base_model: AI-MO/NuminaMath-7B-TIR
license: apache-2.0
pipeline_tag: text-generation
tags:
- alignment-handbook
- generated_from_trainer
quantized_by: bartowski
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
model-index:
- name: NuminaMath-7B-TIR
results: []
Llamacpp imatrix Quantizations of NuminaMath-7B-TIR
Using llama.cpp release b3356 for quantization.
Original model: https://huggingface.co/AI-MO/NuminaMath-7B-TIR
All quants made using imatrix option with dataset from here
Prompt format
### Problem: {prompt}
### Solution:
Download a file (not the whole branch) from below:
| Filename | Quant type | File Size | Split | Description |
|---|---|---|---|---|
| NuminaMath-7B-TIR-f32.gguf | f32 | 27.65GB | false | Full F32 weights. |
| NuminaMath-7B-TIR-Q8_0.gguf | Q8_0 | 7.35GB | false | Extremely high quality, generally unneeded but max available quant. |
| NuminaMath-7B-TIR-Q6_K_L.gguf | Q6_K_L | 5.88GB | false | Uses Q8_0 for embed and output weights. Very high quality, near perfect, recommended. |
| NuminaMath-7B-TIR-Q6_K.gguf | Q6_K | 5.67GB | false | Very high quality, near perfect, recommended. |
| NuminaMath-7B-TIR-Q5_K_L.gguf | Q5_K_L | 5.19GB | false | Uses Q8_0 for embed and output weights. High quality, recommended. |
| NuminaMath-7B-TIR-Q5_K_M.gguf | Q5_K_M | 4.93GB | false | High quality, recommended. |
| NuminaMath-7B-TIR-Q5_K_S.gguf | Q5_K_S | 4.81GB | false | High quality, recommended. |
| NuminaMath-7B-TIR-Q4_K_L.gguf | Q4_K_L | 4.53GB | false | Uses Q8_0 for embed and output weights. Good quality, recommended. |
| NuminaMath-7B-TIR-Q4_K_M.gguf | Q4_K_M | 4.22GB | false | Good quality, default size for must use cases, recommended. |
| NuminaMath-7B-TIR-Q4_K_S.gguf | Q4_K_S | 4.03GB | false | Slightly lower quality with more space savings, recommended. |
| NuminaMath-7B-TIR-IQ4_XS.gguf | IQ4_XS | 3.80GB | false | Decent quality, smaller than Q4_K_S with similar performance, recommended. |
| NuminaMath-7B-TIR-Q3_K_L.gguf | Q3_K_L | 3.75GB | false | Lower quality but usable, good for low RAM availability. |
| NuminaMath-7B-TIR-Q3_K_M.gguf | Q3_K_M | 3.46GB | false | Low quality. |
| NuminaMath-7B-TIR-IQ3_M.gguf | IQ3_M | 3.29GB | false | Medium-low quality, new method with decent performance comparable to Q3_K_M. |
| NuminaMath-7B-TIR-Q3_K_S.gguf | Q3_K_S | 3.14GB | false | Low quality, not recommended. |
| NuminaMath-7B-TIR-IQ3_XS.gguf | IQ3_XS | 2.99GB | false | Lower quality, new method with decent performance, slightly better than Q3_K_S. |
| NuminaMath-7B-TIR-IQ3_XXS.gguf | IQ3_XXS | 2.76GB | false | Lower quality, new method with decent performance, comparable to Q3 quants. |
| NuminaMath-7B-TIR-Q2_K.gguf | Q2_K | 2.72GB | false | Very low quality but surprisingly usable. |
| NuminaMath-7B-TIR-IQ2_M.gguf | IQ2_M | 2.54GB | false | Relatively low quality, uses SOTA techniques to be surprisingly usable. |
| NuminaMath-7B-TIR-IQ2_S.gguf | IQ2_S | 2.39GB | false | Low quality, uses SOTA techniques to be usable. |
| NuminaMath-7B-TIR-IQ2_XS.gguf | IQ2_XS | 2.21GB | false | Low quality, uses SOTA techniques to be usable. |
Credits
Thank you kalomaze and Dampf for assistance in creating the imatrix calibration dataset
Thank you ZeroWw for the inspiration to experiment with embed/output
Downloading using huggingface-cli
First, make sure you have hugginface-cli installed:
pip install -U "huggingface_hub[cli]"
Then, you can target the specific file you want:
huggingface-cli download bartowski/NuminaMath-7B-TIR-GGUF --include "NuminaMath-7B-TIR-Q4_K_M.gguf" --local-dir ./
If the model is bigger than 50GB, it will have been split into multiple files. In order to download them all to a local folder, run:
huggingface-cli download bartowski/NuminaMath-7B-TIR-GGUF --include "NuminaMath-7B-TIR-Q8_0.gguf/*" --local-dir NuminaMath-7B-TIR-Q8_0
You can either specify a new local-dir (NuminaMath-7B-TIR-Q8_0) or download them all in place (./)
Which file should I choose?
A great write up with charts showing various performances is provided by Artefact2 here
The first thing to figure out is how big a model you can run. To do this, you'll need to figure out how much RAM and/or VRAM you have.
If you want your model running as FAST as possible, you'll want to fit the whole thing on your GPU's VRAM. Aim for a quant with a file size 1-2GB smaller than your GPU's total VRAM.
If you want the absolute maximum quality, add both your system RAM and your GPU's VRAM together, then similarly grab a quant with a file size 1-2GB Smaller than that total.
Next, you'll need to decide if you want to use an 'I-quant' or a 'K-quant'.
If you don't want to think too much, grab one of the K-quants. These are in format 'QX_K_X', like Q5_K_M.
If you want to get more into the weeds, you can check out this extremely useful feature chart:
But basically, if you're aiming for below Q4, and you're running cuBLAS (Nvidia) or rocBLAS (AMD), you should look towards the I-quants. These are in format IQX_X, like IQ3_M. These are newer and offer better performance for their size.
These I-quants can also be used on CPU and Apple Metal, but will be slower than their K-quant equivalent, so speed vs performance is a tradeoff you'll have to decide.
The I-quants are not compatible with Vulcan, which is also AMD, so if you have an AMD card double check if you're using the rocBLAS build or the Vulcan build. At the time of writing this, LM Studio has a preview with ROCm support, and other inference engines have specific builds for ROCm.
Want to support my work? Visit my ko-fi page here: https://ko-fi.com/bartowski