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 frameworks, using this regularizer explicitly. Empirically, this regularization yields vastly higher ground-state convergence rates than standard real-valued alternatives. Our models achieved zero error in large-scale 160x160 QUBO tasks under severe noise (sigma=0.25), and outperformed traditional algorithms (OMP and LASSO) in underdefined sparse coding with perfect recovery at sigma=0.15. The solver's robustness was further validated by recovering exact ground-state configurations in 8 out of 11 rigorously engineered planted-solution benchmarks.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Bimodal Distributed Binarized Neural Networks
Binary Neural Networks (BNNs) are an extremely promising method to reduce deep neural networks' complexity and power consumption massively. Binarization techniques, however, suffer from ineligible performance degradation…
BinarizationQuantizationReBNet: Residual Binarized Neural Network
This paper proposes ReBNet, an end-to-end framework for training reconfigurable binary neural networks on software and developing efficient accelerators for execution on FPGA. Binary neural networks offer an intriguing o…
BinarizationGeneral ClassificationGSB: Group Superposition Binarization for Vision Transformer with Limited Training Samples
Vision Transformer (ViT) has performed remarkably in various computer vision tasks. Nonetheless, affected by the massive amount of parameters, ViT usually suffers from serious overfitting problems with a relatively limit…
BinarizationKnowledge DistillationModel CompressionQuantizationDegraded Historical Documents Images Binarization Using a Combination of Enhanced Techniques
Document image binarization is the initial step and a crucial in many document analysis and recognition scheme. In fact, it is still a relevant research subject and a fundamental challenge due to its importance and influ…
BinarizationHighly Efficient and Effective LLMs with Multi-Boolean Architectures
Weight binarization has emerged as a promising strategy to drastically reduce the complexity of large language models (LLMs). It is mainly classified into two approaches: post-training binarization and finetuning with tr…
BinarizationQuantization