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Complex-Valued Deep Boltzmann Machines

Deep Boltzmann Machines (DBMs) are a type of undirected deep generative models. They are part of the class of models used for performing unsupervised pretraining of deep neural networks. This paper presents the full deduction of the learning algorithm for DBMs with values in the complex domain. Experiments done using the MNIST and FashionMNIST datasets show a better performance of complex-valued DBMs compared with real-valued DBMs, both in terms of average log-probability, and in terms of classification error for the deep neural network models initialized using complex-valued DBMs.