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

**Authors:** Sourav Banerjee, Ayushi Agarwal, Saloni Singla  
**arXiv:** [2409.05746](https://arxiv.org/abs/2409.05746)  
**Date:** 2024-09-09  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2409.05746v1/

## Key points

- Large Language Models (LLMs) inevitably produce hallucinations due to their fundamental mathematical and logical structure.
- Hallucinations occur at every stage of the LLM process, including training data compilation, fact retrieval, intent classification, and text generation.
- Structural Hallucination is introduced as an intrinsic nature of LLMs.
- Ensemble Neural Networks are proposed as an alternative approach to mitigate hallucinations by using independent models for predictions.
- Uncertainty quantification methods like Shannon entropy and norm of the gradient can help identify potential hallucinations but cannot entirely prevent them.
- Faithful explanation generation is crucial in critical applications using LLMs to evaluate how models arrive at conclusions accurately.

## Summary

The paper titled "LLMs Will Always Hallucinate, and We Need to Live With This" by Sourav Banerjee, Ayushi Agarwal, and Saloni Singla delves into the inherent limitations of Large Language Models (LLMs) that are becoming increasingly prevalent across various domains. The authors argue that hallucinations in language models are not merely occasional errors but rather an inevitable feature of these systems. They demonstrate that these hallucinations stem from the fundamental mathematical and logical structure of LLMs, making it impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Drawing on computational theory and Godel's First Incompleteness Theorem , which highlights the undecidability of problems like the Halting , Emptiness , and Acceptance  Problems, the authors establish 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. They introduce the concept of Structural Hallucination as an intrinsic nature of these systems. Furthermore, the paper discusses Ensemble Neural Networks as an alternative approach where independent models make predictions separately from each other. Uncertainty quantification methods such as Shannon entropy  and norm of the gradient  are explored to identify potential hallucinations but do not prevent them entirely. Additionally, in critical applications where LLMs are used, there is a need for faithful explanation generation to evaluate how models arrive at conclusions accurately. In conclusion, this work challenges the prevailing notion that hallucinations in LLMs can be fully mitigated by establishing the mathematical certainty of their presence. It sheds light on the complexity and inevitability of hallucinations in language models and emphasizes the importance of understanding and living with this inherent limitation.