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.