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Model: lm-provers/QED-Nano-SFT Source: Original Platform
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README.md
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---
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license: apache-2.0
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base_model: Qwen/Qwen3-4B-Thinking-2507
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tags:
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- math
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- reasoning
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- olympiad
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- proof-generation
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- sft
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- distillation
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library_name: transformers
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pipeline_tag: text-generation
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datasets:
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- lm-provers/FineProofs-SFT
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---
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# QED-Nano SFT
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## Table of Contents
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1. [Model Summary](#model-summary)
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2. [How to use](#how-to-use)
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3. [Evaluation](#evaluation)
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4. [Training](#training)
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5. [Limitations](#limitations)
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6. [License](#license)
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## Model Summary
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**QED-Nano SFT** is a 4B parameter mathematical reasoning model fine-tuned on olympiad-level proof problems. This is the supervised fine-tuning (SFT) checkpoint trained via knowledge distillation from [deepseek-ai/DeepSeek-Math-V2](https://huggingface.co/deepseek-ai/DeepSeek-Math-V2) (685B parameters). The model generates mathematical proofs with explicit chain-of-thought reasoning enclosed in `<think>` tags.
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This model serves as the foundation for the full QED-Nano pipeline, which includes subsequent reinforcement learning and reasoning cache extensions. For the complete trained model, see [lm-provers/QED-Nano](https://huggingface.co/lm-provers/QED-Nano).
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### Key features
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- Reasoning model optimized for **theorem proving**
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- **Supervised fine-tuning checkpoint**: Foundation for the full QED-Nano model (SFT + RL + Reasoning Cache)
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- **Distilled from DeepSeek-Math-V2 (685B)**: Knowledge distillation to 4B parameters
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- **Fully open**: open weights + full training details including public data mixture and training configs
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For more details refer to our blog post: https://huggingface.co/spaces/lm-provers/qed-nano-blogpost
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## How to use
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```python
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from transformers import AutoModelForCausalLM, AutoTokenizer
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model_name = "lm-provers/QED-Nano-SFT"
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device = "cuda" # for GPU usage or "cpu" for CPU usage
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# load the tokenizer and the model
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tokenizer = AutoTokenizer.from_pretrained(model_name)
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model = AutoModelForCausalLM.from_pretrained(
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model_name,
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).to(device)
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# prepare the model input
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prompt = "Generate a rigorous proof to the following question: is \sqrt{2} rational or irrational?"
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messages_think = [
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{"role": "user", "content": prompt}
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]
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text = tokenizer.apply_chat_template(
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messages_think,
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tokenize=False,
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add_generation_prompt=True,
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)
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model_inputs = tokenizer([text], return_tensors="pt").to(model.device)
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# Generate the output
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generated_ids = model.generate(**model_inputs, max_new_tokens=32768)
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# Get and decode the output
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output_ids = generated_ids[0][len(model_inputs.input_ids[0]) :]
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print(tokenizer.decode(output_ids, skip_special_tokens=True))
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```
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>[!TIP]
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> We recommend setting `temperature=0.6` and `top_p=0.95` in the sampling parameters.
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### vLLM and SGLang
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You can use vLLM and SGLang to deploy the model in an API compatible with OpenAI format.
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#### SGLang
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```bash
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python -m sglang.launch_server --model-path lm-provers/QED-Nano-SFT
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```
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#### vLLM
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```bash
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vllm serve lm-provers/QED-Nano-SFT
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```
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## Evaluation
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In this section, we report the evaluation results of QED-Nano on IMO-ProofBench, ProofBench, and IMO-AnswerBench. All evaluations except those on IMO-AnswerBench are reported as avg@3 unless stated otherwise.
