Revisiting Chain-of-Thought Reasoning under Limited Supervision: Semi-supervised Chain-of-Thought Learning
06:00 · July 3, 2026 · arXiv cs.AI RSS
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.
Summary
Chain-of-thought prompting elicits step-by-step reasoning from large language models, yet most prior work has confined the generated traces to inference-time prompts. Semi-CoT reframes these traces as sources of semi-supervised supervision. The method takes unlabeled questions, samples multiple candidate reasoning chains for each, and computes answer-level semantic entropy across the resulting answer distributions. Low-entropy chains are retained as pseudo-demonstrations because their final answers show high internal consistency.
This selection step produces pseudo-answers whose precision ranges from 91.36 % to 100 % across the evaluated math-reasoning collections. When the filtered chains are used to augment training, the resulting models record modest accuracy gains on SVAMP and GSM8K. On AQuA the same procedure yields negative transfer, while MultiArith already reaches a performance ceiling, leaving little room for further improvement.
The findings indicate that unlabeled questions can supply reliable pseudo-reasoning signals, yet consistent downstream benefits still depend on stronger mechanisms for demonstration selection or student-model updates.
Why it matters
This paper is highly relevant for AI researchers and NLP practitioners in the Netherlands focusing on LLM optimization and reasoning. It offers a novel semi-supervised approach to Chain-of-Thought prompting, which can help Dutch AI teams improve model performance with limited labeled data.
