Ensembles of Spiking Neurons with Noise Support Optimal Probabilistic Inference in a Dynamically Changing Environment

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information.Author Summary: The Markov Chain Monte Carlo (MCMC) approach to probabilistic inference for a distribution is to draw a sequence of samples from and to carry out computational operations via simple online computations on such a sequence. But such a sequential computational process takes time, and therefore this simple version of the MCMC approach runs into problems when one needs to carry out probabilistic inference for rapidly varying distributions. This difficulty also affects all currently existing models for emulating MCMC sampling by networks of stochastically firing neurons. We show here that by moving to a space-rate approach where salient probabilities are encoded through the spiking activity of ensembles of neurons, rather than by single neurons, this problem can be solved. In this way even theoretically optimal models for dealing with time varying distributions through sequential Monte Carlo sampling, so called particle filters, can be emulated by networks of spiking neurons. Each spike of a neuron in an ensemble represents in this approach a “particle” (or vote) for a particular value of a time-varying random variable. In other words, neural circuits can speed up computations based on Monte Carlo sampling through their inherent parallelism.