NN2Poly: A polynomial representation for deep feed-forward artificial neural networks
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Interpretability of neural networks and their underlying theoretical behaviour remain being 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 that allows to obtain polynomials that provide an alternative representation of an already trained deep neural network. This extends the previous idea proposed in arXiv:2102.03865, which was limited to single hidden layer neural networks, to work with arbitrarily deep feed-forward neural networks in both regression and classification tasks. The objective of this paper is achieved by using a Taylor expansion on the activation function, at each layer, and then using several combinatorial properties that allow to identify the coefficients of the desired polynomials. The main computational limitations when implementing this theoretical method are discussed and it is presented an example of the constraints on the neural network weights that are necessary for NN2Poly to work. Finally, some simulations are presented were it is concluded that using NN2Poly it is possible to obtain a representation for the given neural network with low error between the obtained predictions.
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