I should add that the complexity of the Legendre transform is O(n). The value of this tweet is that (i) the method is trivial to code (ii) it is gpu friendly and parallizable (iii) in introduce a smoothing which is often desirable. https://link.springer.com/arti...

@gabrielpeyre Softmax strikes again! Didn't thought about it that way!

@Dirque_L Exactly! This is just Sinkhorn iterarion!

@gabrielpeyre computational convex analysis. https://x.com/FrnkNlsn/status/...

@gabrielpeyre I created an #animation on the Legendre transform https://www.annevanrossum.com/... I think it's nice. :-)