Breaking Local-Minimum Traps in Spiking Neural Network-Based Solvers for CSPs via Parallel Tempering

2026-07-09

AI Summary

This work addresses the tendency of spiking neural network (SNN)-based solvers to become trapped in local minima when tackling constraint satisfaction problems (CSPs), particularly on hard instances. To enhance global exploration while preserving the intrinsic asynchronous dynamics of SNNs, the study introduces parallel tempering—a technique previously unexplored in this context—by running multiple temperature replicas asynchronously and periodically exchanging their states. The proposed method integrates stochastic neurons, connectivity-based constraint encoding, and a spike-based sampling strategy. Evaluated on 1,000 instances from SATLIB uf20–91, the approach outperforms independent SNN solvers with equivalent computational resources, achieving higher success rates on 332 instances (with only 5 showing degradation). Notably, improvements are concentrated on problems where the baseline method fails, effectively overcoming energy barriers inherent to fixed-temperature dynamics.

Abstract

Spiking neural networks (SNNs) with stochastic neurons can solve constraint satisfaction problems (CSPs) by encoding constraints via connectivity and performing probabilistic search via spike dynamics. However, fixed-temperature stochastic dynamics often get trapped in local minima - near-satisfying configurations - a vulnerability that escalates with problem difficulty. To overcome this, we integrate parallel tempering (PT) into the neural sampling solver, running multiple parallel replicas at varying inverse temperatures. Replicas periodically exchange temperatures rather than network states, managing the trade-off between exploration and concentration around low-energy configurations while preserving asynchronous, spike-based computation. We evaluate this architecture against a parallel baseline of four independent, fixed-temperature solvers using equal computational resources across 1000 instances from the SATLIB uf20-91 benchmark. Parallel tempering improves success probability on 332 instances while worsening only 5. Crucially, these gains are concentrated on hard instances where independent solvers fail. Violation trajectory analysis confirms the underlying mechanism: temperature exchanges allow replicas to traverse energy barriers unreachable by fixed-temperature dynamics, successfully escaping the narrow basins that constrain the baseline. To our knowledge, this represents the first integration of parallel tempering into an SNN-based CSP solver.

Problem

• Spiking Neural Networks
• Constraint Satisfaction Problems
• Local Minima
• Stochastic Dynamics
• Parallel Tempering

Innovation

• Spiking Neural Networks
• Parallel Tempering
• Constraint Satisfaction Problems
• Stochastic Dynamics
• Local Minima Escape