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Fast Differentiable Sorting and Ranking


Mathieu Blondel: Our contribution towards differentiable programming: O(n log n) differentiable sorting and ranking operators. Key techniques: projections onto permutahedra & isotonic optimization. Applications to top-k classification, label ranking, least trimmed squares.

12 replies, 827 likes

Mathieu Blondel: V2 of the paper with minor corrections and source code (NumPy, TF, JAX, PyTorch) are out! I'm particularly proud of our implementation of isotonic regression with KL divergence (might well be the only one available on the internet!)

5 replies, 496 likes

Jacques Carette: This is really cool - and a great counter-point to those who think that programming is intimately tied to 'logic' with no geometric content. Once you understand the idea of "relaxation" (from optimization), you start to see the cage that logic-based programming is in.

0 replies, 22 likes

Hacker News: Fast Differentiable Sorting and Ranking

0 replies, 19 likes

Kyle Cranmer: The permutahedron is the mother of the @amplituhedron #Physics∩ML

0 replies, 12 likes

Hector Yee: Another cool example of converting a discrete problem into a continuous one

1 replies, 12 likes

Chad Scherrer: The "make everything continuous" approach is really picking up steam in machine learning. And that's great! But sometimes discrete methods can lead to better optimizations. In the long run, we'll need to get better and when to do which, and how to switch easily between the two

0 replies, 11 likes

Bharath Ramsundar: @pfau @zzznah I agree there's not much use of differential geometry tools in differentiable programming yet. But there is some fascinating new math happening. For example, this paper partially triggered my tweet

0 replies, 6 likes

alex rubinsteyn: Mathieu is endlessly performing magic.

0 replies, 6 likes

Ethan Rosenthal: Cool paper, and also TIL about least trimmed squares

0 replies, 4 likes

Erik Nijkamp: Differentiable sorting in O(n log n) time, "Fast Differentiable Sorting and Ranking" (@mblondel_ml, O. Teboul, Q. Berthet, J. Djolonga):

0 replies, 3 likes

HotComputerScience: Most popular computer science paper of the day: "Fast Differentiable Sorting and Ranking"

0 replies, 3 likes

Brad Neuberg: This seems important from a machine learning perspective: Fast Differentiable Sorting and Ranking:

0 replies, 3 likes

Statistics Papers: Fast Differentiable Sorting and Ranking.

0 replies, 3 likes

Hacker News 150: Fast Differentiable Sorting and Ranking (

0 replies, 1 likes

Dr Simon Osindero: Interesting

0 replies, 1 likes


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