PromptCoT: Synthesizing Olympiad-Level Problems for Mathematical Reasoning in Large Language Models

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Highlights

✨ The Missing Piece for Test-Time Scaling

A lightweight yet powerful problem generation model that enables the construction of prompt sets at any scale with sufficient quality—perfect for initializing your post-training project, whether it's Supervised Fine-Tuning (SFT) or Reinforcement Learning (RL). Say goodbye to the limitations of open-source data!

📖 A Fully Open Project

• 📂 Open-Source Problem Generation Model
  • Model: Hugging Face | ModelScope
  • Training Data: Hugging Face | ModelScope
• 🔹 Open-Source Distilled Models for Mathematical Reasoning
  • PromptCoT-DS-1.5B (Distilled from DeepSeek-R1-Distill-Qwen-7B, 1.5B parameters)
    Hugging Face | ModelScope
  • PromptCoT-DS-7B (Distilled from DeepSeek-R1-Distill-Qwen-7B, 7B parameters)
    Hugging Face | ModelScope
  • [New] 🚀🚀🚀 PromptCoT-QwQ-32B (Distilled from QwQ-32B, 32B parameters) Hugging Face | ModelScope
  • Training Data for Supervised Fine-Tuning (SFT) of PromptCoT-DS Series Models
    Hugging Face | ModelScope
  • [New] 🚀🚀🚀 Training Data for Supervised Fine-Tuning (SFT) of PromptCoT-QwQ-32B
    Hugging Face | ModelScope

🏆 Superior Performance

• Consistent Improvements over Deepseek Counterparts PromptCoT-DS-7B surpasses DeepSeek-R1-Distill-Qwen-7B across all major benchmarks, achieving consistent improvements in problem-solving accuracy. The results, averaged over 8 random seeds, highlight the following gains:

  • +0.9% absolute improvement on MATH-500 (93.7% vs. 92.8%)
  • +3.2% absolute improvement on AIME2024 (58.7% vs. 55.5%)
  • +9.2% absolute improvement on AIME2025 (49.2% vs. 40.0%)

• Competitive with 32B Models
  Despite having only 7B parameters, PromptCoT-DS-7B achieves results comparable to larger 32B models such as S1-32B and LIMO-32B.

Performance Comparison of Different Models

Model	GSM8K	MATH-500	AIME2024	AIME2025
🔹 1.5B Models
DeepSeek-R1-Distill-Qwen-1.5B	-	83.9%	28.9%	28.1%
STILL-3-1.5B-preview	-	85.5%	39.3%	-
DeepScaleR-1.5B-Preview	-	🟢 87.8%	🟢 43.1%	🟢 37.1%
PromptCoT-DS-1.5B (ours)	🟢 87.6% ± 0.5%	85.3% ± 1.1%	41.2% ± 6.9%	36.7% ± 6.2%
🔹 7B Models
DeepSeek-R1-Distill-Qwen-7B	-	92.8%	55.5%	40.0%
Qwen2.5-7B-SimpleRL	-	82.4%	26.7%	-
OpenThinker-7B	-	89.6%	30.0%	33.3%
OpenR1-Qwen-7B	-	90.6%	36.7%	40.0%
PromptCoT-DS-7B (ours)	🔥 92.8% ± 0.5%	🔥 93.7% ± 0.7%	🔥 58.7% ± 3.1%	🔥 49.2% ± 7.9%
🔹 32B Models
DeepSeek-R1-Distill-Qwen-32B	-	94.3%	72.6%	-
S1-32B	-	93.0%	56.7%	26.6%
LIMO-32B	-	94.8%	57.1%	46.6%
QwQ-32B	-	-	82.1%	70.8%
PromptCoT-QwQ-32B (ours)	🔥🔥 96.4% ± 0.2%	🔥🔥 96.7% ± 0.5%	🔥🔥 83.8% ± 2.8%	🔥🔥 75.4% ± 4.7%

• Challenging RL-Based Methods Without RL
  Despite relying purely on distillation, PromptCoT-DS-1.5B achieves competitive results against RL-based models like STILL-3-1.5B-preview and DeepScaleR-1.5B-Preview, highlighting the strength of our problem generation pipeline.

⚡ Efficiency Without Compromise

Compared to DeepScaleR-1.5B-Preview, PromptCoT-DS-1.5B achieves 40+% AIME scores while using over 15× fewer A100 GPU hours (240 A100 hours vs. 3,800 A100 hours). This makes PromptCoT-DS-1.5B a highly efficient and cost-effective solution for mathematical reasoning.

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Overview

Large language models (LLMs) have demonstrated remarkable advancements in mathematical reasoning. However, acquiring challenging and high-quality Olympiad-level problems at scale remains a significant challenge. Existing datasets often lack the necessary complexity to further enhance the capabilities of state-of-the-art models.

