  Tasks like image reconstruction in computer vision, matrix completion in
recommender systems and link prediction in graph theory, are well studied in
machine learning literature. In this work, we apply a denoising
autoencoder-based neural network architecture to the task of completing partial
multiplication (Cayley) tables of finite semigroups. We suggest a novel loss
function for that task based on the algebraic nature of the semigroup data. We
also provide a software package for conducting experiments similar to those
carried out in this work. Our experiments showed that with only about 10% of
the available data, it is possible to build a model capable of reconstructing a
full Cayley from only half of it in about 80% of cases.
