Chisao: 一种基于收敛-反收敛振荡的多模态黑盒函数的GPU原生并行优化器
\chisao{}: A GPU-Native Parallel Optimizer for Multimodal Black-Box Functions via Convergence-Anticonvergence Oscillation
AI总结：
提出GPU原生群体优化器Chisao，通过收敛-反收敛振荡循环逃离局部陷阱并冻结确认模态，在42个基准函数上实现100%模态恢复，速度提升达39倍。
摘要：
寻找多模态黑盒函数的所有模态是优化、贝叶斯推断和科学计算中的一个基本挑战。现有方法——盆地跳跃、CMA-ES、多起点梯度下降——顺序运行，无法利用现代GPU硬件的巨大并行性。我们引入\chisao{}（\textbf{C}onvergence-\textbf{H}alt-\textbf{I}nvert-\textbf{S}tick-\textbf{A}nd-\textbf{O}scillate），一种GPU原生群体优化器，它同时运行整个样本批次，并利用故意的收敛-反收敛振荡循环来逃离局部陷阱，同时冻结已确认的模态。结构性的移动是非对称的：达到真正峰值的样本被冻结（“粘住”）并保留，而其余样本则通过基于动量的反收敛和随机平滑梯度继续探索。通过两种互补策略（Repulse Monkey和Golden Rooster）的自适应重播种维持了整个过程中的群体多样性。在Simon Fraser大学优化基准套件的所有42个函数上，维度$d \in \{2, 4, 8, 16, 32, 64\}$，\chisao{}实现了\textbf{100\%}的模态恢复，而在最困难的多模态函数上，所有CPU基线在$d \geq 8$时崩溃，在所有方法都成功的函数上（Michalewicz $d=64$），速度提升高达\textbf{$34\times$}，在单峰函数上（Rotated Hyper-Ellipsoid $d=64$，纯GPU红利）速度提升高达\textbf{$39\times$}。所有基准测试仅通过值评估目标——梯度来自有限差分——因此报告的速度提升是无导数的最坏情况。在显著的似然噪声下（$\sigma_{\mathrm{noise}}$高达1.0），模态检测仍然100\%可靠。该算法作为独立的开源Python包在PyPI上可用。
英文摘要：
Finding all modes of a multimodal black-box function is a fundamental challenge in optimization, Bayesian inference, and scientific computing. Existing approaches -- basin-hopping, CMA-ES, multistart gradient descent -- operate sequentially and cannot exploit the massive parallelism of modern GPU hardware. We introduce \chisao{} (\textbf{C}onvergence-\textbf{H}alt-\textbf{I}nvert-\textbf{S}tick-\textbf{A}nd-\textbf{O}scillate), a GPU-native population optimizer that runs an entire sample batch simultaneously and exploits a deliberate convergence-anticonvergence oscillation cycle to escape local traps while freezing confirmed modes. The structural move is asymmetric: samples that reach true peaks are frozen (``stuck'') and preserved, while the rest keep exploring via momentum-based anti-convergence and stochastically smoothed gradients. Adaptive reseeding via two complementary strategies (Repulse Monkey and Golden Rooster) maintains population diversity throughout. On all 42 functions of the Simon Fraser University optimization benchmark suite across dimensions $d \in \{2, 4, 8, 16, 32, 64\}$, \chisao{} achieves \textbf{100\%} mode recovery where all CPU baselines collapse at $d \geq 8$ on the hardest multimodal functions, at up to \textbf{$34\times$} speedup over basin-hopping on functions where all methods succeed (Michalewicz $d=64$) and up to \textbf{$39\times$} on unimodal functions (Rotated Hyper-Ellipsoid $d=64$, pure GPU dividend). All benchmarks evaluate the objective by value alone -- gradients come from finite differences -- so the reported speedups are a derivative-free worst case. Under substantial likelihood noise ($σ_{\mathrm{noise}}$ up to 1.0), mode detection remains 100\% reliable. The algorithm is available as a standalone open-source Python package on PyPI.
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