Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring is a prototypical constraint satisfaction problem characterized by phase transitions that fragment the solution space into distinct clusters, making the search for valid solutions challenging. Here we introduce a physics-inspired neural framework that learns to solve large-scale graph coloring instances by combining graph neural networks with statistical-mechanics principles. Our approach integrates a planting-based supervised signal, symmetry-breaking regularization, and iterative noise-annealed neural dynamics to navigate complex solution landscapes. When the number of iterations scales quadratically with graph size, the learned solver successfully tackles increasingly challenging instances, even in regimes where finding valid solutions becomes particularly difficult, demonstrating its ability to extract meaningful information from the graph structure. The model generalizes from small training graphs to instances up to 20 times larger, demonstrating that neural architectures can learn scalable algorithmic strategies that remain effective in hard connectivity regions. These results establish a general framework for learning neural solvers that operate near fundamental phase boundaries in combinatorial optimization and inference.
Graph Coloring with Physics-Inspired Graph Neural Networks
Amazon Quantum Solutions Lab（亚马逊量子解决方案实验室）；AWS Intelligent and Advanced Compute Technologies, Professional Services（AWS智能与高级计算技术专业服务部）；AWS Center for Quantum Computing（AWS量子计算中心）
Quantum-inspired annealers as Boltzmann generators for machine learning and statistical physics
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；University of Oxford（牛津大学）；P. N. Lebedev Physics Institute（P. N. 列别杰夫物理研究所）
HankelKANet: Lightweight Path Loss Estimation via Physics-Inspired Hankel Convolution
School of Computer Science and Technology, Anhui University of Technology（安徽工业大学计算机科学与技术学院）；Department of Electrical and Electronic Engineering, Imperial College London（帝国理工学院电气电子工程系）
Physics-inspired transformer quantum states via latent imaginary-time evolution
Graduate School of Information Science and Technology, The University of Osaka（信息科学与技术研究生学校，大阪大学）；Fujitsu Laboratories, Fujitsu Limited（富士通实验室，富士通有限公司）；Center for Advanced Intelligence Project, RIKEN（先进智能项目中心，理化学研究所）
