# LLMs Will Always Hallucinate, and We Need to Live With This

arXiv: https://arxiv.org/abs/2409.05746 · HTML: https://mlsanity.com/paper/2409.05746/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 72 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [A Comprehensive Survey of Hallucination Mitigation Techniques in Large Language Models](https://mlsanity.com/paper/2401.01313/) (2024)
- [Large Legal Fictions: Profiling Legal Hallucinations in Large Language Models](https://mlsanity.com/paper/2401.01301/) (2024)
- [Towards Faithful Model Explanation in NLP: A Survey](https://mlsanity.com/paper/2209.11326/) (2022)
- [Modeling Coverage for Neural Machine Translation](https://mlsanity.com/paper/1601.04811/) (2016)
- [A Complete Survey on LLM-based AI Chatbots](https://mlsanity.com/paper/2406.16937/) (2024)
- [Learning from models beyond fine-tuning](https://mlsanity.com/paper/2310.08184/) (2023)
- [Memory Augmented Large Language Models are Computationally Universal](https://mlsanity.com/paper/2301.04589/) (2023)
- [The Ethics of ChatGPT in Medicine and Healthcare: A Systematic Review on Large Language Models (LLMs)](https://mlsanity.com/paper/2403.14473/) (2024)
- [How fine can fine-tuning be? Learning efficient language models](https://mlsanity.com/paper/2004.14129/) (2020)
- [Deficiency of Large Language Models in Finance: An Empirical Examination of Hallucination](https://mlsanity.com/paper/2311.15548/) (2023)
- [Needle in the Haystack for Memory Based Large Language Models](https://mlsanity.com/paper/2407.01437/) (2024)
- [Hallucination is the last thing you need](https://mlsanity.com/paper/2306.11520/) (2023)
- [I am a Strange Dataset: Metalinguistic Tests for Language Models](https://mlsanity.com/paper/2401.05300/) (2024)
- [Efficient Time-Series Approximation with Linear Recurrent Neural Networks: Architecture Learning and Predictive Power](https://mlsanity.com/paper/1802.03308/) (2018)

## Built on by (most cited first, 30 of 78)

- [Evaluating Step-by-step Reasoning Traces: A Survey](https://mlsanity.com/paper/2502.12289/) (2025)
- [A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice](https://mlsanity.com/paper/2410.15326/) (2024)
- [Large Language Models Hallucination: A Comprehensive Survey](https://mlsanity.com/paper/2510.06265/) (2025)
- [Position: Uncertainty Quantification Needs Reassessment for Large-language Model Agents](https://mlsanity.com/paper/2505.22655/) (2025)
- [Think More, Hallucinate Less: Mitigating Hallucinations via Dual Process of Fast and Slow Thinking](https://mlsanity.com/paper/2501.01306/) (2025)
- [Knowledge Graphs, Large Language Models, and Hallucinations: An NLP Perspective](https://mlsanity.com/paper/2411.14258/) (2024)
- [Estimating LLM Uncertainty with Evidence](https://mlsanity.com/paper/2502.00290/) (2025)
- [Get Experience from Practice: LLM Agents with Record & Replay](https://mlsanity.com/paper/2505.17716/) (2025)
- [MALMM: Multi-Agent Large Language Models for Zero-Shot Robotics Manipulation](https://mlsanity.com/paper/2411.17636/) (2024)
- [RvLLM: LLM Runtime Verification with Domain Knowledge](https://mlsanity.com/paper/2505.18585/) (2025)
- [CondAmbigQA: A Benchmark and Dataset for Conditional Ambiguous Question Answering](https://mlsanity.com/paper/2502.01523/) (2025)
- [Why and How LLMs Hallucinate: Connecting the Dots with Subsequence Associations](https://mlsanity.com/paper/2504.12691/) (2025)
- [HalluVerse25: Fine-grained Multilingual Benchmark Dataset for LLM Hallucinations](https://mlsanity.com/paper/2503.07833/) (2025)
- [Maestro: Learning to Collaborate via Conditional Listwise Policy Optimization for Multi-Agent LLMs](https://mlsanity.com/paper/2511.06134/) (2025)
- [Mitigating Hallucinations in Large Language Models via Causal Reasoning](https://mlsanity.com/paper/2508.12495/) (2025)
- [RoT: Enhancing Table Reasoning with Iterative Row-Wise Traversals](https://mlsanity.com/paper/2505.15110/) (2025)
- [Not All Votes Count! Programs as Verifiers Improve Self-Consistency of Language Models for Math Reasoning](https://mlsanity.com/paper/2410.12608/) (2024)
- [Lost in Cultural Translation: Do LLMs Struggle with Math Across Cultural Contexts?](https://mlsanity.com/paper/2503.18018/) (2025)
- [LLLMs: A Data-Driven Survey of Evolving Research on Limitations of Large Language Models](https://mlsanity.com/paper/2505.19240/) (2025)
- [Graph-Augmented Reasoning: Evolving Step-by-Step Knowledge Graph Retrieval for LLM Reasoning](https://mlsanity.com/paper/2503.01642/) (2025)
- [SAFE: A Sparse Autoencoder-Based Framework for Robust Query Enrichment and Hallucination Mitigation in LLMs](https://mlsanity.com/paper/2503.03032/) (2025)
- [Creativity in AI: Progresses and Challenges](https://mlsanity.com/paper/2410.17218/) (2024)
- [First Train to Generate, then Generate to Train: UnitedSynT5 for Few-Shot NLI](https://mlsanity.com/paper/2412.09263/) (2024)
- [Logic-RAG: Augmenting Large Multimodal Models with Visual-Spatial Knowledge for Road Scene Understanding](https://mlsanity.com/paper/2503.12663/) (2025)
- [Loki's Dance of Illusions: A Comprehensive Survey of Hallucination in Large Language Models](https://mlsanity.com/paper/2507.02870/) (2025)
- [The Lottery LLM Hypothesis, Rethinking What Abilities Should LLM Compression Preserve?](https://mlsanity.com/paper/2502.17535/) (2025)
- [HACK: Hallucinations Along Certainty and Knowledge Axes](https://mlsanity.com/paper/2510.24222/) (2025)
- [Hallucinations are inevitable but can be made statistically negligible](https://mlsanity.com/paper/2502.12187/) (2025)
- [Hallucinations Undermine Trust; Metacognition is a Way Forward](https://mlsanity.com/paper/2605.01428/) (2026)
- [Unraveling Human-AI Teaming: A Review and Outlook](https://mlsanity.com/paper/2504.05755/) (2025)

## Abstract (arXiv)

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.