README.md

---
base_model: deepseek-ai/deepseek-math-7b-base
tags:
- alignment-handbook
- generated_from_trainer
datasets:
- AI-MO/numina-problems-sft-v1.7-preproc
- AI-MO/tora-chosen-v0.7
widget:
  - example_title: Math problem
    messages:
      - role: user
        content: "For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?"
    output:
      text: >-
        ### Solution: 1. For the polynomial \\( x^2 + kx + 36 \\) to have two distinct integer roots, let's denote these roots by \\( r_1 \\) and \\( r_2 \\).\n\n2. According to Vieta's formulas, the sum of the roots \\( r_1 + r_2 \\) is equal to \\(-k\\), and the product of the roots \\( r_1 \\cdot r_2 \\) is equal to 36.\n\n3. To find the distinct integer pairs \\((r_1, r_2)\\) whose product is 36, we need to determine all pairs of integers \\((r_1, r_2)\\) such that \\( r_1 \\cdot r_2 = 36 \\) and \\( r_1 \\neq r_2 \\).\n\n4. From the equation \\( r_1 + r_2 = -k \\), for each valid pair \\((r_1, r_2)\\), we can compute the corresponding value of \\( k \\).\n\n5. Finally, since we need the polynomial to have two distinct integer roots, we need to ensure that \\( r_1 \\) and \\( r_2 \\) are distinct.\n\nLet's start by finding all pairs \\((r_1, r_2)\\) such that \\( r_1 \\cdot r_2 = 36 \\). We'll then determine the values of \\( k \\) and ensure the roots are distinct.\n```python\nimport itertools\n\n# Find all pairs (r1, r2) such that r1 * r2 = 36\nproduct_36 = 36\nfactor_pairs = []\n\nfor i in range(1, product_36 + 1):\n if product_36 % i == 0:\n pair = (i, product_36 // i)\n if pair[0] != pair[1]: # Ensure distinct pairs\n factor_pairs.append(pair)\n\n# Calculate k for each pair and ensure distinct integer roots\nvalid_k_values = set()\nfor r1, r2 in factor_pairs:\n if r1 != r2:\n k = -(r1 + r2)\n valid_k_values.add(k)\n\nprint((len(valid_k_values), sorted(valid_k_values)))\n```\n```output\n(4, [-37, -20, -15, -13])\n```\nThe distinct integer values of \\( k \\) that make the polynomial \\( x^2 + kx + 36 \\) have two distinct integer roots are \\(-37, -20, -15, \\text{and} -13\\).\n\nTherefore, the number of such values of \\( k \\) is:\n\n\\[\n\\boxed{4}\n\\]\n
pipeline_tag: text-generation


model-index:
- name: Numina-Math-7B
  results: []
---

<!-- This model card has been generated automatically according to the information the Trainer had access to. You
should probably proofread and complete it, then remove this comment. -->

<img src="https://cdn-uploads.huggingface.co/production/uploads/6200d0a443eb0913fa2df7cc/4xNbaeRi6HaAeo7UoRDZR.png" alt="Zephyr Logo" width="800" style="margin-left:'auto' margin-right:'auto' display:'block'"/>

# Model Card for Numina-Math-7B

Numina-Math is a series of language models that are trained to solve math problems using tool integrated reasoning.
Numina-Math-7b won the first AI Math Olympiad, with a score of 29/50 on the public and private tests sets.
This model is a fine-tuned version of [deepseek-ai/deepseek-math-7b-base](https://huggingface.co/deepseek-ai/deepseek-math-7b-base) with two stages of training, first on a dataset with 863k math question answer pairs and then on a dataset with 73k examples of multi-step synthetic generations using tool integrated reasoning.


![image/png](https://cdn-uploads.huggingface.co/production/uploads/6200d0a443eb0913fa2df7cc/NyhBs_gzg40iwL995DO9L.png)


## Model description

- **Model type:** A 7B parameter Math model fine-tuned in two stages of training, first on a dataset with 863k math question answer pairs and then on a dataset with 73k examples of multi-step synthetic generations using tool integrated reasoning.
- **Language(s) (NLP):** Primarily English
- **License:** MIT
- **Finetuned from model:** [deepseek-ai/deepseek-math-7b-base](https://huggingface.co/deepseek-ai/deepseek-math-7b-base)

### Model Sources

<!-- Provide the basic links for the model. -->

- **Repository:** Coming soon to https://github.com/huggingface/alignment-handbook
- **Demo:** https://huggingface.co/spaces/AI-MO/math-olympiad-solver

## Intended uses & limitations

Here's how you can run the model using the `pipeline()` function from 🤗 Transformers:

```python
import re
import torch
from transformers import pipeline

pipe = pipeline("text-generation", model="AI-MO/Numina-Math-7B", torch_dtype=torch.bfloat16, device_map="auto")

messages = [
    {"role": "user", "content": "For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?"},
]
prompt = pipe.tokenizer.apply_chat_template(messages, tokenize=False, add_generation_prompt=True)

gen_config = {
    "max_new_tokens": 1024,
    "do_sample": False,
    "stop_strings": ["```output"],
    "tokenizer": pipe.tokenizer,
}

outputs = pipe(prompt, **gen_config)
text = outputs[0]["generated_text"]

print(text)
python_code = re.findall(r"```python(.*?)```", text, re.DOTALL)[0]
# WARNING: This code will execute the python code in the string. We show this for eductional purposes only.
# Please refer to our full pipeline for a safer way to execute code.
exec(python_code)

```
## Bias, Risks, and Limitations

<!-- This section is meant to convey both technical and sociotechnical limitations. -->
Numina-Math-7B was created to solve math problems, the model has not been aligned to preferences beyond the domain of solving math, and should not be used in a general chat setting.


## Training procedure

### Training hyperparameters

The following hyperparameters were used during training:
- learning_rate: 2e-05
- train_batch_size: 4
- eval_batch_size: 8
- seed: 42
- distributed_type: multi-GPU
- num_devices: 8
- total_train_batch_size: 32
- total_eval_batch_size: 64
- optimizer: Adam with betas=(0.9,0.999) and epsilon=1e-08
- lr_scheduler_type: cosine
- lr_scheduler_warmup_ratio: 0.1
- num_epochs: 4.0

### Training results

| Training Loss | Epoch | Step | Validation Loss |
|:-------------:|:-----:|:----:|:---------------:|
| 0.4295        | 1.0   | 1733 | 0.4313          |
| 0.3638        | 2.0   | 3466 | 0.4332          |
| 0.2951        | 3.0   | 5199 | 0.4704          |
| 0.2225        | 4.0   | 6932 | 0.5302          |


### Framework versions

- Transformers 4.40.1
- Pytorch 2.3.1
- Datasets 2.18.0
- Tokenizers 0.19.1

## Citation

If you find Numina-Math useful in your work, please cite it with:

```
@misc{beeching2024numina-math,
      title={Numina Math}, 
      author={Edward Beeching and Lewis Tunstall and Roman Soletskyi and Kashif Rasul and Shengyi Huang and Jia Li},
      year={2024},
      publisher = {Hugging Face},
      journal = {Hugging Face repository},
      howpublished = {\url{https://huggingface.co/AI-MO/Numina-Math-7B}}
}
```