Prompting Test-Time Scaling Is A Strong LLM Reasoning Data Augmentation

Large language models (LLMs) exhibit strong reasoning when guided by chain-of-thought exemplars, yet collecting large, high-quality reasoning datasets remains laborious and resource-intensive. We introduce Prompting Test-Time Scaling (P-TTS), a prompt-space data augmentation framework for enhancing LLM reasoning via fine-tuning. In P-TTS, scaling refers to systematic expansion of the prompt space during offline teacher-data generation, not to increased inference-time compute for the deployed student. Rather than collecting thousands of examples, P-TTS starts from a small pool of 90 manually selected reasoning instances and applies principled instruction templates and paraphrased prompt variants to elicit diverse reasoning trajectories from a teacher model, producing a compact synthetic training set. We fine-tune Qwen-2.5 models of multiple sizes on the resulting data. On reasoning benchmarks including AIME25, MATH500, and GPQA-Diamond, P-TTS consistently improves accuracy over competitive small-data baselines such as S1 and S1.1 (1Kshot), with the largest gains on AIME25 while remaining strong on MATH500 and GPQA-Diamond. P-TTS also improves generalization on out-of-domain reasoning evaluations. Ablations show that exemplar diversity and promptspace scaling are critical drivers of improvement, suggesting that prompt scaling explores the latent space of reasoning patterns, amplifying LLM problem-solving with minimal annotation overhead. P-TTS offers a practical, low-cost way to elicit strong LLM reasoning in resource-constrained or rapidly evolving domains. Our code and data are available at https://github.com/VILA-Lab/PTTS.