基于振荡机制的并行优化器，可在GPU上高效找到多峰函数所有极值点。
\chisao{}: A GPU-Native Parallel Optimizer for Multimodal Black-Box Functions via Convergence-Anticonvergence Oscillation
- 采用收敛-反收敛振荡策略，批量并行探索并冻结已发现极值点。
- 在64维复杂函数上实现100%极值点找回，速度比传统方法快39倍。
- 适合需要高并发、无梯度依赖的科学计算与贝叶斯推断场景。
寻找多峰黑箱函数的所有极值点是优化、贝叶斯推断和科学计算中的基础挑战。现有方法如盆地跳跃、CMA-ES、多起点梯度下降均采用串行策略，无法利用现代GPU的海量并行能力。本文提出 extbf{ extit{chisao}}（Convergence-Halt-Invert-Stick-And-Oscillate），一种原生支持GPU的种群优化器，可同时运行整个样本批次，并通过刻意设计的收敛-反收敛振荡周期，在逃逸局部极值的同时冻结已确认的极值点。其结构动作具有不对称性：达到真实峰值的样本被冻结（“卡住”）并保留，其余样本则通过基于动量的反收敛和随机平滑梯度持续探索。通过两种互补策略（驱逐猴与金鸡）实现自适应重初始化，始终保持种群多样性。在西蒙弗雷泽大学优化基准套件的全部42个函数上， extit{chisao} 在维度 $d \in \{2, 4, 8, 16, 32, 64\}$ 下均实现100%极值点恢复，而所有CPU基线在 $d \geq 8$ 的最难函数上失效；在所有方法均成功的函数上（如Michalewicz $d=64$），速度提升最高达34倍；在单峰函数上（如旋转超椭球 $d=64$），速度提升最高达39倍。所有测试仅依赖目标函数值评估——梯度由有限差分获得，因此报告的速度提升为无梯度情况下的最坏估计。在高达 $σ_{\mathrm{noise}} = 1.0$ 的似然噪声下，极值检测仍保持100%可靠性。该算法已作为独立开源Python包发布于PyPI。
原文摘要 · Abstract (English)
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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