@article{riemannianzerothordergradientestimationw, title = {Riemannian Zeroth-Order Gradient Estimation with Structure-Preserving Metrics for Geodesically Incomplete Manifolds}, author = {Shaocong Ma and Heng Huang}, year = {2026}, eprint = {2601.08039}, archivePrefix = {arXiv}, url = {https://arxiv.org/abs/2601.08039}, }