Deep Learning Is Applied Topology

When I think about AI, I think about topology. Topology is a big scary math word that basically means 'the study of surfaces'. Imagine you had a surface made of play-doh. You could bend it, or twist it, or stretch it. But as long as you don't rip the play-doh up, or poke a hole through it, you can define certain properties that would remain true regardless of the deformation you apply. Here's an example. Let's say I flatten out my play-doh and then draw a circle on it. I could rotate it, or bend it, or twist it, or whatever. And my circle will change shape, for sure. But my circle will never magically become a line, nor will it suddenly become two circles, nor will it ever cross over itself. This is topology in a nutshell. Topology shows up in all sorts of places. For example, data science. Let's say you had a bunch of data that you wanted to classify. A lot of classification problems are equivalent to being able to cleanly separate data with a line. But when you go to plot the data ... Read full article.