# Quantifying perturbation impacts for large language models

arXiv: https://arxiv.org/abs/2412.00868 · HTML: https://mlsanity.com/paper/2412.00868/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 1 Dec 2024.

## Builds on (most cited first, 14 of 14)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [MoverScore: Text Generation Evaluating with Contextualized Embeddings and Earth Mover Distance](https://mlsanity.com/paper/1909.02622/) (2019)
- [The Effect of Sampling Temperature on Problem Solving in Large Language Models](https://mlsanity.com/paper/2402.05201/) (2024)
- [Reducing Gender Bias in Abusive Language Detection](https://mlsanity.com/paper/1808.07231/) (2018)
- [Re-evaluating Evaluation in Text Summarization](https://mlsanity.com/paper/2010.07100/) (2020)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Context-Aware Testing: A New Paradigm for Model Testing with Large Language Models](https://mlsanity.com/paper/2410.24005/) (2024)
- [Self-Healing Machine Learning: A Framework for Autonomous Adaptation in Real-World Environments](https://mlsanity.com/paper/2411.00186/) (2024)
- [Accountability of AI Under the Law: The Role of Explanation](https://mlsanity.com/paper/1711.01134/) (2017)

## Built on by (most cited first, 8 of 8)

- [Are LLMs Stable Formal Logic Translators in Logical Reasoning Across Linguistically Diversified Texts?](https://mlsanity.com/paper/2506.04575/) (2025)
- [Consistency as a Testable Property: Statistical Methods to Evaluate AI Agent Reliability](https://mlsanity.com/paper/2605.10516/) (2026)
- [Syntactic Framing Fragility: An Audit of Robustness in LLM Ethical Decisions](https://mlsanity.com/paper/2601.09724/) (2025)
- [Exploring Membership Inference Vulnerabilities in Clinical Large Language Models](https://mlsanity.com/paper/2510.18674/) (2025)
- [Evaluating LLM Safety Under Repeated Inference via Accelerated Prompt Stress Testing](https://mlsanity.com/paper/2602.11786/) (2026)
- [Evaluating Reliability Gaps in Large Language Model Safety via Repeated Prompt Sampling](https://mlsanity.com/paper/2604.09606/) (2026)
- [LAMP: Extracting Local Decision Surfaces From Large Language Models](https://mlsanity.com/paper/2505.11772/) (2025)
- [Cross-View Correspondence Is a Measurement Intervention: Two-Sided Validation for Agent Evaluation and Credit Assignment](https://mlsanity.com/paper/2608.17713/) (2026)

## Abstract (arXiv)

We consider the problem of quantifying how an input perturbation impacts the outputs of large language models (LLMs), a fundamental task for model reliability and post-hoc interpretability. A key obstacle in this domain is disentangling the meaningful changes in model responses from the intrinsic stochasticity of LLM outputs. To overcome this, we introduce Distribution-Based Perturbation Analysis (DBPA), a framework that reformulates LLM perturbation analysis as a frequentist hypothesis testing problem. DBPA constructs empirical null and alternative output distributions within a low-dimensional semantic similarity space via Monte Carlo sampling. Comparisons of Monte Carlo estimates in the reduced dimensionality space enables tractable frequentist inference without relying on restrictive distributional assumptions. The framework is model-agnostic, supports the evaluation of arbitrary input perturbations on any black-box LLM, yields interpretable p-values, supports multiple perturbation testing via controlled error rates, and provides scalar effect sizes for any chosen similarity or distance metric. We demonstrate the effectiveness of DBPA in evaluating perturbation impacts, showing its versatility for perturbation analysis.