# Density Ridge Selective Prediction for LLM and VLM Hallucination Detection under Calibration Label Scarcity

arXiv: https://arxiv.org/abs/2606.10198 · HTML: https://mlsanity.com/paper/2606.10198/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Hallucination mitigation in LVLMs, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 9 of its 15 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Hallucination mitigation in LVLMs](https://mlsanity.com/mllm/hallucination-mitigation-in-lvlms/)

## Builds on (most cited first, 9 of 9)

- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [Asymptotic theory for density ridges](https://mlsanity.com/paper/1406.5663/) (2014)
- [Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability](https://mlsanity.com/paper/2603.10384/) (2026)
- [MANATEE: Inference-Time Lightweight Diffusion Based Safety Defense for LLMs](https://mlsanity.com/paper/2602.18782/) (2026)

## Built on by (most cited first, 1 of 1)

- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)

## Abstract (arXiv)

Hallucination detection in large language and vision-language models is increasingly framed as selective prediction, where a detector assigns a confidence score and abstains when confidence is low. Unsupervised sampling detectors (Semantic Entropy) avoid labels but plateau in quality, while supervised probes attain stronger in-distribution scores yet degrade sharply when calibration labels are scarce. We recover the response manifold of an LLM as the density ridge of a kernel density estimate built on a six-dimensional kinematic feature map of hidden state generation trajectories. A test generation is scored by the negated Euclidean distance from its projected feature point to the nearest ridge vertex, yielding a low-dimensional geometric skeleton of the stochastic output distribution. We evaluate against Semantic Entropy, topological methods, and log-probability on six QA benchmarks (HaluEval-QA, TriviaQA, GSM8K, POPE, ScienceQA, A-OKVQA) using eight text and vision LLMs in a deliberately label-scarce protocol (ncal=200 queries, N=5 generations). Our ridge-based score beats on AUROC with 5-20 points gain, while demonstrating tempered degradation under calibration-label scarcity.