# Low-Cost Black-Box Detection of LLM Hallucinations via Dynamical System Prediction

arXiv: https://arxiv.org/abs/2605.05134 · HTML: https://mlsanity.com/paper/2605.05134/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 46 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [A Multitask, Multilingual, Multimodal Evaluation of ChatGPT on Reasoning, Hallucination, and Interactivity](https://mlsanity.com/paper/2302.04023/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Benchmarking Large Language Models for News Summarization](https://mlsanity.com/paper/2301.13848/) (2023)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Qwen3-VL-Embedding and Qwen3-VL-Reranker: A Unified Framework for State-of-the-Art Multimodal Retrieval and Ranking](https://mlsanity.com/paper/2601.04720/) (2026)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Calibrated Language Models Must Hallucinate](https://mlsanity.com/paper/2311.14648/) (2023)
- [SAC3: Reliable Hallucination Detection in Black-Box Language Models via Semantic-aware Cross-check Consistency](https://mlsanity.com/paper/2311.01740/) (2023)
- [Unsupervised Real-Time Hallucination Detection based on the Internal States of Large Language Models](https://mlsanity.com/paper/2403.06448/) (2024)
- [FELM: Benchmarking Factuality Evaluation of Large Language Models](https://mlsanity.com/paper/2310.00741/) (2023)
- [Detecting Hallucinations in Large Language Model Generation: A Token Probability Approach](https://mlsanity.com/paper/2405.19648/) (2024)
- [jina-embeddings-v5-text: Task-Targeted Embedding Distillation](https://mlsanity.com/paper/2602.15547/) (2026)
- [FactSelfCheck: Fact-Level Black-Box Hallucination Detection for LLMs](https://mlsanity.com/paper/2503.17229/) (2025)
- [Beyond Next Token Probabilities: Learnable, Fast Detection of Hallucinations and Data Contamination on LLM Output Distributions](https://mlsanity.com/paper/2503.14043/) (2025)
- [F2LLM-v2: Inclusive, Performant, and Efficient Embeddings for a Multilingual World](https://mlsanity.com/paper/2603.19223/) (2026)
- [Beyond the Next Token: Towards Prompt-Robust Zero-Shot Classification via Efficient Multi-Token Prediction](https://mlsanity.com/paper/2504.03159/) (2025)
- [Zero-knowledge LLM hallucination detection and mitigation through fine-grained cross-model consistency](https://mlsanity.com/paper/2508.14314/) (2025)

## Built on by (most cited first, 3 of 3)

- [Guarantees on Dynamical System Distinguishability for LLM Token Generation](https://mlsanity.com/paper/2607.28667/) (2026)
- [Enforcing LLM Safety through DMD-based Classification of Prompt-Response Embedding Dynamics](https://mlsanity.com/paper/2608.19579/) (2026)
- [Prediction of Prediction (PoP): Inter-Layer Activation Fusion for Single-Pass Hallucination Detection in Large Language Models](https://mlsanity.com/paper/2608.27165/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) frequently generate plausible but non-factual content, a phenomenon known as hallucination. While existing detection methods typically rely on computationally expensive sampling-based consistency checks or external knowledge retrieval, we propose a new method that treats the LLM as a black-box dynamical system. By projecting LLM responses into a high-dimensional manifold via an embedding model, we characterize the resulting vector sequences as observable realizations of the model's latent state-space dynamics. Leveraging Koopman operator theory, we fit the transition operators for both factual and hallucinated regimes and define a differential residual score based on their respective prediction errors. This approach enables low-cost hallucination detection in a single-sample pass, avoiding the need for secondary sampling or external grounding. Extensive testing across three data benchmarks demonstrates that our method achieves state-of-the-art performance with reduced resource overhead.