  Artificial Neural Networks (ANNs) are prevalent machine learning models that
are applied across various real-world classification tasks. However, training
ANNs is time-consuming and the resulting models take a lot of memory to deploy.
In order to train more parsimonious ANNs, we propose a novel mixed-integer
programming (MIP) formulation for training fully-connected ANNs. Our
formulations can account for both binary and rectified linear unit (ReLU)
activations, and for the use of a log-likelihood loss. We present numerical
experiments comparing our MIP-based methods against existing approaches and
show that we are able to achieve competitive out-of-sample performance with
more parsimonious models.
