# PromptCoT 2.0: Scaling Prompt Synthesis for Large Language Model Reasoning

arXiv: https://arxiv.org/abs/2509.19894 · HTML: https://mlsanity.com/paper/2509.19894/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 32)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [SWE-smith: Scaling Data for Software Engineering Agents](https://mlsanity.com/paper/2504.21798/) (2025)
- [Magicoder: Empowering Code Generation with OSS-Instruct](https://mlsanity.com/paper/2312.02120/) (2023)
- [WebSailor: Navigating Super-human Reasoning for Web Agent](https://mlsanity.com/paper/2507.02592/) (2025)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [Nemotron-4 340B Technical Report](https://mlsanity.com/paper/2406.11704/) (2024)
- [OpenCoder: The Open Cookbook for Top-Tier Code Large Language Models](https://mlsanity.com/paper/2411.04905/) (2024)
- [KodCode: A Diverse, Challenging, and Verifiable Synthetic Dataset for Coding](https://mlsanity.com/paper/2503.02951/) (2025)
- [CodeElo: Benchmarking Competition-level Code Generation of LLMs with Human-comparable Elo Ratings](https://mlsanity.com/paper/2501.01257/) (2025)
- [OpenCodeReasoning: Advancing Data Distillation for Competitive Coding](https://mlsanity.com/paper/2504.01943/) (2025)
- [WebExplorer: Explore and Evolve for Training Long-Horizon Web Agents](https://mlsanity.com/paper/2509.06501/) (2025)
- [PromptCoT: Synthesizing Olympiad-level Problems for Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2503.02324/) (2025)

## Built on by (most cited first, 9 of 9)

- [Agentic Proposing: Enhancing Large Language Model Reasoning via Compositional Skill Synthesis](https://mlsanity.com/paper/2602.03279/) (2026)
- [DreamReasoner-8B: Block-Size Curriculum Learning for Diffusion Reasoning Models](https://mlsanity.com/paper/2606.19257/) (2026)
- [DynaAct: Large Language Model Reasoning with Dynamic Action Spaces](https://mlsanity.com/paper/2511.08043/) (2025)
- [Ouroboros-Spatial: Closing the Data-Model Loop for Spatial Reasoning](https://mlsanity.com/paper/2606.11719/) (2026)
- [CoDiQ: Test-Time Scaling for Controllable Difficult Question Generation](https://mlsanity.com/paper/2602.01660/) (2026)
- [KT4EQG: Personalized Exercise Question Generation via Knowledge Tracing](https://mlsanity.com/paper/2605.23933/) (2026)
- [Lightning Weave: Improving the Accuracy-Efficiency Frontier of Reasoning Models through Capability Composition](https://mlsanity.com/paper/2609.14708/) (2026)
- [ImproveAnyTask: An Autonomous Post-Training Harness for Iterative Model Self-Improvement](https://mlsanity.com/paper/2610.06347/) (2026)
- [SAGE: Semantic Anchor-Guided Evolution for Grounded Medical QA Data Synthesis](https://mlsanity.com/paper/2610.08093/) (2026)

## Abstract (arXiv)

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 1.0 showed that injecting rationales into prompt synthesis increases problem difficulty. Building on this, we present PromptCoT 2.0, 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) Self-Play, where strong models improve autonomously via verifiable feedback without stronger teachers; and (2) Supervised Fine-Tuning (SFT), where weaker models learn from teacher-distilled traces. Extensive experiments demonstrate the effectiveness of this approach. In self-play, applying PromptCoT 2.0 to Qwen3-30B-A3B-Thinking-2507 sets new state-of-the-art results 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 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 PromptCoT 2.0 yields fundamentally harder and distributionally distinct problems. These results establish prompt synthesis as a new axis for scaling reasoning and position PromptCoT 2.0 as a scalable foundation for future open-source models. The implementation is available at https://github.com/inclusionAI/PromptCoT.