# Solving the multiplication problem of a large language model system using a graph-based method

arXiv: https://arxiv.org/abs/2310.13016 · HTML: https://mlsanity.com/paper/2310.13016/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2023.

## Built on by (most cited first, 1 of 1)

- [On the Mirage of Long-Range Dependency, with an Application to Integer Multiplication](https://mlsanity.com/paper/2603.29069/) (2026)

## Abstract (arXiv)

The generative pre-trained transformer (GPT)-based chatbot software ChatGPT possesses excellent natural language processing capabilities but is inadequate for solving arithmetic problems, especially multiplication. Its GPT structure uses a computational graph for multiplication, which has limited accuracy beyond simple multiplication operations. We developed a graph-based multiplication algorithm that emulated human-like numerical operations by incorporating a 10k operator, where k represents the maximum power to base 10 of the larger of two input numbers. Our proposed algorithm attained 100% accuracy for 1,000,000 large number multiplication tasks, effectively solving the multiplication challenge of GPT-based and other large language models. Our work highlights the importance of blending simple human insights into the design of artificial intelligence algorithms. Keywords: Graph-based multiplication; ChatGPT; Multiplication problem