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--- |
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base_model: AI-MO/NuminaMath-7B-TIR |
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tags: |
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- alignment-handbook |
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- generated_from_trainer |
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- TensorBlock |
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- GGUF |
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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 $x^{2}+kx+36$ |
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have two distinct integer roots? |
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output: |
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text: "### Solution: \n1- For the polynomial \\\\( x^2 + kx + 36 \\\\) to have\ |
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\ two distinct integer roots, let's denote these roots by \\\\( r_1 \\\\) and\ |
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\ \\\\( r_2 \\\\).\n\n\n2- According to Vieta's formulas, the sum of the roots\ |
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\ \\\\( r_1 + r_2 \\\\) is equal to \\\\(-k\\\\), and the product of the roots\ |
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\ \\\\( r_1 \\\\cdot r_2 \\\\) is equal to 36.\n\n\n3- To find the distinct\ |
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\ integer pairs \\\\((r_1, r_2)\\\\) whose product is 36, we need to determine\ |
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\ all pairs of integers \\\\((r_1, r_2)\\\\) such that \\\\( r_1 \\\\cdot r_2\ |
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\ = 36 \\\\) and \\\\( r_1 \\\\neq r_2 \\\\).\n\n\n4- From the equation \\\\\ |
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( r_1 + r_2 = -k \\\\), for each valid pair \\\\((r_1, r_2)\\\\), we can compute\ |
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\ the corresponding value of \\\\( k \\\\).\n\n\n5- Finally, since we need the\ |
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\ polynomial to have two distinct integer roots, we need to ensure that \\\\\ |
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( r_1 \\\\) and \\\\( r_2 \\\\) are distinct.\nLet's start by finding all pairs\ |
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\ \\\\((r_1, r_2)\\\\) such that \\\\( r_1 \\\\cdot r_2 = 36 \\\\). We'll then\ |
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\ determine the values of \\\\( k \\\\) and ensure the roots are distinct.\n\ |
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```python import itertools\n# Find all pairs (r1, r2) such that r1 * r2 = 36\ |
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\ product_36 = 36 factor_pairs = []\nfor i in range(1, product_36 + 1):\n if\ |
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\ product_36 % i == 0:\n pair = (i, product_36 // i)\n if pair[0] != pair[1]:\ |
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\ # Ensure distinct pairs\n factor_pairs.append(pair)\n \n # Calculate\ |
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\ k for each pair and ensure distinct integer roots\n valid_k_values = set()\n\ |
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\ for r1, r2 in factor_pairs:\n if r1 != r2:\n k = -(r1 + r2)\n\ |
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\ valid_k_values.add(k)\n \n print((len(valid_k_values), sorted(valid_k_values)))\n\ |
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\ ```\n \n ```output\n (4, [-37, -20, -15,-13])\n ```\n The distinct integer\ |
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\ values of \\\\( k \\\\) that make the\npolynomial \\\\( x^2 + kx + 36 \\\\\ |
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) have two distinct integer roots are \\\\(-37, -20, -15, \\\\text{and} -13\\\ |
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\\).\nTherefore, the number of such values of \\\\( k \\\\) is:\n[ \\\\boxed{4}\ |
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\ \\\\]" |
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pipeline_tag: text-generation |
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license: apache-2.0 |
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model-index: |
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- name: NuminaMath-7B-TIR |
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results: [] |
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--- |
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<div style="width: auto; margin-left: auto; margin-right: auto"> |
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<img src="https://i.imgur.com/jC7kdl8.jpeg" alt="TensorBlock" style="width: 100%; min-width: 400px; display: block; margin: auto;"> |
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</div> |
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<div style="display: flex; justify-content: space-between; width: 100%;"> |
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<div style="display: flex; flex-direction: column; align-items: flex-start;"> |
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<p style="margin-top: 0.5em; margin-bottom: 0em;"> |
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Feedback and support: TensorBlock's <a href="https://x.com/tensorblock_aoi">Twitter/X</a>, <a href="https://t.me/TensorBlock">Telegram Group</a> and <a href="https://x.com/tensorblock_aoi">Discord server</a> |
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</p> |
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</div> |
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</div> |
