Manifolds, neural subspaces, and “shared structure”

44:22your brain state lives in a highdimensional space. Here's what that means. Yeah. >> Okay. So suppose I only have three neurons. >> Mhm. >> Okay. Imagine a brain with only three neurons. That brain is going to live in a 3D space because the X-axis is going to tell you how neuron 1 is behaving. The Y-axis is going to tell you how neuron 2 and the Z neuron 3. So where I am here >> at any given moment [clears throat] is going to tell me what this three neuron brain is doing. >> Now imagine a thousand neurons. I've got a thousand different axes, right? And each state in this thousand dimensional

45:04space is a brain state. Okay. The curse of dimensionality is that if there's unstructured data all over the place, then the amount of data that is required to figure out where I am is going to be like ridiculous. >> Yeah. >> Okay. So, clearly the brain doesn't do that. And we know that it doesn't do that because >> like more of a brute force approach. >> Yeah. It it it would be like just a really terrible way to do any kind of learning anything like that right highly inefficient. It would take like longer than the >> lifespan of the organism to actually like get any learning done, get any cognition done. Okay. So instead what the brain does is correlate these neurons. >> Okay. >> Okay. Because neurons are connected to

45:45each other. So if one of them fires then it's going to then it's going to influence its neighbors to fire and so on and so forth. So the neural activity is actually constrained in what's called a lowdimensional manifold. A manifold you can think of as a surface. And here