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

arXiv: https://arxiv.org/abs/2607.01511 · HTML: https://mlsanity.com/paper/2607.01511/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 8 of its 46 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 8 of 8)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Evaluation of OpenAI o1: Opportunities and Challenges of AGI](https://mlsanity.com/paper/2409.18486/) (2024)
- [Concise Thoughts: Impact of Output Length on LLM Reasoning and Cost](https://mlsanity.com/paper/2407.19825/) (2024)
- [Contrastive Chain-of-Thought Prompting](https://mlsanity.com/paper/2311.09277/) (2023)
- [How Much Can RAG Help the Reasoning of LLM?](https://mlsanity.com/paper/2410.02338/) (2024)
- [Rethinking Chain-of-Thought from the Perspective of Self-Training](https://mlsanity.com/paper/2412.10827/) (2024)

## Built on by (most cited first, 4 of 4)

- [Recursive Self-Improvement in AI: From Bounded Self-Refinement to Autonomous Research Loops](https://mlsanity.com/paper/2607.07663/) (2026)
- [Triple Expert Learning from Noisy Labels for Semi-Supervised Vision Foundation Model Adaptation](https://mlsanity.com/paper/2608.09052/) (2026)
- [Geometric Regularization for Long-Tailed Semi-Supervised Learning via Gaussian Feature Bridges](https://mlsanity.com/paper/2608.20710/) (2026)
- [ReCalMatch:Reliability-Calibrated Semantic Guidance for Semi-Supervised Fine-Grained Recognition](https://mlsanity.com/paper/2609.29678/) (2026)

## Abstract (arXiv)

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 Semi-supervised Chain-of-Thought Learning and propose 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.