Scaling LLM Reasoning from Minimal Labels: A Semi-Supervised Framework with a Lightweight Verifier
2026-06-15 • Artificial Intelligence
Artificial IntelligenceComputation and Language
AI summaryⓘ
The authors developed a method to help language models learn how to reason better without needing tons of labeled examples. They train a small classifier to check if the model’s step-by-step reasoning makes sense and use only the most confident checks to improve the model further. Their approach works well on math and image-question tasks, reaching similar accuracy to methods that use much more labeled data. This shows it’s possible to improve reasoning with minimal human labeling by verifying reasoning steps instead of just answers.
Large Language ModelsReasoning VerificationSemi-Supervised LearningPseudo-LabelingEntropy ThresholdingVerifiable Math ProblemsQuestion AnsweringConfidence FilteringFine-TuningData Efficiency
Authors
Keizo Kato, Chenhui Chu, Yugo Murawaki, Sado Kurohashi
Abstract
For the development of Large language models (LLMs), recent approaches to generating pseudo intermediate reasoning have shown remarkable progress. But they typically rely on large numbers of correctly annotated answers to assess reasoning quality. This paper presents a semi-supervised framework that scales reasoning learning from minimal supervision, turning reasoning verification itself into a data creation mechanism. We train a lightweight reasoning-correctness classifier on only a few labeled samples, which judges whether intermediate reasoning traces generated by an LLM are valid. Furthermore, an entropy-based confidence threshold filters out unreliable samples, and the remaining high-confidence reasoning traces are used to fine-tune the model. Experiments on Verifiable Math Problems (Orca-Math subset) and Question Answering on Image Scene Graphs (GQA) with Visual Programming show that our method achieves accuracy comparable to using 10-15x more labeled data. Ablation analyses confirm that both the classifier and entropy filtering are essential for scalable and noise-resistant pseudo-labeling. By replacing expensive answer-level supervision with lightweight reasoning verification, our method provides a practical path toward constructing large-scale reasoning resources and paves the way for future autonomous reasoning systems that learn from minimal human input.