How can Large Language Models (LLMs) solve problems they currently cannot? Repeated sampling scales test-time compute but GPU cost grows linearly with attempts, while reinforcement learning (RL) with verifiable rewards improves single-attempt accuracy at the expense of sample diversity. Both strategies ultimately fail when the base policy has near-zero probability of producing a correct solution: no amount of sampling or gradient signal can overcome a search space that is simply too large. We take a different approach: rather than sampling harder, we make the task easier by decomposing problems into smaller, independently solvable sub-functions whose implementations can be recombined. Since off-the-shelf models are not trained for this modular generation, we introduce DecompRL, an RL algorithm that explicitly learns to decompose and implement hierarchical code structures. Recombining k implementations of n modules yields up to kn candidate solutions, shifting the bottleneck from GPU inference to cheap CPU evaluation and cutting GPU token cost by ∼50×. On LiveCodeBench and CodeContests (Qwen2.57B, Code World Model~32B), DecompRL outperforms standard and diversity-optimized RL baselines beyond 105 tokens per problem, solving problems that standard generation cannot reach.
Large language models increasingly tackle hard reasoning problems by spending more test-time compute, yet the dominant strategy remains naive repeated sampling: draw many independent solutions and hope one is correct. Because such sampling explores only through local decoding noise, it tends to produce many near duplicate attempts rather than genuinely different ideas. We ask whether exploration can instead be steered at a semantic level, by first sampling problem specific concepts, hints, or strategies and then conditioning answer generation on them. We refine this into a simple, more exploratory procedure that emits many diverse concepts in a single trajectory, and evaluate it on hard problems where repeated sampling struggles. We then go a step further and make concept generation trainable: a small concept generator is optimized with reinforcement learning so that its concepts maximize the downstream success of a larger, frozen answer generator. On hard mathematical reasoning problems, the trained concept generator substantially improves the answer generator's pass@k over naive repeated sampling at the same answer generation allocation, surpasses concepts drawn from much larger untuned models, and transfers to answer generators it was never trained against, including a model from a different family. A small model can thus be trained into an effective, reusable search policy for a much larger one.
Ismail Labiad, Matthieu Kowalski, Marc Schoenauer +2
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.
LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of thought. The typical approach to code generation is to prompt the model and generate samples until an appropriate program is obtained. Within this process, sampling n programs from the language model requires n GPU compute-intensive generations which becomes prohibitively expensive for larger values of n. In this work, we address this limitation by exposing the LLM's distribution within the generated programs themselves. We propose a novel test-time framework we dub probabilistic programs of thought to obtain more samples from the model with fewer LLM generations. Given a program generated by a model and the associated next-token probabilities, we build a probabilistic program that compactly represents exponentially many deterministic programs. Since performing probabilistic reasoning in this probabilistic program is much cheaper, our approach allows sampling new programs without any additional GPU compute and little CPU overhead. We instantiate our approach on benchmarks for code generation, code understanding and mathematical reasoning and report improvements in performance with fewer generations from the LLM.