  Stochastic gradient descent (SGD) is a key ingredient in the training of deep
neural networks and yet its geometrical significance appears elusive. We study
a deterministic model in which the trajectories of our dynamical systems are
described via geodesics of a family of metrics arising from the diffusion
matrix. These metrics encode information about the highly non-isotropic
gradient noise in SGD. We establish a parallel with General Relativity models,
where the role of the electromagnetic field is played by the gradient of the
loss function. We compute an example of a two layer network.
