# The Discrete Langevin Machine: Bridging the Gap Between Thermodynamic and Neuromorphic Systems

## TL;DR

This paper introduces the Discrete Langevin Machine, a novel neural network architecture that uses Langevin dynamics for discrete systems, enabling efficient computation of Boltzmann distributions with neuromorphic hardware.

## Contribution

It derives a Langevin dynamics formulation for discrete systems and proposes the Langevin machine architecture for neuromorphic implementation, bridging thermodynamic and neuromorphic computing.

## Key findings

- The Langevin machine can accurately compute Boltzmann distributed results.
- Simplified models show robustness against hardware-induced errors.
- The approach offers a promising pathway for neuromorphic probabilistic computing.

## Abstract

A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The Langevin machine represents a promising approach to compute successfully quantitative exact results of Boltzmann distributed systems by LIF neurons. Besides a detailed introduction of the dynamics, different simplified models of a neuromorphic hardware system are studied with respect to a control of emerging sources of errors.