Parallel Tempering-Inspired Distributed Binary Optimization with In-Memory Computing

TL;DR

This paper introduces a physics-inspired parallel tempering framework for in-memory computing that enhances binary optimization solvers like WalkSAT, achieving faster solutions with minimal energy overhead.

Contribution

It proposes a novel IMC-compatible parallelism framework based on parallel tempering, applicable to various IMC solvers, and demonstrates its effectiveness on SAT problems.

Findings

PTIC-WalkSAT outperforms standard WalkSAT in 84% of instances

The naive parallel variant outperforms in 65% of instances

Energy overhead of the framework is less than 1% of total energy

Abstract

In-memory computing (IMC) has been shown to be a promising approach for solving binary optimization problems while significantly reducing energy and latency. Building on the advantages of parallel computation, we propose an IMC-compatible parallelism framework based on the physics-inspired parallel tempering (PT) algorithm, enabling cross-replica communication to improve the performance of IMC solvers. This framework enables an IMC solver not only to improve performance beyond what can be achieved through parallelization, but also affords greater flexibility for the search process with low hardware overhead. We justify that the framework can be applied to almost any IMC solver. We demonstrate the effectiveness of the framework for the Boolean satisfiability (SAT) problem, using the WalkSAT heuristic as a proxy for existing IMC solvers. The resulting PT-inspired cooperative WalkSAT (PTIC-WalkSAT) algorithm outperforms the standard WalkSAT heuristic in terms of the iterations-to-solution in 84.0% of the tested problem instances and its na\"ive parallel variant (PA-WalkSAT) does so in 64.9% of the instances, and with a higher success rate in the majority of instances. An estimate of the energy overhead of the PTIC framework for two hardware accelerator architectures indicates that in both cases the overhead of running the PTIC framework would be less than 1% of the total energy required to run each accelerator.