Discrete Langevin machine: Bridging the gap between thermodynamic and neuromorphic systems

Area of Science:

• Computational Physics
• Neuromorphic Engineering
• Statistical Mechanics

Background:

• Langevin dynamics are crucial for modeling stochastic processes.
• Discrete systems require specialized formulations for accurate simulation.
• Neuromorphic computing aims to mimic the brain's efficiency.

Purpose of the Study:

• To derive a Langevin dynamics formulation for discrete systems.
• To propose a network architecture based on a two-state system simplification.
• To evaluate the Langevin machine for computing Boltzmann distributed systems using LIF neurons.

Main Methods:

• Derivation of a generic stochastic process formulation for discrete Langevin dynamics.
• Simplification of dynamics for a two-state system.
• Implementation and analysis of a Langevin machine using Leaky Integrate-and-Fire (LIF) neurons.
• Study of simplified neuromorphic hardware models for error control.

Main Results:

• A novel formulation of Langevin dynamics for discrete systems was successfully derived.
• The simplified two-state system dynamics informed a practical network architecture.
• The Langevin machine demonstrated potential for quantitative computation of Boltzmann distributed systems.
• Error sources in simplified neuromorphic models were investigated.

Conclusions:

• The derived Langevin dynamics formulation provides a robust framework for discrete systems.
• The Langevin machine, utilizing LIF neurons, presents a viable approach for accurate quantitative computations.
• Further research into error control in neuromorphic hardware is warranted for practical applications.