Goat: Fine-tuned LLaMA Outperforms GPT-4 on Arithmetic Tasks
Authors: name: Tiedong Liu, name: Bryan Kian Hsiang Low

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.