A Spiking Neural Network Implementation of Gaussian Belief Propagation

TL;DR

This paper demonstrates how a spiking neural network can perform Gaussian belief propagation, enabling biologically plausible probabilistic inference for static and dynamic tasks like Kalman filtering.

Contribution

It introduces a neural implementation of Gaussian belief propagation using leaky integrate-and-fire neurons, bridging Bayesian inference and neuromorphic computing.

Findings

Accurate message passing validated against standard algorithms

Successful application to Kalman filtering and Bayesian linear regression

Demonstrates feasibility of neuromorphic probabilistic reasoning

Abstract

Bayesian inference offers a principled account of information processing in natural agents. However, it remains an open question how neural mechanisms perform their abstract operations. We investigate a hypothesis where a distributed form of Bayesian inference, namely message passing on factor graphs, is performed by a simulated network of leaky-integrate-and-fire neurons. Specifically, we perform Gaussian belief propagation by encoding messages that come into factor nodes as spike-based signals, propagating these signals through a spiking neural network (SNN) and decoding the spike-based signal back to an outgoing message. Three core linear operations, equality (branching), addition, and multiplication, are realized in networks of leaky integrate-and-fire models. Validation against the standard sum-product algorithm shows accurate message updates, while applications to Kalman filtering and Bayesian linear regression demonstrate the framework's potential for both static and dynamic inference tasks. Our results provide a step toward biologically grounded, neuromorphic implementations of probabilistic reasoning.