Group Invariant Convolutional Boltzmann Machines

Abstract: We investigate group invariance in unsupervised learning in the context of certain generative networks based on Boltzmann machines. Specifically, we introduce a generalization of restricted Boltzmann machines which is adapted to input data that is acted upon by any compact group G. This is done by using certain G-equivariant convolutions between layers. We prove that the deep belief networks constructed from such Boltzmann machines define probability distributions that are invariant with respect to the action of G.