Cosm: collective switched motion for sparse Ising optimization

This repository contains the preprint “Cosm: collective switched motion for sparse Ising optimization”. Version v3.0 is a substantially revised version with additional results and discussion. An arXiv version of this manuscript is available at arXiv:2605.30355

Abstract
We introduce Collective Switched Motion (Cosm), a heuristic optimization framework based on switched collective dynamics. Cosm compiles the objective into subobjectives that are activated sequentially, temporally separating competing local influences. The interplay of switching and local interactions among variables gives rise to collective search behavior, while a new correlated perturbation mechanism encourages coordinated cluster motion. Tests on tuned-hardness spin-glass benchmarks suggest more favorable algorithmic scaling than that reported for leading dynamical solvers. Cosm heuristically attains the certified optima of three of the largest Gset instances (G72, G77, G81), exceeding the previously reported heuristic solutions. On the large random-graph instances G61 and G70, a CPU implementation reliably attains the best-known solutions, reaching cuts of 5799 and 9595 with 99%-confidence times-to-target of 15 s and 2.4 s, respectively. On the heterogeneous-degree G64 instance, Cosm establishes a new best-known cut of 8753. Broadly, the results suggest an alternative approach to heuristic design in which local dynamics and orchestration mechanisms are carefully designed so that effective search emerges.