arXiv:2608. 06276v1 Announce Type: cross Abstract: Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure.
By Farzana Nasrin
arXiv:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
By Nicole Abreu, Parker B. Edwards, Francis Motta
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
By Guangyu Meng, Pengfei Gu, Xueyang Li, Yiyu Shi, Erin Wolf Chambers, Danny Z. Chen
arXiv:2608.22044v1 Announce Type: new
Abstract: Modern machine learning (ML) methods are highly effective for prediction tasks, but many commonly used representations reduce complex data to fixed dim...
By George Babus, Farzana Nasrin
HoloAegis is a minimally parametric topological inference framework that uses frozen representations to map text onto the unit sphere and makes decisions via Gibbs‑Boltzmann free‑energy differences over pre‑computed anchor centroids. On a frozen three‑benchmark protocol, it matches WildGuard‑7B on toxicity, outperforms it on harmful behaviors, but underperforms on oversafety detection, while ShieldGemma‑2B fails on indirect harms. The study demonstrates that geometric guardrails can substitute for LLM judges in some cases and must defer to them in others, with anchor banks reducing score variance and boundary displacement.
By Tak Ho Alex Li, Kaijie Liu, Lik-Hang Lee, Kin Chung Ho, Ping Shum, Michael K. Ng
arXiv:2607. 27126v1 Announce Type: new Abstract: Persistence Diagram (PD) is known to capture point cloud topology effectively, but its computation has high time complexity.
By Kaifeng Zhang, Kai Ming Ting