Stochasticity from function -- why the Bayesian brain may need no noise

TL;DR

This paper proposes that deterministic spiking neural networks can perform Bayesian inference without the need for noise, challenging the common assumption that stochasticity is essential for probabilistic computation in the brain.

Contribution

It analytically demonstrates how correlations in deterministic networks can enable Bayesian sampling, reducing the need for explicit noise and broadening the understanding of neural computation.

Findings

Deterministic networks can perform Bayesian inference without added noise.

Correlations in neural activity can be controlled via synaptic plasticity.

Simulations and neuromorphic experiments validate the theoretical claims.

Abstract

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may, in fact, have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functionally Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial.