Learning to Reason with Curriculum II: Compositional Generalization

• URL: http://arxiv.org/abs/2606.27721v1
• Date: Fri, 26 Jun 2026 05:09:08 GMT
• Title: Learning to Reason with Curriculum II: Compositional Generalization
• Abstract summary: We show that an autocurriculum-based approach building on Part I of this series achieves better statistical complexity than direct methods.<n>For a setting inspired by supervised fine-tuning (SFT), curriculum facilitates learning from only $2mathcalO(sqrtlog T)$ tokens of supervision.<n>For a setting inspired by reinforcement learning with verifiable rewards (RLVR), we show that curriculum reduces the requirement on the reference model from coverage at the full sequence length $T$ to coverage at a shorter block length $B ll T$.
• Score: 27.242998212645784
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Compositional generalization, the ability to solve complex problems by combining solutions to simpler sub-problems, is a fundamental capability of both natural and artificial intelligence, and a key mechanism underlying chain-of-thought reasoning. However, the theoretical underpinnings of compositional generalization remain poorly understood: when and why does decomposing a problem into parts yield more efficient learning than solving it directly? We study this question through the canonical problem of learning to simulate semiautomata (predicting the outcome of $T$ steps of sequential computation), a model that captures state tracking, regular language recognition, and modular arithmetic. We show that an autocurriculum-based approach building on Part I of this series, recursively decomposing longer sequences into shorter sub-problems, learning to solve them, and composing the solutions, achieves dramatically better statistical complexity than direct methods. (i) For a setting inspired by supervised fine-tuning (SFT) where the learner receives interactive feedback on intermediate states of the computation, curriculum facilitates learning from only $2^{\mathcal{O}(\sqrt{\log T})}$ tokens of supervision; i.e., subpolynomial in the sequence length $T$, overcoming the $Ω(T)$ token barrier required by direct simulation. (ii) For a setting inspired by reinforcement learning with verifiable rewards (RLVR), where the learner improves a pre-trained reference model using an outcome verifier, we show that curriculum reduces the requirement on the reference model from coverage at the full sequence length $T$ to coverage at a shorter block length $B \ll T$, an exponentially weaker condition.

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