Not yet reviewed by Pith; the record is open.

We study the use of binary activated neural networks as interpretable and explainable predictors in the context of regression tasks on tabular data; more specifically, we provide guarantees on their expressiveness, present an approach based on the efficient computation of SHAP values for quantifying the relative importance of the features, hidden neurons and even weights. As the model's simplicity is instrumental in achieving interpretability, we propose a greedy algorithm for building compact binary activated networks. This approach doesn't need to fix an architecture for the network in advance: it is built one layer at a time, one neuron at a time, leading to predictors that aren't needlessly complex for a given task.