{"slug": "graph-coarsening-enables-escaping-local-optima-in-compute-constrained-nonconvex", "title": "Graph Coarsening Enables Escaping Local Optima in Compute-Constrained Nonconvex MAX-CUT", "summary": "A combined CMG+PPR pipeline reaches 97.5% of the known exact optimum on average and 98.4% on its best run on the t2g20 benchmark instance (n=400), according to arXiv:2610.19043v1. The method warm-starts Particle Polynomial Relaxation (PPR), a moment-based nonconvex continuous reformulation, with Combinatorial Multigrid (CMG), a spectral graph-coarsening technique that produces structure-aware initial solutions in near-linear time without training data. An extended variant with discrete local-search refinement reaches the published optimum on all sixty Biq Mac instances evaluated by a recent neural branch-and-bound method, and a sparse CSR representation scales the approach to G-set instances with up to 20,000 vertices while cutting memory requirements by up to 3333x.", "body_md": "arXiv:2610.19043v1 Announce Type: new \nAbstract: Because its binary optimization landscape contains exponentially many local optima, MAX-CUT is highly sensitive to initialization. We study Particle Polynomial Relaxation (PPR), a moment-based nonconvex continuous reformulation possessing an advantageous optimization landscape. We warm-start PPR with Combinatorial Multigrid (CMG), a spectral graph-coarsening method that produces structure-aware initial solutions in near-linear time without training data. On \\texttt{t2g20} ($n=400$), benchmark instance with known exact optimum, the combined CMG+PPR pipeline reaches $97.5\\%$ of optimum on average and $98.4\\%$ on the best run. An extended variant with discrete local-search refinement reaches the published optimum on all sixty Biq Mac instances evaluated by a recent neural branch-and-bound method. Using a sparse CSR representation, the same approach scales to G-set instances with up to $20{,}000$ vertices reducing memory requirements by up to $3333\\times$ while maintaining a consistent improvement over the CMG warm start. Gains are largest on sparse weighted graphs; on dense graphs we complement the pipeline with spectral sparsification.", "url": "https://wpnews.pro/news/graph-coarsening-enables-escaping-local-optima-in-compute-constrained-nonconvex", "canonical_source": "https://arxiv.org/abs/2610.19043", "published_at": "2026-10-15 04:00:00+00:00", "updated_at": "2026-10-15 05:51:01.551159+00:00", "lang": "en", "topics": ["machine-learning", "ai-research", "neural-networks"], "entities": ["arXiv", "Particle Polynomial Relaxation", "Combinatorial Multigrid", "Biq Mac", "G-set", "t2g20"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/graph-coarsening-enables-escaping-local-optima-in-compute-constrained-nonconvex", "markdown": "https://wpnews.pro/news/graph-coarsening-enables-escaping-local-optima-in-compute-constrained-nonconvex.md", "text": "https://wpnews.pro/news/graph-coarsening-enables-escaping-local-optima-in-compute-constrained-nonconvex.txt", "jsonld": "https://wpnews.pro/news/graph-coarsening-enables-escaping-local-optima-in-compute-constrained-nonconvex.jsonld"}}