We consider the problem of estimating the parameters of a Markov Random Field with hard-constraints using a single sample. As our main running examples, we use the $k$-SAT and the proper coloring models, as well as general $H$-coloring models; for all of these we obtain both positive and negative results. In contrast to the soft-constrained case, we show in particular that single-sample estimation is not always possible, and that the existence of an estimator is related to the existence of non-satisfiable instances.
Our algorithms are based on the pseudo-likelihood estimator. We show variance bounds for this estimator using coupling techniques inspired, in the case of $k$-SAT, by Moitra's sampling algorithm (JACM, 2019); our positive results for colorings build on this new coupling approach. For $q$-colorings on graphs with maximum degree $d$, we give a linear-time estimator when $q>d+1$, whereas the problem is non-identifiable when $q\leq d+1$. For general $H$-colorings, we show that standard conditions that guarantee sampling, such as Dobrushin's condition, are insufficient for one-sample learning; on the positive side, we provide a general condition that is sufficient to guarantee linear-time learning and obtain applications for proper colorings and permissive models. For the $k$-SAT model on formulas with maximum degree $d$, we provide a linear-time estimator when $k\gtrsim 6.45\log d$, whereas the problem becomes non-identifiable when $k\lesssim \log d$.
École des Ponts ParisTech（巴黎高科桥路学校）；CAS（中国科学院）；MINES ParisTech, PSL（巴黎高等矿业学院（巴黎文理研究大学））；Center of Applied Mathematics, CNRS（法国国家科学研究中心应用数学中心）；École Polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院（巴黎理工学院））
Knowledge Integration in Differentiable Models: A Comparative Study of Data-Driven, Soft-Constrained, and Hard-Constrained Paradigms for Identification and Control of the Single Machine Infinite Bus System
Korea University（高丽大学）；Hyundai Motor Company（现代汽车公司）
DAE-HardNet: A Physics Constrained Neural Network Enforcing Differential-Algebraic Hard Constraints
Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122, USA（德克萨斯A&M大学化学工程艺术与科学系）；Texas A&M Energy Institute, Texas A&M University, College Station, TX 77843, USA（德克萨斯A&M大学能源研究所）
Efficient Relaxed Gradient Support Pursuit for Sparsity Constrained Non-convex Optimization
Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education（教育部智能感知与图像理解重点实验室）；School of Artificial Intelligence, Xidian University（西安电子科技大学人工智能学院）；Department of Computer Science, The University of Texas at Austin（德克萨斯大学奥斯汀分校计算机科学系）
Quantum Algorithms for solving Hard Constrained Optimisation Problems
La Salle - Ramon Llull University（拉蒙柳尔大学拉萨尔学院）；IBMQ（IBM量子）；AWS-Braket（AWS布拉凯特）
本文研究了求解硬约束优化问题的量子算法。它展示了量子计算机如何解决困难的日常问题，例如为社会工作者找到最佳时间表或机器人在仓库中挑选和整理的路径。解决方案的路径导致了一种新的人工智能范式的定义，包括量子计算，量子基于案例推理（qCBR），以及使用Raspberry Pi 4作为处理器（qRobot）将量子计算的能力集成到移动机器人中的概念验证，能够与IBMQ，Amazon Braket（D-Wave）和Pennylane等领先的技术参与者一起运行。为了提高变分算法在这个NISQ时代和下一个时代的执行时间，我们提出了EVA：一种量子指数值近似算法，它可以加速VQE，也就是说，到目前为止，量子计算的旗舰。为了提高变分算法在这个NISQ时代和下一个时代的执行时间，我们提出了EVA：一种量子指数值近似算法，它可以加速VQE，也就是说，到目前为止，量子计算的旗舰。
Constrained and Composite Sampling via Proximal Sampler
Department of Computer Science, University of Rochester（计算机科学系，罗切斯特大学）；Goergen Institute for Data Science and Artificial Intelligence (GIDS-AI)（数据科学与人工智能研究所（GIDS-AI））
A Scalable Global Optimization Algorithm For Constrained Clustering
Department of Industrial and Systems Engineering, University of South Florida（南佛罗里达大学工业与系统工程系）；Bellini College of AI, Cybersecurity, and Computing, University of South Florida（南佛罗里达大学人工智能、网络安全与计算学院）
Hard Sample Aware Network for Contrastive Deep Graph Clustering
College of Computer, National University of Defense Technology（国防科技大学计算机学院）；College of Intelligence Science and Technology, National University of Defense Technology（国防科技大学智能科学学院）；Northwestern Polytechnical University（西北工业大学）；Beijing Information Science and Technology University（北京信息科技大学）
Hard-Constrained Deep Learning for Climate Downscaling
Fraunhofer ITWM（弗劳恩霍夫信息技术与数学研究所）；Mila Quebec AI Institute（米拉魁北克人工智能研究所）；University of Montreal（蒙特利尔大学）；New York University（纽约大学）；IBM Research（IBM研究院）；McGill University（麦吉尔大学）
Adaptive Hard-Soft Physics-Informed Neural Networks for Robust Boundary-Constrained PDE Solving
College of Engineering and Computer Science, VinUniversity（VinUniversity工程与计算机科学学院）；Center for AI Research, VinUniversity（VinUniversity人工智能研究中心）；Group of Materials and Structures, School of Mechanical Engineering, Hanoi University of Science and Technology（河内科技大学机械工程学院材料与结构组）；Department of Mathematics and Informatics, Hanoi University of Science and Technology（河内科技大学数学与信息学系）
