Optimizing p-spin models through hypergraph neural networks and deep reinforcement learning

TL;DR

This paper introduces PLANCK, a deep reinforcement learning framework using hypergraph neural networks, capable of efficiently solving large-scale p-spin models and various NP-hard combinatorial problems by leveraging physics-inspired symmetry exploitation.

Contribution

The paper presents a novel physics-inspired deep RL approach that directly optimizes high-order interactions and generalizes well to larger systems, outperforming existing methods.

Findings

PLANCK outperforms state-of-the-art thermal annealing methods.

Exhibits strong zero-shot generalization to larger systems.

Achieves near-optimal solutions for various NP-hard problems.

Abstract

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.