arXiv Machine Learning By Juliette Murris, Bernadette Stolz, Karsten Borgwardt

From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features

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arXiv:2606. 11911v1 Announce Type: cross Abstract: Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction.

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arXiv Machine Learning
Jun 18

Unreduced Persistence Diagrams for Topological Machine Learning

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 AI
Sep 16

HoloAegis: Frozen Representation, Topological Inference --- Minimally Parametric Safety Manifolds and Their Capability Boundaries for LLM Guardrails

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