Regional, Lattice and Logical Representations of Neural Networks

Neural networks are computational models that aim to generalize patterns found in datasets from which they are determined by means of a learning algorithm [8]. Despite the undeniable advancement in the state of the art of intelligent systems promoted by neural networks, their lack of interpretability is subject to criticism. Neural networks suffer from the black box problem due to the lack of justification for their results and the impossibility to directly inspect their learned information [3, 5]. As several architectures of neural networks realize piecewise linear functions or may be approximated by them, a path towards interpretability is through regional format representations of such neural networks and functions by explicit sets of pairs p, Ω of a linear piece p and a region Ω such that, for a vector of input values x Ω, the output is given by p(x). An algorithm for establishing regional representations from feedforward neural networks with rectified linear units as activation functions is proposed in [15]. The main goal of this work is to introduce an algorithm for computing regional format representations of ReLU-TId neural networks, which are feedforward neural networks with rectified linear units as activation functions in hidden layers and truncated identity as activation functions in the output layer.