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

**R. Legenstein and W. Maass**

### Abstract:

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.

**Reference:** R. Legenstein and W. Maass.
Ensembles of spiking neurons with noise support optimal probabilistic
inference in a dynamically changing environment.
*PLOS Computational Biology*, 10(10):e1003859, 2014.