Mathematics Behind Large Language Models and Transformers

Welcome to the Mathematics of Transformers, an in-depth course crafted for those eager to understand the mathematical foundations of large language models like This course delves into the complex mathematical algorithms that allow these sophisticated models to process, understand, and generate human-like text. Starting with tokenization, students will learn how raw text is converted into a format understandable by models through techniques such as the WordPiece algorithm. We’ll explore the core components of transformer architectures—key matrices, query matrices, and value matrices—and their roles in encoding information. A significant focus will be on the mechanics of the attention mechanism, including detailed studies of multi-head attention and attention masks. These concepts are pivotal in enabling models to focus on relevant parts of the input data, enhancing their ability to understand context and nuance. We will also cover positional encodings, essential for maintaining the sequence of words in inputs, utilizing cosine and sine functions to embed the position information mathematically. Additionally, the course will include comprehensive insights into bidirectional and masked language models, vectors, dot products, and multi-dimensional word embeddings, crucial for creating dense representations of words. By the end of this course, participants will not only master the theoretical underpinnings of transformers but also gain practical insights into their functionality and application. This knowledge will prepare you to innovate and excel in the field of machine learning, placing you among the top echelons of AI engineers and researchers