Scaling Prompt Synthesis for Large Language Model Reasoning

Large language models (LLMs) are evolving from conversational systems into strong reasoners for tasks such as Olympiad mathematics and competitive programming. While scaling parameters and test-time computation has driven progress, a key bottleneck is the lack of high-quality training problems: human-curated datasets are costly and limited, while existing synthetic corpora are often too easy or narrow. PromptCoT showed that injecting rationales into prompt synthesis increases problem difficulty. Building on this, we present PromptScale, a scalable framework that replaces hand-crafted heuristics with an expectation-maximization (EM) loop, where rationales are iteratively refined to guide prompt construction. This produces problems that are both harder and more diverse than prior corpora. The synthetic prompts support two post-training regimes: (1) \emph{Self-Play}, where strong models improve autonomously via verifiable feedback without stronger teachers; and (2) \emph{Supervised Fine-Tuning (SFT)}, where weaker models learn from teacher-distilled traces. Extensive experiments demonstrate the effectiveness of this approach. In self-play, applying PromptScale to \texttt{Qwen3-30B-A3B-Thinking-2507} sets new state-of-the-art results \emph{at the 30B scale}, with +4.4, +4.8, and +5.3 on AIME 24/25 and HMMT 25, +6.1 and +5.0 on LiveCodeBench v5/v6, and +35 Elo on Codeforces. In SFT, training \texttt{Qwen2.5-7B-Instruct} solely on synthetic prompts boosts accuracy to 73.1 (AIME 24), 65.6 (AIME 25), and 53.4 (LiveCodeBench v5), surpassing models trained on human or hybrid data. Analyses further confirm that PromptScale yields fundamentally harder and distributionally distinct problems. These results establish prompt synthesis as a new axis for scaling reasoning and position PromptScale as a scalable foundation for future open-source models.