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| Model | IMO-ProofBench | ProofBench | IMO-AnswerBench |
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|:---|:---:|:---:|:---:|
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| Qwen3-4B-Thinking-2507 | 20.4 (2.6) | 19.5 (0.9) | 55.8 |
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| **QED-Nano-SFT** | **39.5 (2.9)** | **33.3 (0.5)** | **57.5** |
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| **QED-Nano** | **40.0 (0.6)** | **44.9 (3.4)** | **67.5** |
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| **QED-Nano (Agent)** | **54.0 (3.7)** | **54.4 (2.4)** | **-** |
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| Qwen3-30B-A3B-Thinking-2507 | 27.6 (1.0) | 26.1 (2.4) | 67.0 |
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| Qwen3-235B-A22B-Thinking-2507 | 34.1 (0.7) | 33.7 (1.1) | 70.5 |
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| Nomos-1 | 40.3 (3.5) | 28.3 (3.9) | 49.0 |
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| GPT-OSS-20B | 38.3 (1.2) | 38.4 (3.9) | 61.5 |
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| GPT-OSS-120B | 43.1 (3.2) | 47.5 (1.7) | 70.5 |
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| DeepSeek-Math-V2 | 57.9 (2.0) | 60.6 (0.1) | 75.8 |
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| Gemini 3 Pro | 58.7 (2.9) | 66.7 (3.1) | 83.2 |
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**Note**: This is the SFT-only checkpoint. Performance improves significantly with RL training and reasoning cache. See the full [lm-provers/QED-Nano](https://huggingface.co/lm-provers/QED-Nano) model for complete results.
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## Training
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### Model
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- **Architecture:** Transformer decoder
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- **Precision:** bfloat16
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- **Base Model**: [Qwen/Qwen3-4B-Thinking-2507](https://huggingface.co/Qwen/Qwen3-4B-Thinking-2507)
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- **Parameters**: 4 billion
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- **Training Data**: [lm-provers/FineProofs-SFT](https://huggingface.co/datasets/lm-provers/FineProofs-SFT) (4,300 unique problems)
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- **Teacher Model**: [deepseek-ai/DeepSeek-Math-V2](https://huggingface.co/deepseek-ai/DeepSeek-Math-V2) (685B)
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### Training Hyperparameters
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- **Optimization Steps**: 620
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- **Global Batch Size**: 32
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- **Learning Rate Schedule**: Cosine with peak at 3×10⁻⁵
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- **Max Sequence Length**: 45,056 tokens
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- **Training Configuration**: Unique problems only (4.3k samples outperformed 7.7k with duplicates)
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### Software & hardware
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- **GPUs:** 1 node with 8 H100
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- **Training time:** 5 hours
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- **Training Framework:** [TRL (Transformer Reinforcement Learning)](https://github.com/huggingface/trl)
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- **Evaluation framework:** [CMU-AIRe/QED-Nano](https://github.com/CMU-AIRe/QED-Nano)
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### Training script
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You can reproduce this training using the TRL library:
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```python
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from datasets import load_dataset
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from transformers import AutoModelForCausalLM, AutoTokenizer
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from trl import SFTConfig, SFTTrainer
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# Load model and tokenizer
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model = AutoModelForCausalLM.from_pretrained(
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"Qwen/Qwen3-4B-Thinking-2507",
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torch_dtype="auto",
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attn_implementation="kernels-community/vllm-flash-attn3",
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)
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tokenizer = AutoTokenizer.from_pretrained("Qwen/Qwen3-4B-Thinking-2507")
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# Load dataset
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dataset = load_dataset("lm-provers/Olympiads-SFT", split="train")
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# Training configuration
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training_args = SFTConfig(
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output_dir="./qed-nano-sft",
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max_steps=620,
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per_device_train_batch_size=2,
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gradient_accumulation_steps=2,
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learning_rate=3.0e-5,
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lr_scheduler_type="cosine",
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warmup_ratio=0.03,
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max_length=45056,
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bf16=True,
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gradient_checkpointing=True,
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logging_steps=1,
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save_steps=62,
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push_to_hub=True,
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)
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# Train
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trainer = SFTTrainer(model=model, tokenizer=tokenizer, args=training_args, train_dataset=dataset)
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trainer.train()
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```
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## Limitations
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QED-Nano SFT is a supervised fine-tuning checkpoint with several important limitations:
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### Critical Limitations
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1. **Length Explosion**: This SFT-only model suffers from uncontrolled reasoning length growth. It frequently generates responses exceeding 100k tokens, often meandering or repeating steps without converging to a solution. This is a known limitation of pure supervised learning on long-form reasoning tasks.
