and yes, all ML folks will probably know this ;)

Interestingly, most students in my DL course didn't.

If the Gaussian is centered at zero, won’t both angles be uniformly distributed on the circle, and thus have undefined expected value? And doesn’t this imply the expectation of the difference is undefined?

(For the case of n = 2.)

Is a take home message that many of the neuroscience studies that find orthogonal neural coding of different features, are probably not particularly informative?

that was not my thought but I see your point. I was more thinking about it from an ML perspective - it easily explains why we can learn one thing without messing (massively) with lots of other things.

pic.twitter.com/MR0XuWIwov

@bayesianbrain

1/ Do any of you posting your musings here know how to establish that the answer is pi/2? It is not done by simulations or by looking it up in mathoverflow. It is only established through a mathematical proof. Figure it out. It involves solid angles.

I assume most of my readers would go through the distribution of dot product path. Or do you mean how to derive the ab=||a||||b||cos \theta equation in the first place?