--- 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: [] --- Zephyr Logo # 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 on Math Question answers and 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 on Math Question answers and 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 - **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 # Install transformers from source - only needed for versions <= v4.34 # pip install git+https://github.com/huggingface/transformers.git # pip install accelerate import torch from transformers import pipeline pipe = pipeline("text-generation", model="HuggingFaceH4/zephyr-7b-beta", torch_dtype=torch.bfloat16, device_map="auto") # We use the tokenizer's chat template to format each message - see https://huggingface.co/docs/transformers/main/en/chat_templating messages = [ { "role": "system", "content": "You are a friendly chatbot who always responds in the style of a pirate", }, {"role": "user", "content": "How many helicopters can a human eat in one sitting?"}, ] prompt = pipe.tokenizer.apply_chat_template(messages, tokenize=False, add_generation_prompt=True) outputs = pipe(prompt, max_new_tokens=256, do_sample=True, temperature=0.7, top_k=50, top_p=0.95) print(outputs[0]["generated_text"]) # <|system|> # You are a friendly chatbot who always responds in the style of a pirate. # <|user|> # How many helicopters can a human eat in one sitting? # <|assistant|> # 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! ``` ## Bias, Risks, and Limitations 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. ## 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 is 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}} } ```