How I woke up one day and decided to solve a math conjecture from the 1970s ⤵️

Applied maths is dead, long live AI!

#maths

New blog post up about concentration inequalities for quadratic forms xᵀAx with random vectors x drawn from the sphere! The conclusion: xᵀAx has much smaller tail probabilities than gᵀAg for a Gaussian vector g ethanepperly.com/index.php/2024…

Ask GPT-4 to "visualize in its head" selecting a random point in the unit square. Do that 500 times, that’s what you get. Not sure what I expected, and I don’t quite understand where this “distribution” is coming from.

Nate, I don't trust you on this. How many 80,000 simulations runs did you perform before getting one that so perfectly matched your storytelling? You accused pollsters of herding. I accuse you of seed-hacking for clicks.

We often think of an "equilibrium" as something standing still, like a scale in perfect balance. But many equilibria are dynamic, like a flowing river which is never changing—yet never standing still. These dynamic equilibria are nicely described by so-called "detailed balance"

Friday dilemma: enter the "how to code a fast matmul" rabbit hole or not 😅

All my daily tweets are available here samuelvaiter.com/one-piece/ (sometimes with a slight delay) They are also on the two other usual suspects.

Cute, the "17 Camels trick" is #maths: mathoverflow.net/questions/2716…

Variational approximation with Gaussian mixtures is looking cute! So here it's just gradient descent on K(q||p) for optimising the mixtures means & covariances & weights...