# LLM Hallucination Detection: A Fast Fourier Transform Method Based on Hidden Layer Temporal Signals

arXiv: https://arxiv.org/abs/2509.13154 · HTML: https://mlsanity.com/paper/2509.13154/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 18 of 18)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [BLEURT: Learning Robust Metrics for Text Generation](https://mlsanity.com/paper/2004.04696/) (2020)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Alignment faking in large language models](https://mlsanity.com/paper/2412.14093/) (2024)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [HaloScope: Harnessing Unlabeled LLM Generations for Hallucination Detection](https://mlsanity.com/paper/2409.17504/) (2024)
- [The Dawn After the Dark: An Empirical Study on Factuality Hallucination in Large Language Models](https://mlsanity.com/paper/2401.03205/) (2024)
- [TruthX: Alleviating Hallucinations by Editing Large Language Models in Truthful Space](https://mlsanity.com/paper/2402.17811/) (2024)
- [Truth is Universal: Robust Detection of Lies in LLMs](https://mlsanity.com/paper/2407.12831/) (2024)
- [How Large Language Models Encode Context Knowledge? A Layer-Wise Probing Study](https://mlsanity.com/paper/2402.16061/) (2024)
- [Steer LLM Latents for Hallucination Detection](https://mlsanity.com/paper/2503.01917/) (2025)
- [Fact-and-Reflection (FaR) Improves Confidence Calibration of Large Language Models](https://mlsanity.com/paper/2402.17124/) (2024)
- [Decoding Probing: Revealing Internal Linguistic Structures in Neural Language Models using Minimal Pairs](https://mlsanity.com/paper/2403.17299/) (2024)
- [ANAH: Analytical Annotation of Hallucinations in Large Language Models](https://mlsanity.com/paper/2405.20315/) (2024)
- [Automated Natural Language Explanation of Deep Visual Neurons with Large Models](https://mlsanity.com/paper/2310.10708/) (2023)
- [An Analysis of Multilingual FActScore](https://mlsanity.com/paper/2406.19415/) (2024)

## Built on by (most cited first, 4 of 4)

- [Detecting Contextual Hallucinations in LLMs with Frequency-Aware Attention](https://mlsanity.com/paper/2602.18145/) (2026)
- [Detection Without Correction: A Robust Asymmetry in Activation-Based Hallucination Probing](https://mlsanity.com/paper/2604.13068/) (2026)
- [The Anatomy of a Truth Direction: Knowledge-Dependent Dimensionality, a Relational Law, and a Shared Category Geometry in Small Language Models](https://mlsanity.com/paper/2607.16741/) (2026)
- [Leveraging Low-Level Symbolic Competences for Unsupervised Grounding in Hallucination Detection](https://mlsanity.com/paper/2609.05025/) (2026)

## Abstract (arXiv)

Hallucination remains a critical barrier for deploying large language models (LLMs) in reliability-sensitive applications. Existing detection methods largely fall into two categories: factuality checking, which is fundamentally constrained by external knowledge coverage, and static hidden-state analysis, that fails to capture deviations in reasoning dynamics. As a result, their effectiveness and robustness remain limited. We propose HSAD (Hidden Signal Analysis-based Detection), a novel hallucination detection framework that models the temporal dynamics of hidden representations during autoregressive generation. HSAD constructs hidden-layer signals by sampling activations across layers, applies Fast Fourier Transform (FFT) to obtain frequency-domain representations, and extracts the strongest non-DC frequency component as spectral features. Furthermore, by leveraging the autoregressive nature of LLMs, HSAD identifies optimal observation points for effective and reliable detection. Across multiple benchmarks, including TruthfulQA, HSAD achieves over 10 percentage points improvement compared to prior state-of-the-art methods. By integrating reasoning-process modeling with frequency-domain analysis, HSAD establishes a new paradigm for robust hallucination detection in LLMs.