Hala Nelson - Essential Math for AI (Final Version)

• 2023-01-04: First Release

AI is built on mathematical models. We need to know how.

I wrote this book in purely colloquial language, leaving most of the technical details out. It is a math book about AI with very few mathematical formulas and equations, no theorems, no proofs, and no coding. My goal is to not keep this important knowledge in the hands of the very few elite, and to attract more people to technical fields. I believe that many people get turned off by math before they ever get a chance to know that they might love it and be naturally good at it. This also happens in college or in graduate school, where many students switch their majors from math, or start a Ph.D. and never finish it. The reason is not that they do not have the ability, but that they saw no motivation or an end goal for learning torturous methods and techniques that did not seem to transfer to anything useful in their lives. It is like going to a strenuous mental gym every day only for the sake of going there. No one even wants to go to a real gym every day (this is a biased statement, but you get the point). In math, formalizing objects into functions, spaces, measure spaces, and entire mathematical fields comes after motivation, not before. Unfortunately, it gets taught in reverse, with formality first and then, if we are lucky, some motivation.

The most beautiful thing about math is that it has the expressive ability to connect seemingly disparate things together. A field as big and as consequential as AI not only builds on math, as that is a given; it also needs the binding ability that only math can provide in order to tell its big story concisely. In this book I will extract the math required for AI in a way that does not deviate at all from the real-life AI application in mind. It is infeasible to go through existing tools in detail and not fall into an encyclopedic and overwhelming treatment. What I do instead is try to teach you how to think about these tools and view them from above, as a means to an end that we can tweak and adjust when we need to. I hope that you will get out of this book a way of seeing how things relate to each other and why we develop or use certain methods among others. In a way, this book provides a platform that launches you to whatever area you find interesting or want to specialize in.

Another goal of this book is to democratize mathematics, and to build more confidence to ask about how things work. Common answers such as Its complicated mathematics, Its complicated technology, or Its complex models, are no longer satisfying, especially since the technologies that build on mathematical models currently affect every aspect of our lives. We do not need to be experts in every field in mathematics (no one is) in order to understand how things are built and why they operate the way they do. There is one thing about mathematical models that everyone needs to know: they always give an answer. They always spit out a number. A model that is vetted, validated, and backed with sound theory gives an answer. Also, a model that is complete trash gives an answer. Both compute mathematical functions. Saying that our decisions are based on mathematical models and algorithms does not make them sacred. What are the models built on? What are their assumptions? Limitations? Data they were trained on? Tested on? What variables did they take into account? And what did they leave out? Do they have a feedback loop for improvement, ground truths to compare to and improve on? Is there any theory backing them up? We need to be transparent with this information when the models are ours, and ask for it when the models are deciding our livelihoods for us.