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From f(x) and g(x) to f(g(x)): LLMs Learn New Skills in RL by Composing Old Ones

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When an LLM has already learned f and g prior to RL, our experiments reveal that RL enables it to learn unseen compositions of them h(x)=g(f(x)). ... In contrast, next-token training with the same data yields none of these findings.

Outcome-reward reinforcement learning enables language models to compose learned atomic skills into new skills beyond next-token training on the same data.Supported

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Further, this compositional ability generalizes to more difficult problems such as compositions of >2 functions unseen during RL training. ... In contrast, next-token training with the same data yields none of these findings.

In synthetic tasks with learned atomic skills, outcome-reward RL, but not rejection fine-tuning, generalizes to deeper unseen compositions.Supported

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From f(x) and g(x) to f(g(x)): LLMs Learn New Skills in RL by Composing Old Ones

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Link: https://arxiv.org/abs/2509.25123
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