Arithmo2-Mistral-7B model improves initially released Arithmo-Mistral-7B model on both GSM8K and MATH benchmarks. Specifically, there is absolute improvement of:

+1.7% on GSM8K
+3.0% on GSM8K PoT
+1.9% on MATH

Note: It is recommended to use Arithmo2-Mistral-7B model. Here is the merged model and corresponding LoRA Adapter.

Model Card for Model ID

Code License

Model Weight License

Python 3.9+

P.S.: Please reach out to Ashvini Jindal 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 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, Ankur Parikh
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 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 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: <question>

Answer:

PoT Format (generate a python program):

Question: <question> <python_prompt>

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 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.

Support My Work

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Citation

To cite Arithmo models:

@misc{jindal_2023_arithmo,
  author = {Jindal, Ashvini},
  title = {Arithmo-Mistral-7B: Mathematical Reasoning Model},
  howpublished = {Hugging Face},
  month = {October},
  year = {2023},
  url = {https://huggingface.co/akjindal53244/Arithmo-Mistral-7B}
}

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}
}