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
This repo contains LoRA adapter weights. If you are interested in final merged model, use Arithmo2-Mistral-7B instead.
Model Description
- Project GitHub Page: https://github.com/akjindal53244/Arithmo
- Developed by: Ashvini Kumar Jindal
- Funded by: self-work
- Model type: fine-tuned using QLoRA on Single GPU
- Language(s) (NLP): English
- Finetuned from model: mistralai/Mistral-7B-v0.1
Results
Arithmo2-Mistral-7B is improved version of Arithmo-Mistral-7B model and is competitive with full fine-tuned state-of-the-art 7B Mathematical Reasoning models. Refer to Comparing Arithmo models with other SFT LLM models section for more details.
Prompt Approach | GSM8k | MATH |
---|---|---|
Zero-Shot CoT | 76.4 | 27.2 |
Zero-Shot PoT | 74.2 | - |
- 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.
Training procedure
The following bitsandbytes
quantization config was used during training:
- quant_method: bitsandbytes
- load_in_8bit: False
- load_in_4bit: True
- llm_int8_threshold: 6.0
- llm_int8_skip_modules: None
- llm_int8_enable_fp32_cpu_offload: False
- llm_int8_has_fp16_weight: False
- bnb_4bit_quant_type: nf4
- bnb_4bit_use_double_quant: True
- bnb_4bit_compute_dtype: bfloat16
Framework versions
- PEFT 0.6.0.dev0
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
Arithmo2-Mistral-7B is trained with same format as Arithmo-Mistral-7B:
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 models with other SFT LLM models
Results for all models except Arithmo2-Mistral-7B
are taken from MetaMath repository.
Model | GSM8k Pass@1 | MATH Pass@1 | Fine-tuning |
---|---|---|---|
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 (PoT) | 71.2 | -- | SFT: 4-bit QLoRA |
Arithmo2-Mistral-7B (PoT) | 74.2 | -- | SFT: 4-bit QLoRA |
MetaMath-Mistral-7B | 77.7 | 28.2 | SFT: Full fine-tuned |
Arithmo-Mistral-7B | 74.7 | 25.3 | SFT: 4-bit QLoRA |
🔥 Arithmo2-Mistral-7B | 76.4 | 27.2 | SFT: 4-bit QLoRA |
If you are interested in reproducing the resullts, visit https://github.com/akjindal53244/Arithmo#reproducing-results section.
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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}
}
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Model tree for upaya07/Arithmo2-Mistral-7B-adapter
Base model
mistralai/Mistral-7B-v0.1