Revisiting Chain-of-Thought Reasoning under Limited Supervision: Semi-supervised Chain-of-Thought Learning

2026-07-01

AI Summary

This work addresses the challenge of enhancing large language models’ reasoning capabilities in settings with scarce supervision by leveraging unlabeled questions. The authors propose Semi-CoT, a novel framework that extends chain-of-thought (CoT) reasoning from an inference-time prompting strategy to a semi-supervised learning signal. Specifically, the model generates multiple pseudo-reasoning chains for unlabeled questions and employs answer semantic entropy to automatically select high-confidence samples for self-training. Evaluated on AQuA, SVAMP, GSM8K, and MultiArith benchmarks, the approach achieves pseudo-answer accuracy ranging from 91.36% to 100% and yields consistent, albeit modest, performance gains on several tasks, thereby demonstrating the efficacy of semantic entropy–guided semi-supervised CoT learning.

Abstract

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent reasoning capabilities in large language models. However, most existing CoT methods use reasoning chains mainly as inference-time prompts, while the generated reasoning traces are rarely reused as semi-supervised learning signals. In this report, we define \textbf{Semi-supervised Chain-of-Thought Learning} and propose \textbf{Semi-CoT}, a simple framework that uses unlabeled questions to construct pseudo reasoning supervision. Semi-CoT samples multiple pseudo-CoTs for each unlabeled question, estimates answer-level semantic entropy, and selects low-entropy reasoning chains as reliable pseudo-CoT demonstrations. This extends the self-training view of CoT from inference-time refinement to semi-supervised pseudo-supervision. Pilot experiments on AQuA, SVAMP, GSM8K, and MultiArith show that the entropy gate selects high-precision pseudo-CoTs, with pseudo-answer precision ranging from $91.36\%$ to $100\%$. Semi-CoT also gives small gains on SVAMP and GSM8K, while AQuA shows negative transfer and MultiArith reaches a ceiling. These results suggest that unlabeled questions can provide reliable pseudo reasoning signals, but their effective use still requires stronger demonstration selection or student training.

Problem

• Chain-of-Thought
• Semi-supervised Learning
• Reasoning
• Pseudo-labeling
• Large Language Models

Innovation

• Semi-supervised Learning
• Chain-of-Thought Reasoning
• Pseudo-labeling
• Semantic Entropy
• Self-training