As specialized large language models (LLMs) become increasingly prevalent, model merging methods are being used to combine them to create a single multi-task model without requiring any additional data or training. However, these approaches fall short when the objective of merging is to increase the downstream model's performance on a particular task-specific benchmark. In this work, we propose LEWIS (Layer Wise Sparsity), a guided model-merging framework that uses activation-based layer importance to dynamically adjust layer-wise task-vector sparsity required for the merge process. LEWIS uses a calibration dataset to prioritize critical layers during the task-vector pruning process required for model merging. This approach guides existing merging methods by preserving essential layer-wise task-specific knowledge while ensuring the merged model performs the best at benchmarks resembling the calibration dataset. Our experiments demonstrate the effectiveness of LEWIS with performance improvements of code instruction-following and math-solving models created through model merging up to 4 percent and 11.3 percent, respectively, outperforming unguided data-less model merging approaches that use uniform-sparsity.

The recently released GPT-4 Code Interpreter has demonstrated remarkable proficiency in solving challenging math problems, primarily attributed to its ability to seamlessly reason with natural language, generate code, execute code, and continue reasoning based on the execution output. In this paper, we present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations and, consequently, enhancing their mathematical reasoning abilities. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions, referred to as MathCodeInstruct. Each solution interleaves natural language, code, and execution results. We also introduce a customized supervised fine-tuning and inference approach. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems. Impressively, the MathCoder models achieve state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K (83.9%) datasets, substantially outperforming other open-source alternatives. Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The dataset and models will be released at https://github.com/mathllm/MathCoder.