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--- |
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base_model: deepseek-ai/deepseek-math-7b-base |
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tags: |
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- alignment-handbook |
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- generated_from_trainer |
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datasets: |
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- AI-MO/tora-chosen-v0.7 |
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widget: |
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- example_title: Math problem |
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messages: |
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- role: user |
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content: "For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$ have two distinct integer roots?" |
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output: |
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text: >- |
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### 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 |
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pipeline_tag: text-generation |
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model-index: |
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- name: Numina-Math-7B |
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results: [] |
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--- |
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<!-- This model card has been generated automatically according to the information the Trainer had access to. You |
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should probably proofread and complete it, then remove this comment. --> |
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<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'"/> |
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# Model Card for Numina-Math-7B |
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Numina-Math is a series of language models that are trained to solve math problems using tool integrated reasoning. |
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Numina-Math-7b won the first AI Math Olympiad, with a score of 29/50 on the public and private tests sets. |
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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 on Math Question answers and multi-step synthetic generations using tool integrated reasoning. |
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## Model description |
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- **Model type:** A 7B parameter Math model fine-tuned in two stages on Math Question answers and multi-step synthetic generations using tool integrated reasoning. |
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- **Language(s) (NLP):** Primarily English |
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- **License:** MIT |
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- **Finetuned from model:** [deepseek-ai/deepseek-math-7b-base](https://huggingface.co/deepseek-ai/deepseek-math-7b-base) |
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### Model Sources |
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<!-- Provide the basic links for the model. --> |
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- **Repository:** Coming soon to https://github.com/huggingface/alignment-handbook |
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- **Demo:** https://huggingface.co/spaces/AI-MO/math-olympiad-solver |
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## Intended uses & limitations |
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Here's how you can run the model using the `pipeline()` function from 🤗 Transformers: |
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```python |
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# Install transformers from source - only needed for versions <= v4.34 |
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# pip install git+https://github.com/huggingface/transformers.git |
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# pip install accelerate |
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import torch |
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from transformers import pipeline |
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pipe = pipeline("text-generation", model="HuggingFaceH4/zephyr-7b-beta", torch_dtype=torch.bfloat16, device_map="auto") |
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# We use the tokenizer's chat template to format each message - see https://huggingface.co/docs/transformers/main/en/chat_templating |
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messages = [ |
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{ |
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"role": "system", |
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"content": "You are a friendly chatbot who always responds in the style of a pirate", |
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}, |
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{"role": "user", "content": "How many helicopters can a human eat in one sitting?"}, |
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] |
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prompt = pipe.tokenizer.apply_chat_template(messages, tokenize=False, add_generation_prompt=True) |
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outputs = pipe(prompt, max_new_tokens=256, do_sample=True, temperature=0.7, top_k=50, top_p=0.95) |
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print(outputs[0]["generated_text"]) |
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# <|system|> |
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# You are a friendly chatbot who always responds in the style of a pirate.</s> |
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# <|user|> |
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# How many helicopters can a human eat in one sitting?</s> |
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# <|assistant|> |
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# Ah, me hearty matey! But yer question be a puzzler! A human cannot eat a helicopter in one sitting, as helicopters are not edible. They be made of metal, plastic, and other materials, not food! |
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``` |
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## Bias, Risks, and Limitations |
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<!-- This section is meant to convey both technical and sociotechnical limitations. --> |
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Numina-Math-7B was create to solve math problems, the model has not been align to preferences beyond the domain of solving math, and should not be used in a general chat setting. |
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## Training procedure |
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### Training hyperparameters |
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The following hyperparameters were used during training: |
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- learning_rate: 2e-05 |
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- train_batch_size: 4 |
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- eval_batch_size: 8 |
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- seed: 42 |
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- distributed_type: multi-GPU |
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- num_devices: 8 |
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- total_train_batch_size: 32 |
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- total_eval_batch_size: 64 |
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- optimizer: Adam with betas=(0.9,0.999) and epsilon=1e-08 |
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- lr_scheduler_type: cosine |
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- lr_scheduler_warmup_ratio: 0.1 |
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- num_epochs: 4.0 |
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### Training results |
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| Training Loss | Epoch | Step | Validation Loss | |
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|:-------------:|:-----:|:----:|:---------------:| |
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| 0.4295 | 1.0 | 1733 | 0.4313 | |
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| 0.3638 | 2.0 | 3466 | 0.4332 | |
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| 0.2951 | 3.0 | 5199 | 0.4704 | |
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| 0.2225 | 4.0 | 6932 | 0.5302 | |
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### Framework versions |
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- Transformers 4.40.1 |
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- Pytorch 2.3.1 |
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- Datasets 2.18.0 |
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- Tokenizers 0.19.1 |
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## Citation |
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If you find Numina-Math is useful in your work, please cite it with: |
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``` |
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@misc{beeching2024numina-math, |
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title={Numina Math}, |
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author={Edward Beeching and Lewis Tunstall and Roman Soletskyi and Kashif Rasul and Shengyi Huang and Jia Li}, |
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year={2024}, |
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publisher = {Hugging Face}, |
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journal = {Hugging Face repository}, |
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howpublished = {\url{https://huggingface.co/AI-MO/Numina-Math-7B}} |
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} |
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``` |
