Martingale Score: An Unsupervised Metric for Bayesian Rationality in LLM Reasoning

• URL: http://arxiv.org/abs/2512.02914v1
• Date: Tue, 02 Dec 2025 16:34:05 GMT
• Title: Martingale Score: An Unsupervised Metric for Bayesian Rationality in LLM Reasoning
• Abstract summary: We propose a systematic evaluation framework for belief entrenchment in large language models.<n>We use the Martingale property from Bayesian statistics to measure violations of this property.<n>We identify the models, reasoning techniques, and domains more prone to belief entrenchment.
• Score: 26.42437186150084
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent advances in reasoning techniques have substantially improved the performance of large language models (LLMs), raising expectations for their ability to provide accurate, truthful, and reliable information. However, emerging evidence suggests that iterative reasoning may foster belief entrenchment and confirmation bias, rather than enhancing truth-seeking behavior. In this study, we propose a systematic evaluation framework for belief entrenchment in LLM reasoning by leveraging the Martingale property from Bayesian statistics. This property implies that, under rational belief updating, the expected value of future beliefs should remain equal to the current belief, i.e., belief updates are unpredictable from the current belief. We propose the unsupervised, regression-based Martingale Score to measure violations of this property, which signal deviation from the Bayesian ability of updating on new evidence. In open-ended problem domains including event forecasting, value-laden questions, and academic paper review, we find such violations to be widespread across models and setups, where the current belief positively predicts future belief updates, a phenomenon which we term belief entrenchment. We identify the models, reasoning techniques, and domains more prone to belief entrenchment. Finally, we validate the Martingale Score by showing that it predicts ground-truth accuracy on problem domains where ground truth labels are available. This indicates that, while designed as an unsupervised metric that operates even in domains without access to ground truth, the Martingale Score is a useful proxy of the truth-seeking ability of a reasoning process.

