NN2Poly: A polynomial representation for deep feed-forward artificial neural networks

TL;DR

NN2Poly introduces a method to derive explicit polynomial models from trained deep neural networks, enhancing interpretability by extending previous single-layer approaches to arbitrarily deep multilayer perceptrons for regression and classification.

Contribution

It extends polynomial representation techniques to deep neural networks, enabling explicit, interpretable models for complex multilayer perceptrons in both regression and classification tasks.

Findings

Effective polynomial approximations of deep neural networks.

Demonstrated on real tabular datasets with promising results.

Addressed computational challenges with proposed constraints.

Abstract

Interpretability of neural networks and their underlying theoretical behavior remain an open field of study even after the great success of their practical applications, particularly with the emergence of deep learning. In this work, NN2Poly is proposed: a theoretical approach to obtain an explicit polynomial model that provides an accurate representation of an already trained fully-connected feed-forward artificial neural network (a multilayer perceptron or MLP). This approach extends a previous idea proposed in the literature, which was limited to single hidden layer networks, to work with arbitrarily deep MLPs in both regression and classification tasks. NN2Poly uses a Taylor expansion on the activation function, at each layer, and then applies several combinatorial properties to calculate the coefficients of the desired polynomials. Discussion is presented on the main computational challenges of this method, and the way to overcome them by imposing certain constraints during the training phase. Finally, simulation experiments as well as applications to real tabular data sets are presented to demonstrate the effectiveness of the proposed method.