# Measuring Stability and Failure Behavior in Language Models Under Structured Perturbations

arXiv: https://arxiv.org/abs/2608.22138 · HTML: https://mlsanity.com/paper/2608.22138/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 31 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Builds on (most cited first, 29 of 29)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Fantastically Ordered Prompts and Where to Find Them: Overcoming Few-Shot Prompt Order Sensitivity](https://mlsanity.com/paper/2104.08786/) (2021)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [The Instruction Hierarchy: Training LLMs to Prioritize Privileged Instructions](https://mlsanity.com/paper/2404.13208/) (2024)
- [State of What Art? A Call for Multi-Prompt LLM Evaluation](https://mlsanity.com/paper/2401.00595/) (2023)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)
- [On the Robustness of ChatGPT: An Adversarial and Out-of-distribution Perspective](https://mlsanity.com/paper/2302.12095/) (2023)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [Same Task, More Tokens: the Impact of Input Length on the Reasoning Performance of Large Language Models](https://mlsanity.com/paper/2402.14848/) (2024)
- [When Benchmarks are Targets: Revealing the Sensitivity of Large Language Model Leaderboards](https://mlsanity.com/paper/2402.01781/) (2024)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [Premise Order Matters in Reasoning with Large Language Models](https://mlsanity.com/paper/2402.08939/) (2024)
- [Knowledge of Knowledge: Exploring Known-Unknowns Uncertainty with Large Language Models](https://mlsanity.com/paper/2305.13712/) (2023)
- [Won't Get Fooled Again: Answering Questions with False Premises](https://mlsanity.com/paper/2307.02394/) (2023)
- [Control Illusion: The Failure of Instruction Hierarchies in Large Language Models](https://mlsanity.com/paper/2502.15851/) (2025)
- [Revisit Input Perturbation Problems for LLMs: A Unified Robustness Evaluation Framework for Noisy Slot Filling Task](https://mlsanity.com/paper/2310.06504/) (2023)
- [SCORE: Systematic COnsistency and Robustness Evaluation for Large Language Models](https://mlsanity.com/paper/2503.00137/) (2025)
- [RUPBench: Benchmarking Reasoning Under Perturbations for Robustness Evaluation in Large Language Models](https://mlsanity.com/paper/2406.11020/) (2024)
- [MedDialBench: Benchmarking LLM Diagnostic Robustness under Parametric Adversarial Patient Behaviors](https://mlsanity.com/paper/2604.06846/) (2026)
- [Numerical Sensitivity and Robustness: Exploring the Flaws of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2511.08022/) (2025)
- [Robust Reasoning Benchmark](https://mlsanity.com/paper/2604.08571/) (2026)

## Abstract (arXiv)

Language models are usually judged by a single accuracy score, which does not reveal how their performance degrades as inputs are perturbed. We present a graded, multi-family, failure-aware framework for stress-testing reasoning models. It perturbs each problem along a multi-level severity ladder across seven families: six that preserve the answer, paraphrase, input noise, formatting, irrelevant context, context load, and conflicting instructions, and a Knowledge Boundary family that removes answerability so that refusal becomes the correct response. Every test is validity-gated and labeled by its measured severity, and each model is summarized by per-level Accuracy, a magnitude-weighted Stability, and a per-family Collapse Point defined relative to the model's own baseline. Instantiated on the same 100 seed problems used by GSM-Symbolic, expanded into 4,473 gated tests and run on four models spanning capability tiers, the framework exposes structure that an aggregate score hides: the level at which a model fails is family-specific rather than global, and two stressors expose consistent weaknesses across all models: conflicting instructions and questions built on an impossible premise. Recognition of unanswerability is otherwise uneven, reliable on missing information and fabricated evidence but weak on impossible premises. These failure points are invisible to standard accuracy reporting.