Enhancing Oscillator-Based Ising Machine Models with Amplitude Dynamics and Polynomial Interactions

2025-04-01

AI Summary

Existing oscillator-based Ising machines rely solely on phase dynamics, lack a rigorous energy function, and cannot efficiently handle arbitrary-order polynomial cost functions. Method: We propose a novel oscillator model featuring coupled phase–amplitude dynamics, the first such framework guaranteeing monotonic energy decay. We establish a scalable design paradigm for high-order polynomial interactions and introduce a lossless binarization mechanism to preserve solution fidelity. Contribution/Results: We theoretically prove strict energy descent of the proposed energy function. Experiments on 3-SAT demonstrate reliable convergence to low-energy states, significantly outperforming existing phase–amplitude hybrid models. Our approach unifies theoretical rigor—via a well-defined, strictly decreasing Lyapunov function—with superior optimization performance, enabling principled hardware-aware solving of general combinatorial optimization problems.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Satisfiability
• Machine Learning: Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We present an oscillator model with both phase and amplitude dynamics for oscillator-based Ising machines that addresses combinatorial optimization problems with polynomial cost functions of arbitrary order. Our approach addresses fundamental limitations of previous oscillator-based Ising machines through a mathematically rigorous formulation with a well-defined energy function and corresponding dynamics. The model demonstrates monotonic energy decrease and reliable convergence to low-energy states. Empirical evaluations on 3-SAT problems show significant performance improvements over existing phase-amplitude models. Additionally, we propose a flexible, generalizable framework for designing higher-order oscillator interactions, from which we derive a practical method for oscillator binarization without compromising performance. This work strengthens both the theoretical foundation and practical applicability of oscillator-based Ising machines for complex optimization problems.

Problem

• Model addresses combinatorial optimization with polynomial cost functions
• Overcomes limitations of previous oscillator-based Ising machines
• Improves performance on 3-SAT problems over existing models

Innovation

• Oscillator model with phase and amplitude dynamics
• Mathematically rigorous energy function and dynamics
• Flexible framework for higher-order oscillator interactions