Forward Composition Propagation for Explainable Neural Reasoning

Abstract: This paper proposes an algorithm called Forward Composition Propagation (FCP) to explain the predictions of feed-forward neural networks operating on structured classification problems. In the proposed FCP algorithm, each neuron is described by a composition vector indicating the role of each problem feature in that neuron. Composition vectors are initialized using a given input instance and subsequently propagated through the whole network until reaching the output layer. The sign of each composition value indicates whether the corresponding feature excites or inhibits the neuron, while the absolute value quantifies its impact. The FCP algorithm is executed on a post-hoc basis, i.e., once the learning process is completed. Aiming to illustrate the FCP algorithm, this paper develops a case study concerning bias detection in a fairness problem in which the ground truth is known. The simulation results show that the composition values closely align with the expected behavior of protected features. The source code and supplementary material for this paper are available at https://github.com/igraugar/fcp.