The tool-use Large Language Models (LLMs) that integrate with external Python interpreters have significantly enhanced mathematical reasoning capabilities for open-source LLMs, while tool-free methods chose another track: augmenting math reasoning data. However, a great method to integrate the above two research paths and combine their advantages remains to be explored. In this work, we firstly include new math questions via **mu**lti-perspective data augmenting methods and then synthesize **code**-nested solutions to them. The open LLMs (e.g., Llama-2) are finetuned on the augmented dataset to get the resulting models, **MuMath-Code** (𝜇-Math-Code). During the inference phase, our MuMath-Code generates code and interacts with the external python interpreter to get the execution results. Therefore, MuMath-Code leverages the advantages of both the external tool and data augmentation. To fully leverage the advantages of our augmented data, we propose a two-stage training strategy: In Stage-1, we finetune Llama-2 on pure CoT data to get an intermediate model, which then is trained on the code-nested data in Stage-2 to get the resulting MuMath-Code.Our MuMath-Code-7B achieves 83.8% on GSM8K and 52.4% on MATH, while MuMath-Code-70B model achieves new state-of-the-art performance among open methods—achieving 90.7% on GSM8K and 55.1% on MATH. Extensive experiments validate the combination of tool use and data augmentation, as well as our two-stage training strategy.We release the proposed dataset along with the associated code for public use: https://github.com/youweihao-tal/MuMath-Code.

Recently, the tool-use Large Language Models (LLMs) that integrate with external Python interpreters have significantly enhanced mathematical reasoning capabilities for open-source LLMs. However, these models fall short in demonstrating the calculation process, which compromises user-friendliness and understanding of problem-solving steps. Conversely, while tool-free methods offer a clear display of the problem-solving process, their accuracy leaves room for improvement.These tool-free methods typically employ a somewhat narrow range of augmentation techniques such as rephrasing and difficulty enhancement to boost performance. In response to this issue, we have amalgamated and further refined these strengths while broadening the scope of augmentation methods to construct a **mu**lti-perspective augmentation dataset for **math**ematics—termed **MuMath** (𝜇-Math) Dataset.Subsequently, we finetune LLaMA-2 on the MuMath dataset to derive the MuMath model. Our experiments indicate that our MuMath-70B model achieves new state-of-the-art performance among tool-free methods—achieving 88.3% on GSM8K and 34.5% on MATH .We release the MuMath dataset along with its corresponding models and code for public use.

Parameter-efficient fine-tuning (PEFT) methods have provided an effective way for adapting large vision-language models to specific tasks or scenarios. Typically, they learn a very small scale of parameters for pre-trained models in a white-box formulation, which assumes model architectures to be known and parameters to be accessible. However, large models are often not open-source due to considerations of preventing abuse or commercial factors, hence posing a barrier to the deployment of white-box PEFT methods. To alleviate the dependence on model accessibility, we introduce collaborative black-box tuning (CBBT) for both textual prompt optimization and output feature adaptation for black-box models. Specifically, considering that the backpropagation gradients are blocked, we approximate the gradients of textual prompts by analyzing the predictions with perturbed prompts. Secondly, a lightweight adapter is deployed over the output feature of the inaccessible model, further facilitating the model adaptation process. Empowered with these designs, our CBBT is extensively evaluated on eleven downstream benchmarks and achieves remarkable improvements compared to existing black-box VL adaptation methods. Our code will be made publicly available.