arXiv AI September 16, 2026 By Tak Ho Alex Li, Kaijie Liu, Lik-Hang Lee, Kin Chung Ho, Ping Shum, Michael K. Ng

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.

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arXiv AI

Aug 11

HoloAegis: Frozen Representation, Topological Inference: Minimally Parametric Safety Manifolds for Zero-Shot LLM Guardrails

arXiv:2608. 08485v1 Announce Type: new Abstract: Current LLM safety guardrails face a fundamental tension: fine-tuning distorts pre-trained representations while generative judges incur prohibitive inference costs.

By Tak Ho Alex Li, Kaijie Liu, Lik-Hang Lee, Kin Chung Ho, Ping Shum, Michael K. Ng

llms fine-tuning benchmarks safety

arXiv AI

Jul 21

Topological Signatures of Context-Level Reliability in TabPFN

arXiv:2607. 17962v1 Announce Type: cross Abstract: TabPFN is a transformer-based foundation model for tabular prediction that performs inference without task-specific training by conditioning on a support set and query inputs.

By James Hu, Mahdi Ghelichi

llms benchmarks

arXiv Machine Learning

Jul 7

Statistically Meaningful Geometry (SMG) Beyond the Euclidean Paradigm, with Application to Generative AI

arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.

By Bing Cheng, Yi-Shuai Niu, Howell Tong, Shing-Tung Yau

llms fine-tuning safety

arXiv Machine Learning

Jun 11

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

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.

By Juliette Murris, Bernadette Stolz, Karsten Borgwardt

benchmarks

arXiv AI

Jun 16

Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability

arXiv:2603. 10384v3 Announce Type: replace Abstract: Evaluating LLM reliability via scalar probabilities often fails to capture the structural dynamics of reasoning.

By Xinyan Jiang, Ninghao Liu, Di Wang, Lijie Hu

llms benchmarks safety

arXiv Computation and Language

Sep 11

MindTopo: Can Foundation Models Reason in Topological Space?

MindTopo is a benchmark that tests foundation models on topological reasoning, covering five cognitive properties—continuity, separation, order, enclosure, and knots—across two cognitive levels: reasoning and planning. It contains 11,030 instances from 13 procedurally generated task types, and evaluates 14 multimodal large language models, including agent configurations with image and video generation. Results show that models perform better on reasoning than planning, and even the best model lags far behind human performance, with fine‑tuning and reinforcement learning improving reasoning more than planning.

By Yunfei Ge, Anbang Liu, Qineng Wang, Johnalbert Garnica, Jianwen Lyu, Zihan Wang, Reuben Tan, Jianfeng Gao, Ruohan Zhang, Yining Hong, Jiajun Wu, Manling Li

agents diffusion reinforcement-learning fine-tuning benchmarks

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Related stories

HoloAegis: Frozen Representation, Topological Inference: Minimally Parametric Safety Manifolds for Zero-Shot LLM Guardrails

Topological Signatures of Context-Level Reliability in TabPFN

Statistically Meaningful Geometry (SMG) Beyond the Euclidean Paradigm, with Application to Generative AI

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

Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability

MindTopo: Can Foundation Models Reason in Topological Space?