Mathematics & AI: A Beginner’s Guide to the Math behind Transformers

This is a groundbreaking introductory book that explains the workings of large language models, such as ChatGPT, from a mathematical perspective. By utilizing the latest AI (ChatGPT o1-mini), you can visually and intuitively learn the mathematical foundations that support the mechanism of Transformers—an integral structure behind AI.

This book adopts an unprecedented learning approach: you learn mathematics by leveraging AI, and through that mathematics, you come to understand how AI works. ChatGPT o1-mini, released in September 2024, has gained the ability to solve advanced mathematical problems. By utilizing this cutting-edge technology, you can leave the complex calculations to AI and focus on understanding the essential concepts.

Features of This Book:

Practical Use of AI

Presents specific learning methods using ChatGPT o1-mini
Provides a collection of prompts at the end of each chapter for efficient learning
Promoting Visual Understanding

Rich diagrams and illustrations to visualize complex concepts
Explanations that allow you to intuitively grasp the meaning of formulas
Careful, Step-by-Step Explanations

Explains the basics of vectors, matrices, and dot products from the ground up
Clearly elucidates the workings of the attention mechanism
Guides you to a step-by-step understanding up to cross-entropy loss
Understanding Transformers

How words (tokens) are computed for probabilities
The mechanism of score (logit) calculation
The mathematical framework for understanding context

Chapter 1: Introduction

How AI changes the way we learn mathematics

Chapter 2: How AI Calculates the Probability of the Next Word

Napier’s constant
The softmax function

Chapter 3: How AI Calculates Word Scores

Vectors, dot products, and matrix calculations

Chapter 4: How AI Dynamically Adjusts Word Features According to Context

Detailed workings of the attention mechanism
Linear transformations and activation functions

Chapter 5: How AI Uses Deep Learning to Find Optimal Parameters

Cross-entropy loss
Partial derivatives and the chain rule

Recommended for Those Who:

Want to understand the mechanism of AI from a mathematical perspective
Wish to deepen their understanding and utilization of AI tools like ChatGPT
Aim to acquire the mathematical skills needed in the AI era
Want to understand how Transformers work
Aspire to become AI engineers
Are involved in mathematics education

What You Will Not Gain from This Book:

Strict mathematical proofs or theoretical details:
This book is not suitable for those seeking rigorous proofs or deep theoretical exploration of mathematics.
Detailed and rigorous understanding of Transformers:
While it uses Transformers as a subject and provides an overview, this book does not offer a complete understanding of Transformers.

Acquisition of programming skills:
It does not include implementation methods of AI models or code explanations.
Expert knowledge of other AI models:
It does not provide detailed explanations of AI models other than Transformers.
Exhaustive mathematical knowledge:
This book focuses on the minimum basic mathematics needed to understand AI and does not cover all mathematics required for AI.