PromptCoT introduces a method to systematically generate high-quality Olympiad-level math problems by modeling the rationale behind expert problem design. This approach improves problem diversity and difficulty while ensuring logically consistent problem construction.

📄 Paper: 🔗 PromptCoT: Synthesizing Olympiad-Level Problems for Mathematical Reasoning in Large Language Models.

Key Features

• Concept-Guided Problem Synthesis: PromptCoT generates problems by systematically combining mathematical concepts, allowing for a scalable and flexible way to create a diverse range of challenging problems.

• Rationale-Driven Problem Formulation: Instead of directly generating problems, PromptCoT first constructs an intermediate reasoning process (rationale)—a step-by-step thought process that mimics how expert problem designers craft questions. This rationale helps bridge the gap between abstract mathematical concepts and well-formed problems, ensuring logical consistency and problem difficulty.

• Rejection Sampling for Quality Control: Problems undergo an automated evaluation process where multiple reward models assess their quality. Only problems receiving the highest scores are retained, ensuring the final dataset consists of challenging and high-quality mathematical problems.

• Scalability & Adaptability: The method allows for large-scale problem generation across a wide range of mathematical domains. Additionally, the rationale-driven approach can be adapted to other structured reasoning tasks beyond mathematics.

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Quick Start: Generating Olympiad-Level Problems

Follow these steps to generate problems using PromptCoT.

1. Install Dependencies

pip install sentence_transformers==3.2.1 scikit-learn==1.3.2 scipy==1.10.1 faiss-gpu==1.7.2 vllm==0.6.3 transformers==4.46.3 fire==0.7.0
pip install str2bool

2. Generating Problems

Step 1: Generate Concept Embeddings

We first encode mathematical concepts into embeddings to enable efficient sampling:

python concept_encoding.py \
  --data_path data/mathematics_concepts.jsonl \
  --output_path data/embeddings.jsonl \
  --model_path /path/to/Llama-3.1-8B \
  --n_gpus 4

Step 2: Sample Concept Combinations

We then sample meaningful concept combinations for problem generation:

python concept_sampling.py \
  --data_path data/mathematics_concepts.jsonl \
  --output_path data/problem_generation_inputs.jsonl \
  --data_size 1000 \
  --embed_path data/embeddings.jsonl

Step 3: Generate Math Problems

Using the pre-trained problem generation model – available on Hugging Face | ModelScope – we generate Olympiad-level math problems:

python problem_generation.py \
  --data_path data/problem_generation_inputs.jsonl \
  --output_path data/problem_generation_outputs.jsonl \
  --model_path /path/to/problem_generation_model \
  --n_gpus 4 \
  --temperature 0.6 \
  --max_len 4096 \
  --seed 8000

Step 4: Reward-Based Filtering

To ensure high-quality problem selection, we compute reward scores using two evaluation models:

python rejection_sampling_reward.py \
  --data_path data/problem_generation_outputs.jsonl \
  --output_path data/problem_generation_outputs_reward0.jsonl \
  --model_path /path/to/Llama-3.1-70B-Instruct \
  --n_gpus 4 \
  --temperature 0.6 \
  --use_chat_template True \
  --seed 8000

python rejection_sampling_reward.py \
  --data_path data/problem_generation_outputs.jsonl \
  --output_path data/problem_generation_outputs_reward1.jsonl \
  --model_path /path/to/Qwen2.5-72B-Instruct \
  --n_gpus 4 \
  --temperature 0.6 \
  --use_chat_template True \
  --seed 8000

Step 5: Select High-Quality Problems

To ensure only the highest-quality problems are used for training, we apply a filtering process based on reward scores. Problems that receive perfect ratings from multiple evaluators are retained.

python problem_filtering.py \
  --template data/problem_generation_outputs_reward{}.jsonl \
  --output_path data/problem_generation_training.jsonl \
  --only_perfect True \
  --n_rewards 2

📌 Our curated dataset of high-quality problems (where each problem received perfect ratings across all evaluation criteria) is available here: Hugging Face | ModelScope

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Distillation

After generating high-quality problems, we distill the knowledge into smaller models using Deepseek-R1-Distill-Qwen-7B as the teacher model. We train:

• PromptCoT-DS-1.5B (Student: Deepseek-R1-Distill-Qwen-1.5B)
• PromptCoT-DS-7B (Student: Deepseek-R1-Distill-Qwen-7B)

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Reproducing Our Results

To reproduce the results, follow these steps.

