Cosm: Collective Switched Motion for Fast and Accurate Sparse Ising Optimization

2026-04-16

AI Summary

This work addresses the challenges of slow convergence and susceptibility to local optima in large-scale sparse Ising optimization problems by proposing a heuristic algorithm grounded in structured nonsmooth switching dynamics. The approach leverages continuous circular-variable modeling, a conflict-free edge-partitioned periodically interacting network, and a cooperative perturbation mechanism to drive the collective evolution of spin clusters in phase space, thereby effectively escaping local minima. On three benchmark two-dimensional spin glass instances from the Gset suite—each involving tens of thousands of variables—the method achieves, for the first time with a heuristic, solutions verified to be optimal. Furthermore, on large bounded-degree graphs, it reduces the time to reach high-quality solutions from hundreds of hours to merely 36–303 seconds, substantially enhancing both computational efficiency and scalability.

Abstract

We introduce Collective Switched Motion (Cosm), a heuristic algorithm for solving sparse Ising-type optimization problems. Cosm combines locally interacting continuous circular variables with global coordination rules that facilitate collective dynamics. Pairwise interactions occur sequentially over a set of conflict-free edge partitions, resulting in an interaction network that switches periodically. Unlike conventional gradient-based approaches, Cosm enables structured, non-gradient dynamics that promote exploration beyond local minima. A correlated perturbation mechanism helps enable collective variable rotations. On the three largest Gset instances, which have 10,000-20,000 variables and represent 2D spin glasses, Cosm attains improved solutions that are verified as optimal using an exact solver. On two large bounded-degree Gset instances, a CPU-based implementation of Cosm reduces the state-of-the-art times-to-target from hundreds of hours to 36-303 s, reductions of 2-4 orders of magnitude. Additional tests on planted-solution benchmark instances show a lower scaling exponent than previous dynamical systems heuristics. These results highlight the effectiveness of Cosm in harnessing collective computation for improved sparse combinatorial optimization.

Problem

• Ising optimization
• sparse optimization
• spin glasses
• combinatorial optimization
• large-scale optimization

Innovation

• Collective Switched Motion
• Ising optimization
• switching dynamics
• sparse graphs
• dynamical solver