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2. **Correctness Issues**: While the model produces fluent mathematical text, it may generate incorrect proofs. The SFT stage does not directly optimize for correctness—only for imitating the teacher's reasoning style.
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3. **No Self-Correction**: Unlike the full QED-Nano model with RL training, this checkpoint lacks the ability to verify and refine its solutions.
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### Other Limitations
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- **Domain-specific**: Designed specifically for theorem proving. Using as a general assistant will likely produce nonsense outside of this domain.
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- **Language**: English only
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- **Text-Only**: Cannot handle problems with diagrams or visual elements
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- **Teacher Errors**: May have inherited some errors from the teacher model (DeepSeek-Math-V2)
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### Recommended Mitigations
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- Use the full [lm-provers/QED-Nano](https://huggingface.co/lm-provers/QED-Nano) model for production use
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- Apply length penalties or early stopping to control generation length
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- Combine with external verification tools or judges
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- Consider RL fine-tuning to address correctness and length issues
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These models should be used as assistive tools rather than definitive sources of information. Users should always verify important information and critically evaluate any generated content.
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## License
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[Apache 2.0](https://www.apache.org/licenses/LICENSE-2.0)
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## Citation
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If you use this model in your research, please cite:
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```bibtex
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@model{qed_nano_sft_2026,
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title={QED-Nano SFT: Distilling Olympiad Mathematical Reasoning to 4B Parameters},
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author={Edward Beeching and Jasper Dekoninck and Jia Li and Yuxiao Qu and Amrith Setlur and Ian Wu and Aviral Kumar and Lewis Tunstall},
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year={2026},
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publisher={Hugging Face},
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howpublished={\url{https://huggingface.co/lm-provers/QED-Nano-SFT}}
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}
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```
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Please also cite the training dataset:
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```bibtex
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@dataset{fineproofs_sft_dataset_2026,
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title={FineProofs SFT Dataset: Mathematical Olympiad Problems with Chain-of-Thought Reasoning},
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author={Edward Beeching and Jasper Dekoninck and Jia Li and Yuxiao Qu and Amrith Setlur and Ian Wu and Aviral Kumar and Lewis Tunstall},
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year={2026},
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publisher={Hugging Face},
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howpublished={\url{https://huggingface.co/datasets/lm-provers/FineProofs-SFT}}
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}
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```
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added_tokens.json
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{
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"</think>": 151668,
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"</tool_call>": 151658,
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"</tool_response>": 151666,
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"<think>": 151667,
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"<tool_response>": 151665,
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"<|box_end|>": 151649,
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"<|box_start|>": 151648,
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"<|endoftext|>": 151643,
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"<|file_sep|>": 151664,
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"<|fim_middle|>": 151660,
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"<|object_ref_end|>": 151647,
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"<|object_ref_start|>": 151646,
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}
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chat_template.jinja
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{%- if tools %}
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{{- '<|im_start|>system\n' }}
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{%- if messages[0].role == 'system' %}
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{{- messages[0].content + '\n\n' }}
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{%- endif %}
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{{- "# Tools\n\nYou may call one or more functions to assist with the user query.\n\nYou are provided with function signatures within <tools></tools> XML tags:\n<tools>" }}
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{%- for tool in tools %}
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{{- "\n" }}
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{{- tool | tojson }}
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{%- endfor %}
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{{- "\n</tools>\n\nFor each function call, return a json object with function name and arguments within <tool_call></tool_call> XML tags:\n<tool_call>\n{\"name\": <function-name>, \"arguments\": <args-json-object>}\n</tool_call><|im_end|>\n" }}
