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arXiv · 1311.3211

Stochastic inference with deterministic spiking neurons

Mihai A. Petrovici·Johannes Bill·Ilja Bytschok·Johannes Schemmel·Karlheinz Meier
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Abstract

The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic response to various types of stimulation. We show that an ensemble of deterministic leaky integrate-and-fire neurons embedded in a spiking noisy environment can attain the correct firing statistics in order to sample from a well-defined target distribution. We provide an analytical derivation of the activation function on the single cell level; for recurrent networks, we examine convergence towards stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.

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Mihai A. Petrovici, Johannes Bill, Ilja Bytschok, Johannes Schemmel, Karlheinz Meier. 2013-11-13. Stochastic inference with deterministic spiking neurons. https://arxiv.org/abs/1311.3211

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