Abstract
The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.
Highlights
Attempts to understand the organization of computations in the brain from the perspective of traditional, mostly deterministic, models of computation, such as attractor neural networks or Turing machines, have run into problems: Experimental data suggests that neurons, synapses, and neural systems are inherently stochastic [1], especially in vivo, and seem less suitable for implementing deterministic computations
In this work we propose a detailed neural network model that fulfills these computational requirements and we relate the spiking dynamics of the network to concrete probabilistic computations
Our model suggests that neural systems are suitable to carry out probabilistic inference by using stochastic, rather than deterministic, computing elements
Summary
Attempts to understand the organization of computations in the brain from the perspective of traditional, mostly deterministic, models of computation, such as attractor neural networks or Turing machines, have run into problems: Experimental data suggests that neurons, synapses, and neural systems are inherently stochastic [1], especially in vivo, and seem less suitable for implementing deterministic computations. This holds for ion channels of neurons [2], synaptic release [3], neural response to stimuli (trial-to-trial variability) [4,5], and perception [6]. We will call the set of variables zlz1, . . . ,zK , which we condition on, the observed variables and denote it by o
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