Combinatorial Synthesis: Scaling Code RLVR via Atomic Decomposition and Recombination

Hugging Face Daily Papers Papers
reinforcement-learning code-synthesis llm verifiable-rewards scalability

Summary

Introduces Atomic Decomposition and Recombination (ADR), a framework that generates novel and challenging verifiable code tasks by decomposing and recombining atomic elements, enabling scalable reinforcement learning with verifiable rewards for large language models.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as the cornerstone for shaping the remarkable coding abilities of Large Language Models (LLMs). However, the scalability of RLVR is severely constrained by the scarcity of sufficiently challenging verifiable code tasks that target near the model's edge of competence. Prior studies often rely on heuristic seed expansions for data synthesis, which severely limits both novelty and difficulty. Consequently, the training value of such data fails to scale proportionally with the size of its synthesis. To this end, we propose Atomic Decomposition and Recombination (ADR), a novel framework that generates verifiable code tasks via decomposition into atomic elements and controlled recombination, thereby enabling the generation of genuinely novel and challenging verifiable code tasks. Experiments and analysis demonstrate that ADR achieves superior originality, difficulty, diversity, and test quality over existing baselines, and consistently delivers greater improvements in code ability across RLVR in diverse downstream domains, including algorithmic programming, tool usage, and data science. Our work sheds light on a new paradigm for novel code task synthesis and scalable RLVR training.
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Paper page - Combinatorial Synthesis: Scaling Code RLVR via Atomic Decomposition and Recombination

Source: https://huggingface.co/papers/2605.31058

Abstract

Atomic Decomposition and Recombination (ADR) framework generates novel and challenging verifiable code tasks for scalable reinforcement learning with verifiable rewards in large language models.

Reinforcement Learning with Verifiable Rewards(RLVR) has recently emerged as the cornerstone for shaping the remarkable coding abilities ofLarge Language Models(LLMs). However, thescalabilityof RLVR is severely constrained by the scarcity of sufficiently challengingverifiable code tasksthat target near the model’s edge of competence. Prior studies often rely onheuristic seed expansions for data synthesis, which severely limits both novelty and difficulty. Consequently, the training value of such data fails to scale proportionally with the size of its synthesis. To this end, we proposeAtomic DecompositionandRecombination(ADR), a novel framework that generatesverifiable code tasksvia decomposition into atomic elements and controlledrecombination, thereby enabling the generation of genuinely novel and challengingverifiable code tasks. Experiments and analysis demonstrate that ADR achieves superior originality, difficulty, diversity, and test quality over existing baselines, and consistently delivers greater improvements in code ability across RLVR in diverse downstream domains, includingalgorithmic programming,tool usage, anddata science. Our work sheds light on a new paradigm for novelcode task synthesisand scalable RLVR training.

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