# Statistical Hypothesis Testing for Auditing Robustness in Language Models

arXiv: https://arxiv.org/abs/2506.07947 · HTML: https://mlsanity.com/paper/2506.07947/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Builds on (most cited first, 16 of 16)

- [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)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (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)
- [Nuanced Metrics for Measuring Unintended Bias with Real Data for Text Classification](https://mlsanity.com/paper/1903.04561/) (2019)
- [Better Zero-Shot Reasoning with Role-Play Prompting](https://mlsanity.com/paper/2308.07702/) (2023)
- [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)
- [Counterfactual Fairness in Text Classification through Robustness](https://mlsanity.com/paper/1809.10610/) (2018)
- [Re-evaluating Evaluation in Text Summarization](https://mlsanity.com/paper/2010.07100/) (2020)
- [The Oscars of AI Theater: A Survey on Role-Playing with Language Models](https://mlsanity.com/paper/2407.11484/) (2024)
- [A Triangle Inequality for Cosine Similarity](https://mlsanity.com/paper/2107.04071/) (2021)

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

- [Audit Me If You Can: Query-Efficient Active Fairness Auditing of Black-Box LLMs](https://mlsanity.com/paper/2601.03087/) (2026)
- [Tiny Autoregressive Recursive Models](https://mlsanity.com/paper/2603.08082/) (2026)
- [Deep Hierarchical Learning with Nested Subspace Networks for Large Language Models](https://mlsanity.com/paper/2509.17874/) (2025)
- [Syntactic Framing Fragility: An Audit of Robustness in LLM Ethical Decisions](https://mlsanity.com/paper/2601.09724/) (2025)
- [No More, No Less: Least-Privilege Language Models](https://mlsanity.com/paper/2601.23157/) (2026)
- [Metadata Predictability Is Not Evidence Dependence: An Intervention-Based Audit for Weak-Label Benchmarks](https://mlsanity.com/paper/2605.23701/) (2026)
- [Black-Box Auditing of Epistemic Reliability in Multi-Agent Debate Distillation](https://mlsanity.com/paper/2609.32361/) (2026)
- [A Distributional Framework for Behavioral Characterization and Risk Management of Large Language Models](https://mlsanity.com/paper/2610.12718/) (2026)

## Abstract (arXiv)

Consider the problem of testing whether the outputs of a large language model (LLM) system change under an arbitrary intervention, such as an input perturbation or changing the model variant. We cannot simply compare two LLM outputs since they might differ due to the stochastic nature of the system, nor can we compare the entire output distribution due to computational intractability. While existing methods for analyzing text-based outputs exist, they focus on fundamentally different problems, such as measuring bias or fairness. To this end, we introduce distribution-based perturbation analysis, a framework that reformulates LLM perturbation analysis as a frequentist hypothesis testing problem. We construct empirical null and alternative output distributions within a low-dimensional semantic similarity space via Monte Carlo sampling, enabling tractable inference without restrictive distributional assumptions. The framework is (i) model-agnostic, (ii) supports the evaluation of arbitrary input perturbations on any black-box LLM, (iii) yields interpretable p-values; (iv) supports multiple perturbations via controlled error rates; and (v) provides scalar effect sizes. We demonstrate the usefulness of the framework across multiple case studies, showing how we can quantify response changes, measure true/false positive rates, and evaluate alignment with reference models. Above all, we see this as a reliable frequentist hypothesis testing framework for LLM auditing.