A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning

• URL: http://arxiv.org/abs/2510.15444v1
• Date: Fri, 17 Oct 2025 08:59:30 GMT
• Title: A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning
• Authors: Zhi Zhou, Yuhao Tan, Zenan Li, Yuan Yao, Lan-Zhe Guo, Yu-Feng Li, Xiaoxing Ma,
• Abstract summary: We provide the first theoretical framework for analyzing sampling-based test-time scaling methods.<n>We introduce RPC, a hybrid method that leverages our theoretical insights through two key components: Perplexity Consistency and Reasoning Pruning.<n>RPC achieves reasoning performance comparable to self-consistency while not only enhancing confidence reliability but also reducing sampling costs by 50%.
• Score: 31.861874030715953
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Test-time scaling seeks to improve the reasoning performance of large language models (LLMs) by adding computational resources. A prevalent approach within the field is sampling-based test-time scaling methods, which enhance reasoning by generating multiple reasoning paths for a given input during inference. However, despite its practical success, the theoretical foundations remain underexplored. In this paper, we provide the first theoretical framework for analyzing sampling-based test-time scaling methods, grounded in the perspective of confidence estimation. Based on the framework, we analyze two dominant paradigms: self-consistency and perplexity, and reveal key limitations: self-consistency suffers from high estimation error while perplexity exhibits substantial modeling error and possible degradation of the estimation error convergence. To address these limitations, we introduce RPC, a hybrid method that leverages our theoretical insights through two key components: Perplexity Consistency and Reasoning Pruning. Perplexity Consistency combines the strengths of self-consistency and perplexity, boosting the convergence rate of estimation error from linear to exponential while preserving model error. Reasoning Pruning prevents degradation by eliminating low-probability reasoning paths. Both theoretical analysis and empirical results across seven benchmark datasets demonstrate that RPC has a strong potential for reducing reasoning error. Notably, RPC achieves reasoning performance comparable to self-consistency while not only enhancing confidence reliability but also reducing sampling costs by 50%. The code and resources are available at https://wnjxyk.github.io/RPC.

Related papers

• Observationally Informed Adaptive Causal Experimental Design [55.998153710215654]
  We propose Active Residual Learning, a new paradigm that leverages the observational model as a foundational prior.<n>This approach shifts the experimental focus from learning target causal quantities from scratch to efficiently estimating the residuals required to correct observational bias.<n> Experiments on synthetic and semi-synthetic benchmarks demonstrate that R-Design significantly outperforms baselines.
  arXiv  Detail & Related papers  (2026-03-04T06:52:37Z)
• Reflective Confidence: Correcting Reasoning Flaws via Online Self-Correction [14.164508061248775]
  Large language models (LLMs) have achieved strong performance on complex reasoning tasks using techniques such as chain-of-thought and self-consistency.<n>We propose reflective confidence, a novel reasoning framework that transforms low-confidence signals from termination indicators into reflection triggers.<n> Experiments on mathematical reasoning benchmarks, including AIME 2025, demonstrate significant accuracy improvements over advanced early-stopping baselines at comparable computational cost.
  arXiv  Detail & Related papers  (2025-12-21T05:35:07Z)
• Efficient Thought Space Exploration through Strategic Intervention [54.35208611253168]
  We propose a novel Hint-Practice Reasoning (HPR) framework that operationalizes this insight through two synergistic components.<n>The framework's core innovation lies in Distributional Inconsistency Reduction (DIR), which dynamically identifies intervention points.<n> Experiments across arithmetic and commonsense reasoning benchmarks demonstrate HPR's state-of-the-art efficiency-accuracy tradeoffs.
  arXiv  Detail & Related papers  (2025-11-13T07:26:01Z)
• Statistical Inference for Conditional Group Distributionally Robust Optimization with Cross-Entropy Loss [9.054486124506521]
  We study multi-source unsupervised domain adaptation, where labeled data are drawn from multiple source domains and only unlabeled data from a target domain.<n>We propose a novel Conditional Conditional Optimization (CG-DRO) framework that learns a classifier by minimizing the worst-case cross-entropy loss over the convex combinations of the conditional outcome distributions from the sources.<n>We establish fast statistical convergence rates for the estimator by constructing two surrogate minimax optimization problems that serve as theoretical bridges.
  arXiv  Detail & Related papers  (2025-07-14T04:21:23Z)
• Reward Model Generalization for Compute-Aware Test-Time Reasoning [21.05692631562457]
  External test-time reasoning enhances large language models (LLMs) by decoupling generation and selection.<n>A central challenge in this setting is test-time compute optimality (TCO), i.e., how to maximize answer accuracy under a fixed inference budget.<n>We analyze how the generalization error of the PRM affects compute efficiency and reasoning performance.<n>Motivated by this analysis, we propose Compute-Aware Tree Search (CATS), an actor-critic framework that dynamically controls search behavior.
  arXiv  Detail & Related papers  (2025-05-23T16:12:12Z)
• ConCISE: Confidence-guided Compression in Step-by-step Efficient Reasoning [64.93140713419561]
  Large Reasoning Models (LRMs) perform strongly in complex reasoning tasks via Chain-of-Thought (CoT) prompting, but often suffer from verbose outputs.<n>Existing fine-tuning-based compression methods either operate post-hoc pruning, risking disruption to reasoning coherence, or rely on sampling-based selection.<n>We introduce ConCISE, a framework designed to generate concise reasoning chains, integrating Confidence Injection to boost reasoning confidence, and Early Stopping to terminate reasoning when confidence is sufficient.
  arXiv  Detail & Related papers  (2025-05-08T01:40:40Z)
• Bridging Internal Probability and Self-Consistency for Effective and Efficient LLM Reasoning [53.25336975467293]
  We present the first theoretical error decomposition analysis of methods such as perplexity and self-consistency.<n>Our analysis reveals a fundamental trade-off: perplexity methods suffer from substantial model error due to the absence of a proper consistency function.<n>We propose Reasoning-Pruning Perplexity Consistency (RPC), which integrates perplexity with self-consistency, and Reasoning Pruning, which eliminates low-probability reasoning paths.
  arXiv  Detail & Related papers  (2025-02-01T18:09:49Z)
• MANO: Exploiting Matrix Norm for Unsupervised Accuracy Estimation Under Distribution Shifts [25.643876327918544]
  Leveraging the models' outputs, specifically the logits, is a common approach to estimating the test accuracy of a pre-trained neural network on out-of-distribution samples. Despite their ease of implementation and computational efficiency, current logit-based methods are vulnerable to overconfidence issues, leading to prediction bias. We propose MaNo which applies a data-dependent normalization on the logits to reduce prediction bias and takes the $L_p$ norm of the matrix of normalized logits as the estimation score.
  arXiv  Detail & Related papers  (2024-05-29T10:45:06Z)
• 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)
• False Correlation Reduction for Offline Reinforcement Learning [115.11954432080749]
  We propose falSe COrrelation REduction (SCORE) for offline RL, a practically effective and theoretically provable algorithm. We empirically show that SCORE achieves the SoTA performance with 3.1x acceleration on various tasks in a standard benchmark (D4RL)
  arXiv  Detail & Related papers  (2021-10-24T15:34:03Z)

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.