Unfolding the Origami of AI
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This past month at my internship, I found myself increasingly fascinated by the world of geometric deep learning.
It’s like I’ve stumbled upon a hidden origami master class in the realm of AI, where the art of folding and unfolding complex shapes gives birth to powerful algorithms. Let me take you on a journey through this exciting landscape, translating the complex into the comprehensible.
Imagine you’re trying to teach a computer to recognize a coffee mug. Easy, right? Just show it lots of pictures of mugs. But what if the mug is upside down? Or viewed from the bottom? Suddenly, it’s not so simple. This is where geometric deep learning comes in, treating data not as flat images, but as complex, multi-dimensional shapes.
Think of it like this: traditional deep learning is like trying to understand a 3D sculpture by only looking at its shadow on a wall. Geometric deep learning, on the other hand, lets us walk around the sculpture, touch it, and truly grasp its form. At the heart of this field is the concept of manifolds. If you’re scratching your head, don’t worry – I was too at first. Let’s break it down with an analogy.
Imagine you’re an ant living on the surface of a balloon. From your perspective, the world seems flat (just like we perceive the Earth as flat in our day-to-day lives). But we, as outside observers, know the ant is actually walking on a curved surface. This curved surface that locally looks flat is what mathematicians call a manifold.
In the context of AI, data often lives on these manifold structures. For instance, the space of all possible human faces isn’t just a random collection of pixels – it has an underlying structure. Geometric deep learning aims to understand and leverage this structure.
Another exciting concept I’ve been grappling with is flow matching. Imagine you’re standing by a river, watching leaves float by. If you could control the flow of the river perfectly, you could guide those leaves to form any pattern you want downstream. That’s essentially what flow matching does with data.
In more technical terms, flow matching is about learning to transform one probability distribution into another. It’s proving to be a powerful tool in generative models, potentially offering advantages over other methods like diffusion models in terms of sampling speed and flexibility.
Now, let’s talk about where all this theory meets biology: protein generation. Proteins are the workhorses of our cells, and their function is intimately tied to their 3D structure. Using diffusion models – another class of generative models – we’re working on teaching AI to “fold” digital amino acid sequences into functional proteins.
It’s like teaching a computer to play with a biochemical Lego set, where each piece can connect in myriad ways, and only certain configurations are useful. The potential applications are mind-boggling, from designing new drugs to creating novel materials.
As I continue this journey, I’m constantly amazed by how much there is to learn. Each paper I read, each line of code I write, is sharpening my skills. I’m becoming better at quickly distilling key points from dense academic papers, leveraging ChatGPT for learning, deciphering complex mathematical equations, and navigating intricate codebases. But more than that, I’m learning to see the world – and data – in a new way. It’s not just about flat images or linear sequences anymore. It’s about understanding the intricate shapes and flows of information, the hidden geometries that underlie our reality. And that, to me, is the true excitement of research. It’s not just about learning new facts, but about developing new ways of seeing and thinking. As I stand at the intersection of computation, cognition, and mathematics, I can’t help but feel a thrill of anticipation. What new shapes of thought will we unfold next?