{"type":"rich","version":"1.0","provider_name":"Transistor","provider_url":"https://transistor.fm","author_name":"Daily Paper Cast","title":"A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning","html":"","width":"100%","height":180,"duration":1207,"description":"\n 🤗 Upvotes: 112 | cs.LG, cs.AI\n\n Authors:\n Zhi Zhou, Yuhao Tan, Zenan Li, Yuan Yao, Lan-Zhe Guo, Yu-Feng Li, Xiaoxing Ma\n\n Title:\n A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning\n\n Arxiv:\n http://arxiv.org/abs/2510.15444v1\n\n Abstract:\n 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...","thumbnail_url":"https://img.transistorcdn.com/8lOVNnuwhrA3rxrDMv7Osu4j_t1-jORooO6NfGcQhcw/rs:fill:0:0:1/w:400/h:400/q:60/mb:500000/aHR0cHM6Ly9pbWct/dXBsb2FkLXByb2R1/Y3Rpb24udHJhbnNp/c3Rvci5mbS81Zjg1/YzRhODczMDU4MmE4/OGMwN2FiNDlmYzI2/MDliMi5qcGVn.webp","thumbnail_width":300,"thumbnail_height":300}