Lindström, Maria2020-12-042020-12-042020-12-04http://hdl.handle.net/2077/67106We 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.engConvolutional Boltzmann Machines, Convolutional neural networks, artificial neural networks, machine learning, group invariance, group equivariancetext