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{%- else %}
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{%- if messages[0].role == 'system' %}
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{{- '<|im_start|>system\n' + messages[0].content + '<|im_end|>\n' }}
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{%- endif %}
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{%- endif %}
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{%- set ns = namespace(multi_step_tool=true, last_query_index=messages|length - 1) %}
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{%- for message in messages[::-1] %}
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{%- set index = (messages|length - 1) - loop.index0 %}
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{%- if ns.multi_step_tool and message.role == "user" and message.content is string and not(message.content.startswith('<tool_response>') and message.content.endswith('</tool_response>')) %}
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{%- set ns.multi_step_tool = false %}
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{%- set ns.last_query_index = index %}
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{%- endif %}
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{%- endfor %}
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{%- for message in messages %}
|
||||
{%- if message.content is string %}
|
||||
{%- set content = message.content %}
|
||||
{%- else %}
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{%- set content = '' %}
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||||
{%- endif %}
|
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{%- if (message.role == "user") or (message.role == "system" and not loop.first) %}
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{{- '<|im_start|>' + message.role + '\n' + content + '<|im_end|>' + '\n' }}
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{%- elif message.role == "assistant" %}
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{%- set reasoning_content = '' %}
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{%- if message.reasoning_content is string %}
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{%- set reasoning_content = message.reasoning_content %}
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{%- else %}
|
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{%- if '</think>' in content %}
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{%- set reasoning_content = content.split('</think>')[0].rstrip('\n').split('<think>')[-1].lstrip('\n') %}
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{%- set content = content.split('</think>')[-1].lstrip('\n') %}
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{%- endif %}
|
||||
{%- endif %}
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{%- if loop.index0 > ns.last_query_index %}
|
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{%- if loop.last or (not loop.last and reasoning_content) %}
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{{- '<|im_start|>' + message.role + '\n<think>\n' + reasoning_content.strip('\n') + '\n</think>\n\n' + content.lstrip('\n') }}
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{%- else %}
|
||||
{{- '<|im_start|>' + message.role + '\n' + content }}
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||||
{%- endif %}
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||||
{%- else %}
|
||||
{{- '<|im_start|>' + message.role + '\n' + content }}
|
||||
{%- endif %}
|
||||
{%- if message.tool_calls %}
|
||||
{%- for tool_call in message.tool_calls %}
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||||
{%- if (loop.first and content) or (not loop.first) %}
|
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{{- '\n' }}
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{%- endif %}
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||||
{%- if tool_call.function %}
|
||||
{%- set tool_call = tool_call.function %}
|
||||
{%- endif %}
|
||||
{{- '<tool_call>\n{"name": "' }}
|
||||
{{- tool_call.name }}
|
||||
{{- '", "arguments": ' }}
|
||||
{%- if tool_call.arguments is string %}
|
||||
{{- tool_call.arguments }}
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||||
{%- else %}
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||||
{{- tool_call.arguments | tojson }}
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||||
{%- endif %}
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||||
{{- '}\n</tool_call>' }}
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{%- endfor %}
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||||
{%- endif %}
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||||
{{- '<|im_end|>\n' }}
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||||
{%- elif message.role == "tool" %}
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||||
{%- if loop.first or (messages[loop.index0 - 1].role != "tool") %}
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||||
{{- '<|im_start|>user' }}
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||||
{%- endif %}
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||||
{{- '\n<tool_response>\n' }}
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{{- content }}
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{{- '\n</tool_response>' }}
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{%- if loop.last or (messages[loop.index0 + 1].role != "tool") %}
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config.json
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
"model.norm.weight": "model-00002-of-00002.safetensors"
|
||||
}
|
||||
}
|
||||
31
special_tokens_map.json
Normal file
31
special_tokens_map.json
Normal file
@@ -0,0 +1,31 @@
|
||||
{
|
||||
"additional_special_tokens": [
|
||||
"<|im_start|>",
|
||||
"<|im_end|>",
|
||||
"<|object_ref_start|>",
|
||||
"<|object_ref_end|>",
|
||||
"<|box_start|>",
|
||||
"<|box_end|>",
|
||||
"<|quad_start|>",
|
||||
"<|quad_end|>",
|
||||
"<|vision_start|>",
|
||||
"<|vision_end|>",
|
||||
"<|vision_pad|>",
|
||||
"<|image_pad|>",
|
||||
"<|video_pad|>"
|
||||
],
|
||||
"eos_token": {
|
||||
"content": "<|im_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false
|
||||
},
|
||||
"pad_token": {
|
||||
"content": "<|endoftext|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false
|
||||
}
|
||||
}
|
||||
BIN
tokenizer.json
(Stored with Git LFS)
Normal file
BIN
tokenizer.json
(Stored with Git LFS)
Normal file
Binary file not shown.
