Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization
We introduce a physics-inspired continuous relaxation framework that yields substantially improved solutions for NP-hard combinatorial optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), binary sparse coding, and planted-solution Ising models. By parameterizing discrete binary variables as continuous wave-like states on the complex unit circle, we inherently smooth highly non-convex energy landscapes. We show that representing binary variables as complex phases reveals an implicit regularization mechanism that promotes convergence toward discrete states. Extracting this mechanism yields significant improvements even within standard real-valued optimization...
| Authors | Khen Cohen, Mark Glass, Meir Feder et al. |
|---|---|
| Primary category | cond-mat.stat-mech |
| Published | 23 May 2026 |
| Last updated at source | 23 May 2026 |
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