Modeling and Predicting Multi-Turn Answer Instability in Large Language Models

TL;DR

This paper investigates the robustness of large language models in multi-turn interactions, revealing their answer instability and proposing Markov chain models and linear probes for predicting accuracy changes over turns.

Contribution

It introduces methods to evaluate and predict answer stability in LLMs using Markov chains and linear probes, highlighting their fragility in multi-turn scenarios.

Findings

Answer accuracy drops significantly with repeated prompts.

Markov chains effectively model accuracy dynamics over turns.

Linear probes can predict future answer changes.

Abstract

As large language models (LLMs) are adopted in an increasingly wide range of applications, user-model interactions have grown in both frequency and scale. Consequently, research has focused on evaluating the robustness of LLMs, an essential quality for real-world tasks. In this paper, we employ simple multi-turn follow-up prompts to evaluate models' answer changes, model accuracy dynamics across turns with Markov chains, and examine whether linear probes can predict these changes. Our results show significant vulnerabilities in LLM robustness: a simple "Think again" prompt led to an approximate 10% accuracy drop for Gemini 1.5 Flash over nine turns, while combining this prompt with a semantically equivalent reworded question caused a 7.5% drop for Claude 3.5 Haiku. Additionally, we find that model accuracy across turns can be effectively modeled using Markov chains, enabling the prediction of accuracy probabilities over time. This allows for estimation of the model's stationary (long-run) accuracy, which we find to be on average approximately 8% lower than its first-turn accuracy for Gemini 1.5 Flash. Our results from a model's hidden states also reveal evidence that linear probes can help predict future answer changes. Together, these results establish stationary accuracy as a principled robustness metric for interactive settings and expose the fragility of models under repeated questioning. Addressing this instability will be essential for deploying LLMs in high-stakes and interactive settings where consistent reasoning is as important as initial accuracy.