The mathematics of Transformers and Large Language Models, by Dr David Hoyle

Abstract:
Large Language Models (LLMs) are everywhere. They are extremely powerful, versatile and useful. However, many statisticians and data scientists only use them as a tool, not getting to grips with understanding how they work from a computational and mathematical perspective, nor understanding why they give the output that they do. Yet, at their heart LLMs use simple mathematical ideas and tools, such as “attention” and “transformer” blocks. Those mathematical ideas are accessible to every statistician or data scientist with a grounding in the basics of linear algebra, probability, and machine learning. In this talk I will provide a high-level explanation of the core mathematics concepts behind LLMs and Transformers, focusing on how they use attention to predict the next token in a sequence of tokens. The talk is intended to be introductory. It will not make you a prompting expert, it will not make you an expert in training multi-billion parameter foundational models, nor will it make you rich.
Speaker Bio:
David Hoyle is a Research Data Science Specialist at dunnhumby, where he builds demand forecasting models and algorithms for grocery retailers worldwide. He has worked as a Data Scientist in the commercial sector for 15 years. Before that he was an Associate Professor in Bioinformatics and Machine Learning at the University of Manchester, UK, and at the University of Exeter, UK. He has a PhD in theoretical physics and continues to publish academic articles on various mathematical, statistical, machine learning, and AI topics. He also enjoys explaining mathematical and statistical concepts, showing how they are relevant to real-world problems and challenges, and so he regularly writes posts for his own blog and for dunnhumby. He is heavily involved with the UK Royal Statistical Society, acting as Data Science and AI board member for the society’s annual international conference. He has recently authored a book on mathematics for Data Science – “15 Math Concepts Every Data Scientist Should Know’’ – published by Packt.