χ-sao: A GPU-Native Parallel Optimizer for Multimodal Black-Box Functions via Convergence-Anticonvergence Oscillation
A GPU-native population optimizer, χ-sao (Convergence-Halt-Invert-Stick-And-Oscillate), exploits a deliberate convergence-anticonvergence oscillation cycle to escape local traps while freezing confirmed modes. On all 42 functions of the Simon Fraser University optimization benchmark suite across dimensions d ∈ {2,4,8,16,32,64}, χ-sao achieves 100% mode recovery where all CPU baselines collapse at d ≥ 8 on the hardest multimodal functions, with speedups up to 34× over basin-hopping on Michalewicz d=64 and up to 39× on Rotated Hyper-Ellipsoid d=64. Under substantial likelihood noise (σ_noise up to 1.0), mode detection remains 100% reliable. The algorithm is available as an open-source Python package on PyPI.
[2606.26164] \chisao{}: A GPU-Native Parallel Optimizer for Multimodal Black-Box Functions via Convergence-Anticonvergence Oscillation
[Submitted on 24 Jun 2026]
Title:\chisao{}: A GPU-Native Parallel Optimizer for Multimodal Black-Box Functions via Convergence-Anticonvergence Oscillation
View a PDF of the paper titled \chisao{}: A GPU-Native Parallel Optimizer for Multimodal Black-Box Functions via Convergence-Anticonvergence Oscillation, by Ira Wolfson
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Abstract: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 ($\sigma_{\mathrm{noise}}$ up to 1.0), mode detection remains 100\% reliable. The algorithm is available as a standalone open-source Python package on PyPI.
Comments: 22 pages, 4 Appendixes
Subjects:
Machine Learning (cs.LG); Numerical Analysis (math.NA); Data Analysis, Statistics and Probability (physics.data-an); Computation (stat.CO)
Cite as: arXiv:2606.26164 [cs.LG]
(or arXiv:2606.26164v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.26164
arXiv-issued DOI via DataCite
Submission history
From: Ira Wolfson [view email] [v1] Wed, 24 Jun 2026 06:33:29 UTC (317 KB)
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