---
license: apache-2.0
language:
- en
tags:
- Mathematical Reasoning
datasets:
- akjindal53244/Arithmo-Data
---
# Model Card for Model ID
[](CODE_LICENSE)
[](LICENSE)
[](https://www.python.org/downloads/release/python-390/)
**P.S.:** Please reach out to [Ashvini Jindal](https://www.linkedin.com/in/ashvini-jindal-26653262/) if you would be interested in supporting compute need. We are looking for small-scale support so we'd appreciate any kind of help! :)
## Model Details
Arithmo-Mistral-7B is trained to reason and answer mathematical problems and is also capable of writing a Python program that upon execution prints answer to the question. We used [Mistral-7B](https://huggingface.co/mistralai/Mistral-7B-v0.1) as a base model and used **QLoRA to fine-tune it on a single RTX 4090 GPU**.
### Model Description
- **Project GitHub Page:** https://github.com/akjindal53244/Arithmo-Mistral-7B
- **Developed by:** [Ashvini Kumar Jindal](https://www.linkedin.com/in/ashvini-jindal-26653262/), [Ankur Parikh](https://www.linkedin.com/in/ankurnlpexpert/)
- **Funded by:** self-work
- **Model type:** fine-tuned
- **Language(s) (NLP):** English
- **Finetuned from model:** mistralai/Mistral-7B-v0.1
## Results
Arithmo-Mistral-7B outperforms existing 7B and 13B state-of-the-art Mathematical Reasoning models. Refer to [Comparing Arithmo-Mistral-7B with other LLM models](https://github.com/akjindal53244/Arithmo-Mistral-7B/tree/master#comparing-arithmo-mistral-7b-with-other-llm-models) section for more details.
| Prompt Approach |
GSM8k |
MATH |
| Zero-Shot CoT |
74.7 |
25.3 |
| Zero-Shot PoT |
71.2 |
- |
- **Zero-Shot CoT**: On providing a question as prompt, model generates reasoning steps to solve the question along with answer. We check if answer matches with ground-truth.
- **Zero-Shot PoT**: We prompt the model to generate a Python program for the given question. During inference, we execute the Python program generated by the model and check if the program output matches with ground-truth answer.
## Installation
```
pip install transformers >=4.34.0
pip install accelerate
pip install sentencepiece
pip install protobuf
# If you are GPU poor like me
pip install torch torchvision torchaudio --index-url https://download.pytorch.org/whl/cpu
# If you have a GPU.
pip install --pre torch --index-url https://download.pytorch.org/whl/nightly/cu118
pip install scipy
pip install bitsandbytes
```
## How to query the model
```
# Set `run_model_on_gpu` to `False` if you are running on CPU. Model will generate reasoning steps with answer for your question. If you want to generate Python program, uncomment line-69 that adds a Python prompt.
# This script automatically does formatting for you, so you just need to type question (eg: `What is 2+2?`) without any prefix like `Question:`, etc.**
$ python query_model.py
```
**Note:** Above script automatically does formatting for you, so you just need to type question (eg: `What is 2+2?`) without any prefix like `Question:`, etc. Checkout [query_model.py](https://github.com/akjindal53244/Arithmo-Mistral-7B/blob/master/query_model.py) for more details.
##### Sample Input:
```
Question: There are total 10 children. I have to give 1 apple to first child, 2 apples to second child, 3 apples to third child, and so on. How many apples do I need?
```
##### Model Output:
```
Answer: The total number of apples needed is the sum of the first 10 positive integers.
This can be calculated using the formula for the sum of an arithmetic series:
\[S = \frac{n}{2}(a_1 + a_n),\]
where $S$ is the sum, $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term.
In this case, $n = 10$, $a_1 = 1$, and $a_n = 10$.
Plugging these values into the formula, we get:
\[S = \frac{10}{2}(1 + 10) = 5(11) = \boxed{55}.\]
The answer is: 55
```
Arithmo-Mistral-7B is trained with the following format:
#### CoT Format (generate reasoning steps with answer):
```
Question:
Answer:
```
#### PoT Format (generate a python program):
```
Question:
Answer:
```
It will perform best if queried in this way with your own script.
## Comparing Arithmo-Mistral-7B with other LLM models.
Results for all models except `Arithmo-Mistral-7B` are taken from [MetaMath](https://github.com/meta-math/MetaMath/blob/main/README.MD) repository.
| Model | GSM8k Pass@1 | MATH Pass@1 |
|---------------------|--------------|-------------|
| MPT-7B | 6.8 | 3.0 |
| Falcon-7B | 6.8 | 2.3 |
| LLaMA-1-7B | 11.0 | 2.9 |
| LLaMA-2-7B | 14.6 | 2.5 |
| MPT-30B | 15.2 | 3.1 |
| LLaMA-1-13B | 17.8 | 3.9 |
| GPT-Neo-2.7B | 19.5 | -- |
| Falcon-40B | 19.6 | 2.5 |
| Baichuan-chat-13B | 23.9 | -- |
| Vicuna-v1.3-13B | 27.6 | -- |
| LLaMA-2-13B | 28.7 | 3.9 |
| InternLM-7B | 31.2 | -- |
| ChatGLM-2-6B | 32.4 | -- |
| GPT-J-6B | 34.9 | -- |
| LLaMA-1-33B | 35.6 | 3.9 |
| LLaMA-2-34B | 42.2 | 6.24 |
| RFT-7B | 50.3 | -- |
| LLaMA-1-65B | 50.9 | 10.6 |
| Qwen-7B | 51.6 | -- |
| WizardMath-7B | 54.9 | 10.7 |
| LLaMA-2-70B | 56.8 | 13.5 |
| WizardMath-13B | 63.9 | 14.0 |
| MetaMath-7B | 66.5 | 19.8 |
| MetaMath-13B | 72.3 | 22.4 |
| 🔥 **Arithmo-Mistral-7B Zero-Shot PoT** | **71.2** | -- |
| 🔥 **Arithmo-Mistral-7B Zero-Shot CoT** | **74.7** | **25.3** |
| WizardMath-70B | **81.6** | 22.7 |
| MetaMath-70B | **82.3** | **26.6** |
If you are interested in reproducing the resullts, visit https://github.com/akjindal53244/Arithmo-Mistral-7B#reproducing-results section.
References
```
@article{yu2023metamath,
title={MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models},
author={Yu, Longhui and Jiang, Weisen and Shi, Han and Yu, Jincheng and Liu, Zhengying and Zhang, Yu and Kwok, James T and Li, Zhenguo and Weller, Adrian and Liu, Weiyang},
journal={arXiv preprint arXiv:2309.12284},
year={2023}
}
@article{Yue2023mammoth,
title={MAmmoTH: Building math generalist models through hybrid instruction tuning},
author={Xiang Yue, Xingwei Qu, Ge Zhang, Yao Fu, Wenhao Huang, Huan Sun, Yu Su, and Wenhu Chen},
journal={arXiv preprint arXiv:2309.05653},
year={2023}
}
@article{mishra2022lila,
title={Lila: A unified benchmark for mathematical reasoning},
author={Swaroop Mishra, Matthew Finlayson, Pan Lu, Leonard Tang, Sean Welleck, Chitta Baral, Tanmay Rajpurohit, Oyvind Tafjord, Ashish Sabharwal, Peter Clark, and Ashwin Kalyan},
journal={arXiv preprint arXiv:2210.17517},
year={2022}
}
```