xRAI: Explainable Representations through AI

In this paper, we use Boolean functions or low arity and low-order polynomials as examples. We present xRAI an approach for extracting symbolic However xRAI can be applied to any function family representations of the mathematical functions efficiently learnable by a neural network. For the case of loworder a neural network was supposed to learn from the polynomials, this has been shown by [Andoni et al., trained network. The approach is based on the idea 2014]. of training a so-called interpretation network that For each family of functions, we train a neural network receives the weights and biases of the trained network called interpretation network (I-Net). The I-Net receives the as input and outputs the numerical representation weights and biases of a λ-Net as input and determines an of the function the network was supposed to approximation of a target function of the trained λ-Net. We learn that can be directly translated into a symbolic train the I-Net offline by systematically training λ-Nets on representation. We show that interpretation nets for different functions from the family and using these trained different classes of functions can be trained on synthetic networks as training examples for the I-Net.