发表机构
University of Virginia（弗吉尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示振荡器Potts机器中，标签置换虽不改变能量，但会改变局部稳定性，需调整正则化强度，为多态优化提供新见解。
AI 中文摘要
振荡器Potts机器（OPMs）提供了一种受物理学启发的能量最小化框架，用于解决由$q$态Potts哈密顿量描述的组合优化问题。尽管OPMs可被视为振荡器Ising机器（OIMs）的多态扩展，但在此我们表明它们展现出二值情形中不存在的动力学特性。具体而言，我们针对最近提出的多谐波OPM公式推导出一个依赖于构型的局部稳定性条件，并表明具有相同Potts能量的构型在动力学上不必等价。特别是，对于$q\geq4$，Potts标签的置换可以改变雅可比矩阵谱，从而改变局部稳定给定Potts构型所需的正则化强度。因此，同一Potts解的不同相位编码尽管具有相同的Potts能量，却可能表现出不同的局部稳定性特性。
英文摘要
Oscillator Potts machines (OPMs) provide a physics-inspired, energy-minimization framework for solving combinatorial optimization problems described by the $q$-state Potts Hamiltonian. Although OPMs may be viewed as multistate extensions of oscillator Ising machines (OIMs), here, we show that they exhibit dynamical properties absent in the binary case. Specifically, we derive a configuration-dependent local-stability condition for a recently proposed multiharmonic OPM formulation and show that configurations with the same Potts energy need not be dynamically equivalent. In particular, for $q\geq4$, permutations of the Potts labels can alter the Jacobian spectrum and, consequently, the regularization strength required to locally stabilize a given Potts configuration. Thus, different phase encodings of the same Potts solution can exhibit different local stability properties despite having identical Potts energies.
Comments10 pages, 3 figures
