Emergent Inference of Hidden Markov Models in Spiking Neural Networks Through Winner-Take-All

Hidden Markov models (HMMs) underpin the solution to many problems in computational neuroscience. However, it is still unclear how to implement inference of HMMs with a network of neurons in the brain. The existing methods suffer from the problem of being nonspiking and inaccurate. Here, we build a precise equivalence between the inference equation of HMMs with time-invariant hidden variables and the dynamics of spiking winner-take-all (WTA) neural networks. We show that the membrane potential of each spiking neuron in the WTA circuit encodes the logarithm of the posterior probability of the hidden variable in each state, and the firing rate of each neuron is proportional to the posterior probability of the HMMs. We prove that the time course of the neural firing rate can implement posterior inference of HMMs. Theoretical analysis and experimental results show that the proposed WTA circuit can get accurate inference results of HMMs.