mlsanityData to 7 Oct 2026

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

arXiv 2409.05746 ↗First posted 9 Sep 2024stat.ML cs.LGcited by 77

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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.

Key facts. Cited by 77 papers in the map (data through 7 Oct 2026). Builds on 31 of its 72 references that are in the map. First posted on arXiv 9 Sep 2024.

Builds on

31 of 72 references.

References · 31

  1. 2017Attention Is All You Needcited by 59,932
  2. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,084
  3. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  4. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
  5. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,616
  6. 2021RoFormer: Enhanced Transformer with Rotary Position Embeddingcited by 4,581
  7. 2019Parameter-Efficient Transfer Learning for NLPcited by 4,195
  8. 2022Emergent Abilities of Large Language Modelscited by 2,483
  9. 2022Language Models (Mostly) Know What They Knowcited by 1,783
  10. 2023A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questionscited by 1,582
  11. 2021BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-modelscited by 1,234
  12. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
19 more
  1. 2024Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Surveycited by 641
  2. 2019Data Shapley: Equitable Valuation of Data for Machine Learningcited by 617
  3. 2022Towards Reasoning in Large Language Models: A Surveycited by 593
  4. 2024Jamba: A Hybrid Transformer-Mamba Language Modelcited by 390
  5. 2024A Comprehensive Survey of Hallucination Mitigation Techniques in Large Language Modelscited by 266
  6. 2024Large Legal Fictions: Profiling Legal Hallucinations in Large Language Modelscited by 144
  7. 2022Towards Faithful Model Explanation in NLP: A Surveycited by 129
  8. 2016Modeling Coverage for Neural Machine Translationcited by 110
  9. 2024A Complete Survey on LLM-based AI Chatbotscited by 71
  10. 2023Learning from models beyond fine-tuningcited by 47
  11. 2023Memory Augmented Large Language Models are Computationally Universalcited by 45
  12. 2024The Ethics of ChatGPT in Medicine and Healthcare: A Systematic Review on Large Language Models (LLMs)cited by 45
  13. 2020How fine can fine-tuning be? Learning efficient language modelscited by 41
  14. 2023Deficiency of Large Language Models in Finance: An Empirical Examination of Hallucinationcited by 41
  15. 2024Needle in the Haystack for Memory Based Large Language Modelscited by 32
  16. 2023Hallucination is the last thing you needcited by 11
  17. 2024I am a Strange Dataset: Metalinguistic Tests for Language Modelscited by 10
  18. 2018Efficient Time-Series Approximation with Linear Recurrent Neural Networks: Architecture Learning and Predictive Powercited by 5
  19. 2017Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaoscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 10; 2025: 50; 2026: 17.

77 papers.

