[2604.24737] Learning to Think from Multiple Thinkers

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 $\frac{1}{\varepsilon}\cdot poly\log\frac{1}{\varepsilon}$.

Learning to Think from Multiple Thinkers Nirmit Joshi1 , Roey Magen2 , Nathan Srebro1 , Nikolaos Tsilivis3 , Gal Vardi2 1 Toyota Technological Institute at Chicago. {nirmit,nsrebro}@ttic.edu 2 Weizmann Institute of Science. {roey.magen,gal.vardi}@weizmann.ac.il…

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• Didier Lampard

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