CoFrNets: Interpretable Neural Architecture Inspired by Continued Fractions

TL;DR

This paper introduces CoFrNet, an interpretable neural architecture inspired by continued fractions, demonstrating its universal approximation capabilities and strong performance across various datasets and modalities.

Contribution

The paper presents a novel neural network architecture based on continued fractions, with proven universality and enhanced interpretability compared to existing models.

Findings

CoFrNet can be efficiently trained and interpreted.

It accurately models nonlinear functions and higher-order terms.

Performs comparably or better than other interpretable models on diverse datasets.

Abstract

In recent years there has been a considerable amount of research on local post hoc explanations for neural networks. However, work on building interpretable neural architectures has been relatively sparse. In this paper, we present a novel neural architecture, CoFrNet, inspired by the form of continued fractions which are known to have many attractive properties in number theory, such as fast convergence of approximations to real numbers. We show that CoFrNets can be efficiently trained as well as interpreted leveraging their particular functional form. Moreover, we prove that such architectures are universal approximators based on a proof strategy that is different than the typical strategy used to prove universal approximation results for neural networks based on infinite width (or depth), which is likely to be of independent interest. We experiment on nonlinear synthetic functions and are able to accurately model as well as estimate feature attributions and even higher order terms in some cases, which is a testament to the representational power as well as interpretability of such architectures. To further showcase the power of CoFrNets, we experiment on seven real datasets spanning tabular, text and image modalities, and show that they are either comparable or significantly better than other interpretable models and multilayer perceptrons, sometimes approaching the accuracies of state-of-the-art models.