aiqbench analysis
This arXiv paper is squarely about AI: it studies how reinforcement learning post-training in large language models builds compositional skills, using the Countdown arithmetic task and expression-tree analysis. For AI and ML readers, the useful takeaways are the observed training-order effects (shallow balanced trees mastered before deep unbalanced ones), the persistent weakness on right-heavy structures, and the claim that pass@k alone can miss what RL actually teaches. The results are from a controlled toy setting, so the theorem-proving extension should be read as preliminary.
How Does RL Post-training Induce Skill Composition? A Case Study on Countdown
arXiv:2512.01775v2 Announce Type: replace Abstract: While reinforcement learning (RL) successfully enhances reasoning in large language models, its role in fostering compositional generalization (the ability to synthesize novel skills from known components) is often conflated with mere length generalization. To this end, we study what RL post-training teaches about skill composition and how the composition structure affects the skill transfer. We focus on the Countdown task (given n numbers and a target, form an expression that evaluates to the target) and analyze model solutions as expression trees, where each subtree corresponds to a reusable subtask and thus can be viewed as a "skill." Tracking tree shapes and their success rates over training, we find: (i) out-of-distribution (OOD) generalization to larger n and to unseen tree shapes, indicating compositional reuse of subtasks; (ii) the order of skill acquisition depends upon the composition structure---models master shallow balanced trees (workload is balanced between subtasks) before deep unbalanced ones, with persistent fragility on right-heavy structures for a fixed composition depth. Our diagnostic reveals what is learned, in what order, and where generalization fails, clarifying how RL-only post-training induces OOD generalization beyond what standard metrics such as pass@k reveal. To study the implications of our findings for real-world tasks, we present a preliminary study on formal theorem proving.
Title:How Does RL Post-training Induce Skill Composition? A Case Study on Countdown
Abstract:While reinforcement learning (RL) successfully enhances reasoning in large language models, its role in fostering compositional generalization (the ability to synthesize novel skills from known components) is often conflated with mere length generalization. To this end, we study what RL post-training teaches about skill composition and how the composition structure affects the skill transfer. We focus on the Countdown task (given n numbers and a target, form an expression that evaluates to the target) and analyze model solutions as expression trees, where each subtree corresponds to a reusable subtask and thus can be viewed as a "skill." Tracking tree shapes and their success rates over training, we find: (i) out-of-distribution (OOD) generalization to larger n and to unseen tree shapes, indicating compositional reuse of subtasks; (ii) the order of skill acquisition depends upon the composition structure---models master shallow balanced trees (workload is balanced between subtasks) before deep unbalanced ones, with persistent fragility on right-heavy structures for a fixed composition depth. Our diagnostic reveals what is learned, in what order, and where generalization fails, clarifying how RL-only post-training induces OOD generalization beyond what standard metrics such as pass@k reveal. To study the implications of our findings for real-world tasks, we present a preliminary study on formal theorem proving.
Machine Learning (cs.LG)
arXiv:2512.01775 [cs.LG]
(or arXiv:2512.01775v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2512.01775 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 311 words
