Spiking Neural Algorithms for Markov Process Random Walk

TL;DR

This paper introduces two neural algorithms designed for efficient implementation of random walks on spiking neuromorphic hardware, inspired by biological spatial representations and density tracking, with analysis of their scalability and probabilistic modeling capabilities.

Contribution

It presents novel neural algorithms for simulating random walks on neuromorphic hardware, inspired by biological grid cells and density tracking methods.

Findings

Both algorithms efficiently model random walks under various conditions.

The methods demonstrate scalable complexity suitable for neuromorphic hardware.

They enable probabilistic modeling in neural systems.

Abstract

The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking neuromorphic hardware. The first method tracks the positions of individual walkers independently by using a modular code inspired by the grid cell spatial representation in the brain. The second method tracks the densities of random walkers at each spatial location directly. We analyze the scaling complexity of each of these methods and illustrate their ability to model random walkers under different probabilistic conditions.