Scalable Persistence-Based Topological Optimization via Random Slicing and NW Convolution

A new arXiv preprint proposes a scalable pipeline for persistence-based topological optimization, which deforms point clouds by minimizing objectives involving persistence diagrams. The approach addresses two key issues: persistent homology computed on subsamples and sparse topological gradients. It introduces random slicing for subsampling to improve geometric coverage and reduce density bias, and replaces costly kernel solves with fast Nadaraya-Watson Gaussian convolution for gradient extension. The method is motivated by diffeomorphic interpolation via Reproducing Kernel Hilbert Space (RKHS). The paper is available at arXiv:2605.10996.