Related papers

• Does Reasoning Preserve Alignment? On the Trustworthiness of Large Reasoning Models [55.788110316999166]
  We compare reasoning models produced via supervised fine-tuning, RL-based post-training, and distillation against instruction-tuned baselines.<n>We observe that reasoning models often improve on reasoning benchmarks but exhibit alignment regressions.<n>These regressions are consistent with behavioral drift from the instruction-tuned baseline, measured by KL divergence.
  arXiv  Detail & Related papers  (2026-06-09T16:14:27Z)
• Breaking the Martingale Curse: Multi-Agent Debate via Asymmetric Cognitive Potential Energy [42.25453328861205]
  Multi-Agent Debate (MAD) has emerged as a promising paradigm for enhancing large language model reasoning.<n>We propose AceMAD, a framework that breaks the Martingale Curse by harnessing asymmetric cognitive potential energy.
  arXiv  Detail & Related papers  (2026-03-06T19:10:19Z)
• From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Models [77.04403907729738]
  This survey charts the evolution of uncertainty from a passive diagnostic metric to an active control signal guiding real-time model behavior.<n>We demonstrate how uncertainty is leveraged as an active control signal across three frontiers.<n>This survey argues that mastering the new trend of uncertainty is essential for building the next generation of scalable, reliable, and trustworthy AI.
  arXiv  Detail & Related papers  (2026-01-22T06:21:31Z)
• MR-Align: Meta-Reasoning Informed Factuality Alignment for Large Reasoning Models [43.872922223495586]
  Large reasoning models (LRMs) show strong capabilities in complex reasoning, yet their marginal gains on evidence-dependent factual questions are limited.<n>We find this limitation is partially attributable to a reasoning-answer hit gap, where the model identifies the correct facts during reasoning but fails to incorporate them into the final response.<n>We propose MR-ALIGN, a framework that enhances factuality without relying on external verifiers.
  arXiv  Detail & Related papers  (2025-10-27T15:00:54Z)
• Confidential Guardian: Cryptographically Prohibiting the Abuse of Model Abstention [65.47632669243657]
  A dishonest institution can exploit mechanisms to discriminate or unjustly deny services under the guise of uncertainty.<n>We demonstrate the practicality of this threat by introducing an uncertainty-inducing attack called Mirage.<n>We propose Confidential Guardian, a framework that analyzes calibration metrics on a reference dataset to detect artificially suppressed confidence.
  arXiv  Detail & Related papers  (2025-05-29T19:47:50Z)
• Rectifying Belief Space via Unlearning to Harness LLMs' Reasoning [36.74368293113009]
  We propose a method to rectify the belief space by suppressing spurious beliefs while simultaneously enhancing true ones.<n>Our approach first identifies the beliefs that lead to incorrect or correct answers by prompting the model to generate textual explanations.<n>We then apply unlearning to suppress the identified spurious beliefs and enhance the true ones, effectively rectifying the model's belief space.
  arXiv  Detail & Related papers  (2025-02-28T00:57:45Z)
• Beyond Accuracy: On the Effects of Fine-tuning Towards Vision-Language Model's Prediction Rationality [9.192802430973925]
  We study the impact of fine-tuning on prediction rationality in vision-language models (VLMs)<n>We propose two new metrics called Prediction Trustworthiness and Inference Reliability.<n>We find that the well-adopted fine-tuning methods led to more correct predictions based on invalid evidence.<n>Having identified valid evidence of target objects, fine-tuned VLMs were more likely to make correct predictions.
  arXiv  Detail & Related papers  (2024-12-17T21:09:49Z)
• Automated Trustworthiness Testing for Machine Learning Classifiers [3.3423762257383207]
  This paper proposes TOWER, the first technique to automatically create trustworthiness oracles that determine whether text classifier predictions are trustworthy. Our hypothesis is that a prediction is trustworthy if the words in its explanation are semantically related to the predicted class. The results show that TOWER can detect a decrease in trustworthiness as noise increases, but is not effective when evaluated against the human-labeled dataset.
  arXiv  Detail & Related papers  (2024-06-07T20:25:05Z)
• Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective [4.415371871652809]
  In-context learning (ICL) has emerged as a remarkable characteristic of Large Language Models (LLM) We show that the martingale property is a necessary condition for unambiguous predictions in such scenarios. We derive actionable checks with corresponding theory and test statistics which must hold if the martingale property is satisfied.
  arXiv  Detail & Related papers  (2024-06-02T16:20:30Z)
• Consistent End-to-End Estimation for Counterfactual Fairness [56.9060492313073]
  We propose a novel counterfactual fairness predictor for making predictions under counterfactual fairness.<n>We provide theoretical guarantees that our method is effective in ensuring the notion of counterfactual fairness.
  arXiv  Detail & Related papers  (2023-10-26T17:58:39Z)
• Learning for Counterfactual Fairness from Observational Data [62.43249746968616]
  Fairness-aware machine learning aims to eliminate biases of learning models against certain subgroups described by certain protected (sensitive) attributes such as race, gender, and age. A prerequisite for existing methods to achieve counterfactual fairness is the prior human knowledge of the causal model for the data. In this work, we address the problem of counterfactually fair prediction from observational data without given causal models by proposing a novel framework CLAIRE.
  arXiv  Detail & Related papers  (2023-07-17T04:08:29Z)
• Advancing Counterfactual Inference through Nonlinear Quantile Regression [77.28323341329461]
  We propose a framework for efficient and effective counterfactual inference implemented with neural networks. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.
  arXiv  Detail & Related papers  (2023-06-09T08:30:51Z)
• Logical Satisfiability of Counterfactuals for Faithful Explanations in NLI [60.142926537264714]
  We introduce the methodology of Faithfulness-through-Counterfactuals. It generates a counterfactual hypothesis based on the logical predicates expressed in the explanation. It then evaluates if the model's prediction on the counterfactual is consistent with that expressed logic.
  arXiv  Detail & Related papers  (2022-05-25T03:40:59Z)
• Trust but Verify: Assigning Prediction Credibility by Counterfactual Constrained Learning [123.3472310767721]
  Prediction credibility measures are fundamental in statistics and machine learning. These measures should account for the wide variety of models used in practice. The framework developed in this work expresses the credibility as a risk-fit trade-off.
  arXiv  Detail & Related papers  (2020-11-24T19:52:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.