Semi-CoT Improves Chain-of-Thought Reasoning with Unlabeled Data

Chain-of-Thought (CoT) reasoning has proven effective in activating latent reasoning capabilities in large language models. However, most existing CoT methods primarily use reasoning chains as inference-time prompts, rarely leveraging generated traces as semi-supervised learning signals. A new framework, Semi-CoT, addresses this by defining Semi-supervised Chain-of-Thought Learning. It constructs pseudo reasoning supervision from unlabeled questions. The process involves sampling multiple pseudo-CoTs for each unlabeled question, estimating answer-level semantic entropy, and then selecting low-entropy reasoning chains as reliable pseudo-CoT demonstrations. This extends the self-training aspect of CoT from inference-time refinement to semi-supervised pseudo-supervision. Pilot experiments on datasets like SVAMP and GSM8K showed small gains, with pseudo-answer precision ranging from 91.36% to 100%. While AQuA showed negative transfer and MultiArith reached a ceiling, the results suggest that unlabeled questions can provide reliable pseudo reasoning signals, though effective utilization may require stronger demonstration selection or student training.