Understanding the Prompt Sensitivity
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Abstract (arXiv)
Prompt sensitivity, which refers to how strongly the output of a large language model (LLM) depends on the exact wording of its input prompt, raises concerns among users about the LLM's stability and reliability. In this work, we consider LLMs as multivariate functions and perform a first-order Taylor expansion, thereby analyzing the relationship between meaning-preserving prompts, their gradients, and the log probabilities of the model's next token. We derive an upper bound on the difference between log probabilities using the Cauchy-Schwarz inequality. We show that LLMs do not internally cluster similar inputs like smaller neural networks do, but instead disperse them. This dispersing behavior leads to an excessively high upper bound on the difference of log probabilities between two meaning-preserving prompts, making it difficult to effectively reduce to 0. In our analysis, we also show which types of meaning-preserving prompt variants are more likely to introduce prompt sensitivity risks in LLMs. In addition, we demonstrate that the upper bound is strongly correlated with an existing prompt sensitivity metric, PromptSensiScore. Moreover, by analyzing the logit variance, we find that prompt templates typically exert a greater influence on logits than the questions themselves. Overall, our results provide a general interpretation for why current LLMs can be highly sensitive to prompts with the same meaning, offering crucial evidence for understanding the prompt sensitivity of LLMs. Code for experiments is available at https://github.com/ku-nlp/Understanding_the_Prompt_Sensitivity.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 32 of its 65 references that are in the map. First posted on arXiv 20 Apr 2026.
Builds on
32 of 65 references.
References · 32
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20 more
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Built on by
Citing papers per year: 2026: 3.
3 papers.
- 2026Discourse-Role Labels as Presentation-Time Variables for Context Use in Language Modelscited by 1
- 2026How Much Do LLM-as-a-Judge Design Choices Matter? A Systematic Comparison of Prompt Designs, Rating Scales, and Modelscited by 0
- 2026A Distributional Framework for Behavioral Characterization and Risk Management of Large Language Modelscited by 0
- 2026A Distributional Framework for Behavioral Characterization and Risk Management of Large Language Models8 Oct 2026
- 2026How Much Do LLM-as-a-Judge Design Choices Matter? A Systematic Comparison of Prompt Designs, Rating Scales, and Models4 Oct 2026
- 2026Discourse-Role Labels as Presentation-Time Variables for Context Use in Language Models2 Jun 2026