通过均场约束恢复Potts机中的稀疏性
Restoring Sparsity in Potts Machines via Mean-Field Constraints
AI总结：
本文提出了一种通过引入均场约束来恢复Potts机中稀疏性的方法，通过改进的多状态概率数字（p-dits）和均场约束方案，有效减少了密集耦合，提升了概率硬件在约束优化中的可扩展性和效率。
摘要：
Ising机器及相关概率硬件已逐渐成为解决NP难优化和采样问题的有希望的平台。然而，许多实际问题涉及约束，这些约束会引入密集或全连接耦合，从而影响可扩展性和硬件效率。本文通过两种互补的方法来解决这种约束引起的密度问题。首先，我们引入了一种针对硬件的多状态概率数字（p-dits）的原生公式，该公式避免了二进制Ising编码所需的本地密集内变量耦合。我们通过再现已知的二维Potts模型临界行为来验证p-dit动力学。其次，我们提出了均场约束（MFC），一种混合方案，它用动态更新的单节点偏差代替密集的成对约束耦合。应用于平衡图划分时，MFC在解的质量上与精确的全连接约束公式相当，同时大幅减少了图密度。最后，我们通过FPGA实现展示了恢复稀疏性的实际影响，该实现将划分速度提高了超过一个数量级，比CPU概率求解器快，比Tabu Ising基线快两个数量级。这些结果为在概率硬件上进行受约束优化的扩展提供了路径。
英文摘要：
Ising machines and related probabilistic hardware have emerged as promising platforms for NP-hard optimization and sampling. However, many practical problems involve constraints that induce dense or all-to-all couplings, undermining scalability and hardware efficiency. We address this constraint-induced density through two complementary approaches. First, we introduce a hardware-aware native formulation for multi-state probabilistic digits (p-dits) that avoids the locally dense intra-variable couplings required by binary Ising encodings. We validate p-dit dynamics by reproducing known critical behavior of the 2D Potts model. Second, we propose mean-field constraints (MFC), a hybrid scheme that replaces dense pairwise constraint couplings with dynamically updated single-node biases. Applied to balanced graph partitioning, MFC achieves solution quality comparable to exact all-to-all constraint formulations while dramatically reducing graph density. Finally, we demonstrate the practical impact of restored sparsity through an FPGA implementation. In comparisons using FPGA kernel time and CPU solver-loop time, and excluding the current prototype's host-device schedule transfer overhead, the FPGA reaches the 50% success threshold more than an order of magnitude faster than the CPU probabilistic solvers and more than two orders of magnitude faster than the Tabu Ising baseline. Together, these results outline a pathway for scaling constrained optimization on probabilistic hardware.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