239
tokenizer_config.json
Normal file
239
tokenizer_config.json
Normal file
@@ -0,0 +1,239 @@
|
||||
{
|
||||
"add_bos_token": false,
|
||||
"add_prefix_space": false,
|
||||
"added_tokens_decoder": {
|
||||
"151643": {
|
||||
"content": "<|endoftext|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151644": {
|
||||
"content": "<|im_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151645": {
|
||||
"content": "<|im_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151646": {
|
||||
"content": "<|object_ref_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151647": {
|
||||
"content": "<|object_ref_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151648": {
|
||||
"content": "<|box_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151649": {
|
||||
"content": "<|box_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151650": {
|
||||
"content": "<|quad_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151651": {
|
||||
"content": "<|quad_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151652": {
|
||||
"content": "<|vision_start|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151653": {
|
||||
"content": "<|vision_end|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151654": {
|
||||
"content": "<|vision_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151655": {
|
||||
"content": "<|image_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151656": {
|
||||
"content": "<|video_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": true
|
||||
},
|
||||
"151657": {
|
||||
"content": "<tool_call>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151658": {
|
||||
"content": "</tool_call>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151659": {
|
||||
"content": "<|fim_prefix|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151660": {
|
||||
"content": "<|fim_middle|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151661": {
|
||||
"content": "<|fim_suffix|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151662": {
|
||||
"content": "<|fim_pad|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151663": {
|
||||
"content": "<|repo_name|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151664": {
|
||||
"content": "<|file_sep|>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151665": {
|
||||
"content": "<tool_response>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151666": {
|
||||
"content": "</tool_response>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151667": {
|
||||
"content": "<think>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
},
|
||||
"151668": {
|
||||
"content": "</think>",
|
||||
"lstrip": false,
|
||||
"normalized": false,
|
||||
"rstrip": false,
|
||||
"single_word": false,
|
||||
"special": false
|
||||
}
|
||||
},
|
||||
"additional_special_tokens": [
|
||||
"<|im_start|>",
|
||||
"<|im_end|>",
|
||||
"<|object_ref_start|>",
|
||||
"<|object_ref_end|>",
|
||||
"<|box_start|>",
|
||||
"<|box_end|>",
|
||||
"<|quad_start|>",
|
||||
"<|quad_end|>",
|
||||
"<|vision_start|>",
|
||||
"<|vision_end|>",
|
||||
"<|vision_pad|>",
|
||||
"<|image_pad|>",
|
||||
"<|video_pad|>"
|
||||
],
|
||||
"bos_token": null,
|
||||
"clean_up_tokenization_spaces": false,
|
||||
"eos_token": "<|im_end|>",
|
||||
"errors": "replace",
|
||||
"extra_special_tokens": {},
|
||||
"model_max_length": 262144,
|
||||
"pad_token": "<|endoftext|>",
|
||||
"split_special_tokens": false,
|
||||
"tokenizer_class": "Qwen2Tokenizer",
|
||||
"unk_token": null
|
||||
}
|
||||
1
vocab.json
Normal file
1
vocab.json
Normal file
File diff suppressed because one or more lines are too long
Reference in New Issue
Block a user