  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.
