practice it is often useful to identify relevant input features. Isolating key input elements, ranked according to their respective degree of relevance, can help to elaborate on the process of decision-making. Here, we propose a method to estimate the relative importance of the input components for a Deep Neural Network. This is achieved by leveraging a spectral re-parametrization of the model’s input layer. Eigenvalues associated with input nodes provide in fact a robust proxy to gauge the relevance of the supplied entry features. The spectral features ranking is performed automatically, as a byproduct of the network training, with negligible additional processing to be carried out. Moreover, by leveraging 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.