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## AI-MO/NuminaMath-7B-TIR - GGUF |
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This repo contains GGUF format model files for [AI-MO/NuminaMath-7B-TIR](https://huggingface.co/AI-MO/NuminaMath-7B-TIR). |
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The files were quantized using machines provided by [TensorBlock](https://tensorblock.co/), and they are compatible with llama.cpp as of [commit b4011](https://github.com/ggerganov/llama.cpp/commit/a6744e43e80f4be6398fc7733a01642c846dce1d). |
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<div style="text-align: left; margin: 20px 0;"> |
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<a href="https://tensorblock.co/waitlist/client" style="display: inline-block; padding: 10px 20px; background-color: #007bff; color: white; text-decoration: none; border-radius: 5px; font-weight: bold;"> |
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Run them on the TensorBlock client using your local machine ↗ |
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</a> |
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</div> |
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## Prompt template |
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``` |
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### Problem: {prompt} |
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### Solution: |
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``` |
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## Model file specification |
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| Filename | Quant type | File Size | Description | |
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| -------- | ---------- | --------- | ----------- | |
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| [NuminaMath-7B-TIR-Q2_K.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q2_K.gguf) | Q2_K | 2.532 GB | smallest, significant quality loss - not recommended for most purposes | |
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| [NuminaMath-7B-TIR-Q3_K_S.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q3_K_S.gguf) | Q3_K_S | 2.923 GB | very small, high quality loss | |
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| [NuminaMath-7B-TIR-Q3_K_M.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q3_K_M.gguf) | Q3_K_M | 3.223 GB | very small, high quality loss | |
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| [NuminaMath-7B-TIR-Q3_K_L.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q3_K_L.gguf) | Q3_K_L | 3.489 GB | small, substantial quality loss | |
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| [NuminaMath-7B-TIR-Q4_0.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q4_0.gguf) | Q4_0 | 3.725 GB | legacy; small, very high quality loss - prefer using Q3_K_M | |
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| [NuminaMath-7B-TIR-Q4_K_S.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q4_K_S.gguf) | Q4_K_S | 3.749 GB | small, greater quality loss | |
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| [NuminaMath-7B-TIR-Q4_K_M.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q4_K_M.gguf) | Q4_K_M | 3.933 GB | medium, balanced quality - recommended | |
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| [NuminaMath-7B-TIR-Q5_0.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q5_0.gguf) | Q5_0 | 4.481 GB | legacy; medium, balanced quality - prefer using Q4_K_M | |
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| [NuminaMath-7B-TIR-Q5_K_S.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q5_K_S.gguf) | Q5_K_S | 4.481 GB | large, low quality loss - recommended | |
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| [NuminaMath-7B-TIR-Q5_K_M.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q5_K_M.gguf) | Q5_K_M | 4.588 GB | large, very low quality loss - recommended | |
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| [NuminaMath-7B-TIR-Q6_K.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q6_K.gguf) | Q6_K | 5.284 GB | very large, extremely low quality loss | |
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| [NuminaMath-7B-TIR-Q8_0.gguf](https://huggingface.co/tensorblock/NuminaMath-7B-TIR-GGUF/blob/main/NuminaMath-7B-TIR-Q8_0.gguf) | Q8_0 | 6.842 GB | very large, extremely low quality loss - not recommended | |
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## Downloading instruction |
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### Command line |
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Firstly, install Huggingface Client |
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```shell |
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pip install -U "huggingface_hub[cli]" |
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``` |
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Then, downoad the individual model file the a local directory |
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```shell |
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huggingface-cli download tensorblock/NuminaMath-7B-TIR-GGUF --include "NuminaMath-7B-TIR-Q2_K.gguf" --local-dir MY_LOCAL_DIR |
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``` |
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If you wanna download multiple model files with a pattern (e.g., `*Q4_K*gguf`), you can try: |
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```shell |
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huggingface-cli download tensorblock/NuminaMath-7B-TIR-GGUF --local-dir MY_LOCAL_DIR --local-dir-use-symlinks False --include='*Q4_K*gguf' |
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``` |
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