We introduce Goat, a fine-tuned LLaMA model that significantly outperforms GPT-4 on a range of arithmetic tasks. Fine-tuned on a synthetically generated dataset, Goat achieves state-of-the-art performance on BIG-bench arithmetic sub-task. In particular, the zero-shot Goat-7B matches or even surpasses the accuracy achieved by the few-shot PaLM-540B. Surprisingly, Goat can achieve near-perfect accuracy on large-number addition and subtraction through supervised fine-tuning only, which is almost impossible with previous pretrained language models, such as Bloom, OPT, GPT-NeoX, etc. We attribute Goat's exceptional performance to LLaMA's consistent tokenization of numbers. To tackle more challenging tasks like large-number multiplication and division, we propose an approach that classifies tasks based on their learnability, and subsequently decomposes unlearnable tasks, such as multi-digit multiplication and division, into a series of learnable tasks by leveraging basic arithmetic principles. We thoroughly examine the performance of our model, offering a comprehensive evaluation of the effectiveness of our proposed decomposition steps. Additionally, Goat-7B can be easily trained using LoRA on a 24GB VRAM GPU, facilitating reproducibility for other researchers. We release our model, dataset, and the Python script for dataset generation.

Goat，用LLaMA模型细调后，在一系列算术任务中显著优于GPT-4，特别是在大数字加法和减法方面表现出了非常高的准确性。 对于更具挑战性的任务，如大数字乘法和除法，我们提出了一种根据其可学习性分类任务的方法，并通过利用基本算术原则将不可学习的任务（如多位数乘法和除法）分解为一系列可学习的任务。

Goat：Fine-tuned LLaMA 在算术任务上优于 GPT-4