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  1. 2025Evaluating Step-by-step Reasoning Traces: A Surveycited by 62
  2. 2024A Survey of Uncertainty Estimation in LLMs: Theory Meets Practicecited by 54
  3. 2025Large Language Models Hallucination: A Comprehensive Surveycited by 45
  4. 2024Knowledge Graphs, Large Language Models, and Hallucinations: An NLP Perspectivecited by 29
  5. 2025Think More, Hallucinate Less: Mitigating Hallucinations via Dual Process of Fast and Slow Thinkingcited by 29
  6. 2025Position: Uncertainty Quantification Needs Reassessment for Large-language Model Agentscited by 27
  7. 2025Estimating LLM Uncertainty with Evidencecited by 26
  8. 2025Get Experience from Practice: LLM Agents with Record & Replaycited by 22
  9. 2024MALMM: Multi-Agent Large Language Models for Zero-Shot Robotics Manipulationcited by 18
  10. 2025CondAmbigQA: A Benchmark and Dataset for Conditional Ambiguous Question Answeringcited by 15
  11. 2025RvLLM: LLM Runtime Verification with Domain Knowledgecited by 15
  12. 2025Why and How LLMs Hallucinate: Connecting the Dots with Subsequence Associationscited by 14
38 more
  1. 2025Maestro: Learning to Collaborate via Conditional Listwise Policy Optimization for Multi-Agent LLMscited by 14
  2. 2025HalluVerse25: Fine-grained Multilingual Benchmark Dataset for LLM Hallucinationscited by 13
  3. 2025Mitigating Hallucinations in Large Language Models via Causal Reasoningcited by 13
  4. 2025RoT: Enhancing Table Reasoning with Iterative Row-Wise Traversalscited by 10
  5. 2025Lost in Cultural Translation: Do LLMs Struggle with Math Across Cultural Contexts?cited by 9
  6. 2025LLLMs: A Data-Driven Survey of Evolving Research on Limitations of Large Language Modelscited by 9
  7. 2024Not All Votes Count! Programs as Verifiers Improve Self-Consistency of Language Models for Math Reasoningcited by 8
  8. 2025Graph-Augmented Reasoning: Evolving Step-by-Step Knowledge Graph Retrieval for LLM Reasoningcited by 8
  9. 2024Creativity in AI: Progresses and Challengescited by 7
  10. 2024First Train to Generate, then Generate to Train: UnitedSynT5 for Few-Shot NLIcited by 7
  11. 2025SAFE: A Sparse Autoencoder-Based Framework for Robust Query Enrichment and Hallucination Mitigation in LLMscited by 7
  12. 2025The Lottery LLM Hypothesis, Rethinking What Abilities Should LLM Compression Preserve?cited by 6
  13. 2025Logic-RAG: Augmenting Large Multimodal Models with Visual-Spatial Knowledge for Road Scene Understandingcited by 6
  14. 2025Loki's Dance of Illusions: A Comprehensive Survey of Hallucination in Large Language Modelscited by 6
  15. 2025HACK: Hallucinations Along Certainty and Knowledge Axescited by 6
  16. 2025Hallucinations are inevitable but can be made statistically negligiblecited by 4
  17. 2025HalluRNN: Mitigating Hallucinations via Recurrent Cross-Layer Reasoning in Large Vision-Language Modelscited by 4
  18. 2025Aligning Knowledge Graphs and Language Models for Factual Accuracycited by 4
  19. 2026Hallucinations Undermine Trust; Metacognition is a Way Forwardcited by 4
  20. 2025Unraveling Human-AI Teaming: A Review and Outlookcited by 3
  21. 2026Automated structural testing of LLM-based agents: methods, framework, and case studiescited by 3
  22. 2026Semantic Calibration Prevails Where Token Confidence Fails: Benchmarking Long-Form Scientific QAcited by 3
  23. 2026EquiMem: Calibrating Shared Memory in Multi-Agent Debate via Game-Theoretic Equilibriumcited by 3
  24. 2024Truth or Deceit? A Bayesian Decoding Game Enhances Consistency and Reliabilitycited by 2
  25. 2024No Free Lunch: Fundamental Limits of Learning Non-Hallucinating Generative Modelscited by 2
  26. 2024LLMs as Method Actors: A Model for Prompt Engineering and Architecturecited by 2
  27. 2025Large Language Models as Common-Sense Heuristicscited by 2
  28. 2025From Hallucination to Reliability: Generative Modeling and the Structure of Scientific Inferencecited by 2
  29. 2025Hallucination is Inevitable for LLMs with the Open World Assumptioncited by 2
  30. 2025MOSAIC: Multi-agent Orchestration for Task-Intelligent Scientific Codingcited by 2
  31. 2025The Evolution of Agentic AI in Cybersecurity: From Single LLM Reasoners to Multi-Agent Systems and Autonomous Pipelinescited by 2
  32. 2025The Epistemological Consequences of Large Language Models: Rethinking collective intelligence and institutional knowledgecited by 2
  33. 2026Hallucination is a Consequence of Space-Optimality: A Rate-Distortion Theorem for Membership Testingcited by 2
  34. 2025Automated Factual Benchmarking for In-Car Conversational Systems using Large Language Modelscited by 1
  35. 2025TRIZ Agents: A Multi-Agent LLM Approach for TRIZ-Based Innovationcited by 1
  36. 2025Deploying AI for Signal Processing education: Selected challenges and intriguing opportunitiescited by 1
  37. 2026Do LLMs have core beliefs?cited by 1
  38. 2026OpenHalDet: A Unified Benchmark for Hallucination Detection across Diverse Generation Scenarioscited by 1

50 most cited of 77 All 77 (JSON)