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.
Multimodal Federated Learning (MMFL) enables privacy-preserving collaborative learning across decentralized clients with heterogeneous data and modality availability. However, most existing MMFL methods cast multimodal training as a joint optimization problem, overlooking a key bottleneck: modality competition, where dominant modalities suppress weaker ones and lead to suboptimal global models. To address this, we propose FedMChain, a balanced MMFL framework that structures federated multimodal training as a chain of modality-wise phases. This phase-wise design gives each modality a dedicated local optimization window on multimodal clients to mitigate modality competition, and further promotes cross-modal complementarity via an error-compensated regularizer. On the server side, we employ a sparse sign-guided aggregation strategy that leverages directional sign agreement for robust intra-modality aggregation, avoids destructive averaging, and supports less frequent synchronization to reduce communication overhead. Extensive experiments on multimodal benchmarks demonstrate that FedMChain consistently improves predictive performance while requiring less frequent communication than baselines.