Learning to Think from Multiple Thinkers

2026-04-27

AI Summary

This work addresses the computational challenge of learning from multiple annotators who provide correct yet stylistically diverse chain-of-thought (CoT) rationales. The study is the first to formally characterize the computational complexity of this setting and introduces an efficient active learning algorithm that overcomes the limitations of passive learning. The proposed method requires only a fixed number of CoT examples per annotator, O(log(1/ε) log log(1/ε)) annotators, and Õ(1/ε) supervisory labels on final answers to achieve ε-accurate learning. Notably, its annotation efficiency is independent of the target accuracy ε, substantially enhancing the scalability of learning under heterogeneous CoT supervision.

Technology Category

• Machine Learning: Active Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Representation, semantic annotation, enhancement, enrichments, access and/or integration of a variety of data on the Web

Abstract

We study learning with Chain-of-Thought (CoT) supervision from multiple thinkers, all of whom provide correct but possibly systematically different solutions, e.g., step-by-step solutions to math problems written by different thinkers, or step-by-step execution traces of different programs solving the same problem. We consider classes that are computationally easy to learn using CoT supervision from a single thinker, but hard to learn with only end-result supervision, i.e., without CoT (Joshi et al. 2025). We establish that, under cryptographic assumptions, learning can be hard from CoT supervision provided by two or a few different thinkers, in passive data-collection settings. On the other hand, we provide a generic computationally efficient active learning algorithm that learns with a small amount of CoT data per thinker that is completely independent of the target accuracy $\varepsilon$, a moderate number of thinkers that scales as $\log \frac{1}{\varepsilon}\log \log \frac{1}{\varepsilon}$, and sufficient passive end-result data that scales as $\frac{1}{\varepsilon}\cdot poly\log\frac{1}{\varepsilon}$.

Problem

• Chain-of-Thought
• multi-thinker learning
• supervision
• computational learning
• active learning

Innovation

• Chain-of-Thought
• Multiple Thinkers
• Active Learning
• Computational Hardness
• Supervised Learning