通过自适应正则化退火实现二元压缩感知中的相变
Phase Transition in Binary Compressed Sensing via Annealing with Adaptive Regularization
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中文总结 AI 辅助
该研究提出一种结合系统搜索与随机森林回归的正则化选择方法，用于退火式二元压缩感知，使恢复相变接近理论边界，并发现量子-经典混合求解器在部分参数空间均方误差更小。
中文摘要 AI 辅助
正则化选择改变了基于退火的二元压缩感知的恢复相图。我们开发了一种结合系统参数搜索与随机森林回归的正则化选择方法。在已知稀疏度的无噪声高斯测量下，通过重复模拟退火（SA）试验中最小化均方重建误差，从候选网格中选取参考参数。拟合模型根据信号维度、采样比和稀疏度预测这些参考值。使用预测的正则化，SA恢复转变在考察的较大信号维度上大致遵循盒约束$\ell_1$恢复的渐近参考边界。无需重新训练，同一预测器为SA和量子-经典混合求解器提供相同的正则化值。在匹配的问题实例上，混合求解器在评估参数空间的部分区域比SA产生更小的均方重建误差。所得规则重用已搜索的信息用于后续重建，无需在每个设置下重复候选搜索。结果量化了在所述有限候选网格和求解器设置下的经验性能；它们不构成与求解器无关的恢复保证或时间到解决方案的比较。
英文摘要
Regularization choice changes the recovery phase diagrams of annealing-based binary compressed sensing. We develop a regularization-selection method that combines systematic parameter search with random forest regression. Under noiseless Gaussian measurements with known sparsity, reference parameters are selected from a candidate grid by minimizing mean squared reconstruction error over repeated simulated annealing (SA) trials. The fitted model predicts these reference values from signal dimension, sampling ratio, and sparsity. With predicted regularization, the SA recovery transition broadly follows the asymptotic reference boundary for box-constrained $\ell_1$ recovery at the larger signal dimensions examined. Without retraining, the same predictor supplies identical regularization values to SA and a quantum--classical hybrid solver. On matched problem instances, the hybrid solver yields smaller mean squared reconstruction errors than SA in parts of the evaluated parameter space. The resulting rule reuses the searched information for subsequent reconstruction without repeating candidate searches at each setting. The results quantify empirical performance under the stated finite candidate grid and solver settings; they do not constitute a solver-independent recovery guarantee or a time-to-solution comparison.
