# HalluField: Detecting LLM Hallucinations via Field-Theoretic Modeling

arXiv: https://arxiv.org/abs/2509.10753 · HTML: https://mlsanity.com/paper/2509.10753/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Hallucination detection and mitigation, one of 17 directions in LLM reasoning.
- Builds on 23 of its 37 references that are in the map.
- First posted on arXiv 12 Sep 2025.

## Placed in

- LLM reasoning / [Hallucination detection and mitigation](https://mlsanity.com/lr/hallucination-detection-and-mitigation/)

## Builds on (most cited first, 23 of 23)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [In-context Vectors: Making In Context Learning More Effective and Controllable Through Latent Space Steering](https://mlsanity.com/paper/2311.06668/) (2023)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [On Hallucination and Predictive Uncertainty in Conditional Language Generation](https://mlsanity.com/paper/2103.15025/) (2021)
- [The Capacity for Moral Self-Correction in Large Language Models](https://mlsanity.com/paper/2302.07459/) (2023)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [LM vs LM: Detecting Factual Errors via Cross Examination](https://mlsanity.com/paper/2305.13281/) (2023)
- [Chain-of-Knowledge: Grounding Large Language Models via Dynamic Knowledge Adapting over Heterogeneous Sources](https://mlsanity.com/paper/2305.13269/) (2023)
- [Unfamiliar Finetuning Examples Control How Language Models Hallucinate](https://mlsanity.com/paper/2403.05612/) (2024)
- [Self-Evaluation Improves Selective Generation in Large Language Models](https://mlsanity.com/paper/2312.09300/) (2023)
- [Trapping LLM Hallucinations Using Tagged Context Prompts](https://mlsanity.com/paper/2306.06085/) (2023)

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

- [The Surprising Universality of LLM Outputs: A Real-Time Verification Primitive](https://mlsanity.com/paper/2604.25634/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) exhibit impressive reasoning and question-answering capabilities. However, they often produce inaccurate or unreliable content known as hallucinations. This unreliability significantly limits their deployment in high-stakes applications. Thus, there is a growing need for a general-purpose method to detect hallucinations in LLMs. In this work, we introduce HalluField, a novel field-theoretic approach for hallucination detection based on a parametrized variational principle and thermodynamics. Inspired by thermodynamics, HalluField models an LLM's response to a given query and temperature setting as a collection of discrete likelihood token paths, each associated with a corresponding energy and entropy. By analyzing how energy and entropy distributions vary across token paths under changes in temperature and likelihood, HalluField quantifies the semantic stability of a response. Hallucinations are then detected by identifying unstable or erratic behavior in this energy landscape. HalluField is computationally efficient and highly practical: it operates directly on the model's output logits without requiring fine-tuning or auxiliary neural networks. Notably, the method is grounded in a principled physical interpretation, drawing analogies to the first law of thermodynamics. Remarkably, by modeling LLM behavior through this physical lens, HalluField achieves state-of-the-art hallucination detection performance across models and datasets.