Everyone learns differently. For me, the most intuitive way to grasp complex ideas has always been through geometry and visualization. This is how I learned machine learning techniques like LLE (Local Linear Embedding) and ISOMAP when I was first introduced to them in 2007. Long before that I was thinking about the reduction of big data to small data through various multiscale techniques in the pursuit of constructing reduced order models. When I see the shape of a problem, I begin to understand its structure. This is the simple idea behind a mini project I’m excited to share: an interactive webpage designed to explore the “Geometry of Learning.”
My goal was to take some of the most abstract and powerful concepts in modern AI, ideas like high-dimensional data, manifolds, transfer learning, and latent space, and make them more tangible and accessible. I wanted to simplify these topics so that more of us can understand and use the AI tools effectively, particularly Large Language Models (LLMs), that are rapidly becoming a part of our daily lives.
Whether we realize it or not, LLMs now underline many of the technologies we use, from creative tools to a simple Google search. As these algorithms become more integrated into our world, it’s crucial that we develop an awareness of how they work. Understanding that an LLM learns by creating a compressed, geometric “map” of reality (a latent manifold) helps us appreciate both its incredible power and its inherent weaknesses.
This knowledge is our best defense against falling into the “hallucination trap,” those moments when an AI produces a confident, plausible-sounding answer that is completely wrong. By understanding that the model is navigating a learned map, we can better appreciate when it’s on a well-trodden path versus when it’s wandering into uncharted territory where errors are likely to occur.
I’ve also added a forward-looking section to the webpage. My goal here is to think about how we can build on the massive investments already made in Generative AI to advance the accuracy of predictions and reduce hallucinations. It’s my belief that the current path of simply scaling up models might not be enough to get us to Artificial General Intelligence (AGI). Real breakthroughs will be necessary, and I hope this exploration gives some context for where we might look for them.
I hope you find this webpage helpful. I’ve tried to keep the content as pedantically correct as possible while simplifying it for a broader population. A quick note on the animations you’ll see: they are conceptual tools designed to illustrate the underlying principles. They are not meant to be exact reproductions of the complex reality of these systems, but rather visual aids to help build intuition.
Please explore, interact, and I hope it helps you see the beautiful geometry that underpins modern AI. I have some foundational references at the end for you to explore this topic in-depth.
