Fast Deep Belief Propagation: An Efficient Learning-Based Algorithm for Solving Constraint Optimization Problems

Belief Propagation (BP) is a fundamental heuristic for solving Constraint Optimization Problems (COPs), yet its practical applicability is constrained by slow convergence and instability in loopy factor graphs. While Damped BP (DBP) improves convergence by using manually tuned damping factors, its reliance on labor-intensive hyperparameter optimization limits scalability. Deep Attentive BP (DABP) addresses this by automating damping through recurrent neural networks (RNNs), but introduces significant memory overhead and sequential computation bottlenecks. To reduce memory usage and accelerate deep belief propagation, this paper introduces Fast Deep Belief Propagation (FDBP), a deep learning framework that improves COP solving through online self-supervised learning and graphics processing unit (GPU) acceleration. FDBP decouples the learning of damping factors from BP message passing, inferring all parameters for an entire BP iteration in a single step, and leverages mixed precision to further optimize GPU memory usage. This approach substantially improves both the efficiency and scalability of BP optimization. Extensive evaluations on synthetic and real-world benchmarks highlight the superiority of FDBP, especially for large-scale instances where DABP fails due to memory constraints. Moreover, FDBP achieves an average speedup of 2.87× over DABP with the same restart counts. Because BP for COPs is a mathematically grounded GPU-parallel message-passing framework that bridges applied mathematics, computing, and machine learning, and is widely applicable across science and engineering, our work offers a promising step toward more efficient solutions to these problems.