metadata

base_model: deepseek-ai/deepseek-math-7b-base
tags:
  - alignment-handbook
  - generated_from_trainer
datasets:
  - 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: []

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 with two stages on Math Question answers and multi-step synthetic generations using tool integrated reasoning.

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

Model Sources

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:

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

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}}
}