Step 1: Install Dependencies

conda create -n promptcot python=3.10.14
conda activate promptcot
pip install -r requirements.txt --ignore-installed --no-deps

Step 2: Run Inference on Benchmark Datasets

To run inference for the PromptCoT-DS series models, use the following command:

python infer_longcot.py \
  --data_path data/{dataset_name}.jsonl \
  --output_path data/{dataset_name}_predictions.jsonl \
  --model_path /path/to/{model_name} \
  --tokenizer_path /path/to/Deepseek-R1-Distill-Qwen-1.5B \
  --n_gpus 1 \
  --temperature 0.6 \
  --max_len 32768
  --n 8

where {dataset_name} can be:

• gsm8k
• math500
• aime2024
• aime2025

and {model_name} can be:

• PromptCoT-DS-1.5B
• PromptCoT-DS-7B

To run inference for PromptCoT-QwQ-32B, use the following command:

python infer_longcot.py \
  --data_path data/qwq/qwq_{dataset_name}_test.jsonl \
  --output_path data/qwq/qwq_{dataset_name}_predictions.jsonl \
  --model_path /path/to/PromptCoT-QwQ-32B \
  --tokenizer_path /path/to/QwQ-32B \
  --n_gpus 2 \
  --temperature 0.6 \
  --max_len 16384
  --n 8

where {dataset_name} can be:

• gsm8k
• math500
• aime2024
• aime2025

Step 3: Compute Accuracy

python calc_acc.py \
  --output_path data/{dataset_name}_predictions.jsonl

[New] Step 4: Train with DeepSpeed

You can reproduce the training process for the model using DeepSpeed with the following commands. Make sure to replace the paths with your own data and model paths.

• For PromptCoT-DS-1.5B:

deepspeed --num_gpus=8 train.py --bf16=True --data_path=/path/to/PromptCoT-DS-Dataset --ddp_find_unused_parameters=False --deepspeed=configs/promptcot_ds_1_5b_config.json --evaluation_strategy=no --fp16=False --gradient_accumulation_steps=8 --gradient_checkpointing=True --learning_rate=5e-06 --load_best_model_at_end=False --logging_steps=1 --model_max_length=16384 --model_name_or_path=/path/to/DeepSeek-R1-Distill-Qwen-1.5B --num_train_epochs=2 --output_dir=/path/to/PromptCoT-DS-1.5B --per_device_train_batch_size=1 --resume_from_checkpoint=False --save_steps=500 --save_strategy=steps --save_total_limit=6 --tokenizer_path=/path/to/DeepSeek-R1-Distill-Qwen-1.5B --warmup_steps=100 --weight_decay=0.01

• For PromptCoT-DS-7B:

deepspeed --num_gpus=8 train.py --bf16=True --data_path=/path/to/PromptCoT-DS-Dataset --ddp_find_unused_parameters=False --deepspeed=configs/promptcot_ds_7b_config.json --evaluation_strategy=no --fp16=False --gradient_accumulation_steps=8 --gradient_checkpointing=True --learning_rate=5e-06 --load_best_model_at_end=False --logging_steps=1 --model_max_length=16384 --model_name_or_path=/path/to/DeepSeek-R1-Distill-Qwen-7B --num_train_epochs=2 --output_dir=/path/to/PromptCoT-DS-7B --per_device_train_batch_size=1 --resume_from_checkpoint=False --save_steps=500 --save_strategy=steps --save_total_limit=6 --tokenizer_path=/path/to/DeepSeek-R1-Distill-Qwen-7B --warmup_steps=100 --weight_decay=0.01

• For PromptCoT-QwQ-32B:

deepspeed --num_gpus=8 train.py --bf16=True --data_path=/path/to/PromptCoT-QwQ-Dataset --ddp_find_unused_parameters=False --deepspeed=configs/promptcot_qwq_32b_config.json --evaluation_strategy=no --fp16=False --gradient_accumulation_steps=2 --gradient_checkpointing=True --learning_rate=2e-06 --load_best_model_at_end=False --logging_steps=1 --model_max_length=16384 --model_name_or_path=/path/to/QwQ-32B --num_train_epochs=2 --output_dir=/path/to/PromptCoT-QwQ-32B --per_device_train_batch_size=1 --resume_from_checkpoint=False --save_steps=500 --save_strategy=steps --save_total_limit=6 --tokenizer_path=/path/to/QwQ-32B --warmup_steps=100 --weight_decay=0.01

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Citation

If you find PromptCoT useful, please consider citing:

@article{zhao2025promptcot,
  author    = {Zhao, Xueliang and Wu, Wei and Guan, Jian and Kong, Lingpeng},
  title     = {PromptCoT: Synthesizing Olympiad-Level Problems for Mathematical Reasoning in Large Language Models},
  year      = {2025},
  journal   = {arXiv preprint arXiv:2503.02324},
  url       = {http://arxiv.org/abs/2503.02324}
}