A von Mises-Fisher grounding direction separates grounded from hallucinated responses

measured in 1 paper

Marin L2-normalizes embeddings from five frozen sentence encoders (sentence-t5-large primary, plus all-mpnet-base-v2, all-MiniLM-L6-v2, bge-small-en-v1.5, gte-small) onto the unit hypersphere [marin-2026-a-geometric-taxonomy-of-hallucinations-in-large-language-models] A grounding direction is extracted as the von Mises-Fisher mean of context embeddings [marin-2026-a-geometric-taxonomy-of-hallucinations-in-large-language-models] A Directional Grounding Index (cosine between a response's displacement vector and this direction) separates grounded from hallucinated responses at mean AUROC 0.805 on HaluEval QA (0.535-0.579 on TruthfulQA) [marin-2026-a-geometric-taxonomy-of-hallucinations-in-large-language-models] A companion Spherical Grounding Index gives 1.180 (grounded) versus 0.910 (hallucinated), both computed on frozen off-the-shelf encoders rather than a generative LLM's hidden states [marin-2026-a-geometric-taxonomy-of-hallucinations-in-large-language-models]

Structure

Linear Direction

Context

a mean-direction ("grounding direction") extracted via von Mises-Fisher fit on the unit hypersphere, used analogously to a diff-in-means direction but from a single reference class rather than a contrastive pair, hypersphere-normalized cosine/geodesic-angle detection metrics as an alternative to raw Euclidean distance

Confirmed in models

Sentence-T5-Large · T5, all-mpnet-base-v2 · MPNet, all-MiniLM-L6-v2 · MiniLM, BGE-small-en-v1.5 · BGE, GTE-small · GTE (General Text Embeddings)

Method

Papers

A Geometric Taxonomy of Hallucinations in Large Language Models — Marín, Javier2026 · arXiv:2602.13224