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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.16665 |
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| _version_ | 1866915804707028992 |
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| author | Zeng, Li Shen, Mutian Pu, Tianle Nussinov, Zohar Feng, Qing Chen, Chao Liu, Zhong Fan, Changjun |
| author_facet | Zeng, Li Shen, Mutian Pu, Tianle Nussinov, Zohar Feng, Qing Chen, Chao Liu, Zhong Fan, Changjun |
| contents | p-spin glasses, characterized by frustrated many-body interactions beyond the conventional pairwise case (p>2), are prototypical disordered systems whose ground-state search is NP-hard and computationally prohibitive for large instances. Solving this problem is not only fundamental for understanding high-order disorder, structural glasses, and topological phases, but also central to a wide spectrum of hard combinatorial optimization tasks. Despite decades of progress, there still lacks an efficient and scalable solver for generic large-scale p-spin models. Here we introduce PLANCK, a physics-inspired deep reinforcement learning framework built on hypergraph neural networks. PLANCK directly optimizes arbitrary high-order interactions, and systematically exploits gauge symmetry throughout both training and inference. Trained exclusively on small synthetic instances, PLANCK exhibits strong zero-shot generalization to systems orders of magnitude larger, and consistently outperforms state-of-the-art thermal annealing methods across all tested structural topologies and coupling distributions. Moreover, without any modification, PLANCK achieves near-optimal solutions for a broad class of NP-hard combinatorial problems, including random k-XORSAT, hypergraph max-cut, and conventional max-cut. The presented framework provides a physics-inspired algorithmic paradigm that bridges statistical mechanics and reinforcement learning. The symmetry-aware design not only advances the tractable frontiers of high-order disordered systems, but also opens a promising avenue for machine-learning-based solvers to tackle previously intractable combinatorial optimization challenges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16665 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimizing p-spin models through hypergraph neural networks and deep reinforcement learning Zeng, Li Shen, Mutian Pu, Tianle Nussinov, Zohar Feng, Qing Chen, Chao Liu, Zhong Fan, Changjun Disordered Systems and Neural Networks Computational Physics p-spin glasses, characterized by frustrated many-body interactions beyond the conventional pairwise case (p>2), are prototypical disordered systems whose ground-state search is NP-hard and computationally prohibitive for large instances. Solving this problem is not only fundamental for understanding high-order disorder, structural glasses, and topological phases, but also central to a wide spectrum of hard combinatorial optimization tasks. Despite decades of progress, there still lacks an efficient and scalable solver for generic large-scale p-spin models. Here we introduce PLANCK, a physics-inspired deep reinforcement learning framework built on hypergraph neural networks. PLANCK directly optimizes arbitrary high-order interactions, and systematically exploits gauge symmetry throughout both training and inference. Trained exclusively on small synthetic instances, PLANCK exhibits strong zero-shot generalization to systems orders of magnitude larger, and consistently outperforms state-of-the-art thermal annealing methods across all tested structural topologies and coupling distributions. Moreover, without any modification, PLANCK achieves near-optimal solutions for a broad class of NP-hard combinatorial problems, including random k-XORSAT, hypergraph max-cut, and conventional max-cut. The presented framework provides a physics-inspired algorithmic paradigm that bridges statistical mechanics and reinforcement learning. The symmetry-aware design not only advances the tractable frontiers of high-order disordered systems, but also opens a promising avenue for machine-learning-based solvers to tackle previously intractable combinatorial optimization challenges. |
| title | Optimizing p-spin models through hypergraph neural networks and deep reinforcement learning |
| topic | Disordered Systems and Neural Networks Computational Physics |
| url | https://arxiv.org/abs/2602.16665 |