# Certainty robustness: Evaluating LLM stability under self-challenging prompts

arXiv: https://arxiv.org/abs/2603.03330 · HTML: https://mlsanity.com/paper/2603.03330/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 14 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [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)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Are You Sure? Challenging LLMs Leads to Performance Drops in The FlipFlop Experiment](https://mlsanity.com/paper/2311.08596/) (2023)
- [Won't Get Fooled Again: Answering Questions with False Premises](https://mlsanity.com/paper/2307.02394/) (2023)
- [Calibrating Long-form Generations from Large Language Models](https://mlsanity.com/paper/2402.06544/) (2024)
- [Easy Problems That LLMs Get Wrong](https://mlsanity.com/paper/2405.19616/) (2024)
- [Finetuning Language Models to Emit Linguistic Expressions of Uncertainty](https://mlsanity.com/paper/2409.12180/) (2024)

## Built on by (most cited first, 2 of 2)

- [Who Flips? Self- and Cross-Model Counterarguments Reveal Answer Instability in LLMs](https://mlsanity.com/paper/2606.16011/) (2026)
- [SABER: Stability-Aware Early Exit for LLM Reasoning via Adversarial Branch Probing](https://mlsanity.com/paper/2608.27963/) (2026)

## Abstract (arXiv)

Large language models (LLMs) often present answers with high apparent confidence despite lacking an explicit mechanism for reasoning about certainty or truth. While existing benchmarks primarily evaluate single-turn accuracy, truthfulness or confidence calibration, they do not capture how models behave when their responses are challenged in interactive settings. We introduce the Certainty Robustness Benchmark, a two-turn evaluation framework that measures how LLMs balance stability and adaptability under self-challenging prompts such as uncertainty ("Are you sure?") and explicit contradiction ("You are wrong!"), alongside numeric confidence elicitation. Using 200 reasoning and mathematics questions from LiveBench, we evaluate four state-of-the-art LLMs and distinguish between justified self-corrections and unjustified answer changes. Our results reveal substantial differences in interactive reliability that are not explained by baseline accuracy alone: some models abandon correct answers under conversational pressure, while others demonstrate strong resistance to challenge and better alignment between confidence and correctness. These findings identify certainty robustness as a distinct and critical dimension of LLM evaluation, with important implications for alignment, trustworthiness and real-world deployment.