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.

翻译：尽管神经网络在实际应用中取得了巨大成功，尤其是深度学习的兴起，但其可解释性及背后的理论行为仍是一个开放的研究领域。本文提出NN2Poly：一种理论方法，通过获得显式多项式模型来精确表示已训练的 fully-connected 前馈人工神经网络（多层感知机或MLP）。该方法将文献中先前仅适用于单隐层网络的思路扩展至任意深度的MLP，适用于回归和分类任务。NN2Poly 利用泰勒展开逐层处理激活函数，随后应用多种组合性质计算目标多项式的系数。本文讨论了该方法面临的主要计算挑战，以及通过在训练阶段施加特定约束来克服这些挑战的途径。最后，通过仿真实验和真实表格数据集的应用展示了所提方法的有效性。