Linear-Nonlinear-Poisson Neurons Can Do Inference On Deep Boltzmann Machines

One conjecture in both deep learning and classical connectionist viewpoint is that the biological brain implements certain kinds of deep networks as its backend. However, to our knowledge, a detailed correspondence has not yet been set up, which is important if we want to bridge between neuroscience and machine learning. Recent researches emphasized the biological plausibility of LinearNonlinear-Poisson (LNP) neuron model. We show that with neurally plausible choices of parameters, the whole neural network is capable of representing any Boltzmann machine and performing a semi-stochastic Bayesian inference algorithm lying between Gibbs sampling and variational inference.