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

• URL: http://arxiv.org/abs/2112.11397v4
• Date: Mon, 25 Sep 2023 18:33:01 GMT
• Title: NN2Poly: A polynomial representation for deep feed-forward artificial neural networks
• Authors: Pablo Morala (1 and 2), Jenny Alexandra Cifuentes (3), Rosa E. Lillo (1 and 2), I\~naki Ucar (1 and 2) ((1) uc3m-Santander Big Data Institute, Universidad Carlos III de Madrid. Spain., (2) Department of Statistics, Universidad Carlos III de Madrid. Spain., (3) ICADE, Department of Quantitative Methods, Faculty of Economics and Business Administration, Universidad Pontificia Comillas. Spain.)
• Abstract summary: NN2Poly is a theoretical approach to obtain an explicit model of an already trained fully-connected feed-forward artificial neural network. This approach extends a previous idea proposed in the literature, which was limited to single hidden layer networks.
• Score: 0.6502001911298337
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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