Introduction In everyday life, we show that things exist by producing an example. In order to believe that black sheep exist, I would need someone to show me one. To believe the claim that pigs can...

Introduction Many of the most powerful models you see out there today are built using a two-stage approach: Pre-training: A model learns generally useful representations (e.g., of language or im...

Introduction In the next few posts I want to take you on the learning journey that happened when I tried to wrap my head around this wonderful paper by Brian Kulis and Michael I. Jordan (yes, Micha...

Introduction Optimization problems are everywhere! Whether it’s finding the most efficient way to deliver packages to customers, determining the best next move in a game of chess, or figuring out ...

Introduction In this post I want to introduce a non-standard way of fitting a mathematical model to data that I came across during a course I took this past semester in computer vision. While gradi...

Introduction This will be a quick one. From the very beginning of our mathematical educations, there is a fundamental fact of which we are made aware: If $a$ and $b$ are numbers of any kind (natura...

Introduction Over the past few years, large language models (LLMs) – most recently ChatGPT – have received lots of (well-deserved) press. Though they have their shortcomings, they are able to compo...

Introduction Before I say anything else, create an account and take DALL-E 2 out for a spin. It is an example of generative AI, which, as a field, has seen important, exciting, and viral breakthro...

Introduction In this post I detail a randomized algorithm (that looks rather like black magic) to count the number of distinct elements in a data stream. Naive solution Suppose that data is presen...

In this post, I want to talk through a simple mathematical result that forces us to think twice about relying too heavily on averages. Quick review of expected values Given an opportunity to play ...