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Learning to Think from Multiple Thinkers
arXiv:2604.24737v1 Announce Type: cross Abstract: We study learning with Chain-of-Thought (CoT) supervision from multiple thinkers, all of whom provide correct but possibly systematically different so
arXiv:2604.24737v1 Announce Type: cross 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 arepsilon, a moderate number of thinkers that scales as log frac{1}{arepsilon}log log frac{1}{arepsilon}, and sufficient passive end-result data that scales as frac{1}{arepsilon}dot polylogfrac{1}{arepsilon}.
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Source: arXiv cs.AI | 2026-04-28