From Drift to Coherence: Stabilizing Beliefs in LLMs

2026-06-16

AI Summary

This work addresses the issue of early belief drift in large language models during multiple-choice question answering, which violates the martingale property required by Bayesian inference and leads to inconsistent predictions. The authors propose Prompt-based Prediction Resampling (PPR), a method that, for the first time in real-world QA settings, reveals the self-stabilizing nature of model beliefs. Leveraging this insight, they introduce a seed-answer prompting strategy and a self-consistency fine-tuning loss. This approach significantly reduces belief drift and enhances prediction consistency without compromising accuracy, achieving consistent or even improved performance across multiple multiple-choice QA benchmarks.

Abstract

Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition, the martingale property of predictive beliefs, has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.

Problem

• belief drift
• predictive coherence
• martingale property
• large language models
• in-context learning

Innovation

• Prompted Predictive Resampling
• belief drift
• predictive coherence
• self-consistency loss
• martingale property