Deep learning Gauss-Manin connections (Q2113261)

There has been much activity in the last few years on machine-learning applied to understanding pure mathematics, in order to formulate new conjectures, verify formulae and speed up computations. The current paper is very interesting: it applies a deep neural networks to the computation of Gauss-Manin connections, exemplified by families of hypersurfaces as algebraic varieties. The methods are novel and it demonstrates a significant speed-up in the usually difficult computation of connections on manifolds. It shows that there must be some underlying pattern in connections on which the neural network is picking up.