# A Spiking Neural Network Implementation of Gaussian Belief Propagation

arXiv: https://arxiv.org/abs/2512.10638 · HTML: https://mlsanity.com/paper/2512.10638/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [Spike-based Belief Propagation in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2608.19907/) (2026)

## Abstract (arXiv)

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.