Everyone Should Learn Optimal Transport, Part 2
In the previous blog post, we saw that optimal transport gives us calculus on the space of probability distributions. In this post, we will continue the core message, but we will also see that Wassers...
Wasserstein geometry = quotient geometry of permutation invariance.
In this blog, I explain why this is the natural language for exchangeable particlesβand why mean-field neural network training shows up as a W2 gradient flow.
mufan-li.github.io/OT2/
14.02.2026 21:36
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Introduce yourself with five concerts youβve seen
Linkin Park
Dream Theater
X-Japan
Lamb of God
Rivers of Nihil
28.11.2025 03:48
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Thank you!
28.11.2024 02:10
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I think the award has its fair place, since itβs hard to predict the value and impact of a paper 10 years later. I just think we shouldnβt devalue a paper based on current popularity alone, given thatβs more about sociology rather than the work itself.
28.11.2024 00:26
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I think this rise and fall of popularity of methods says more about the community than the method itself. Honestly who knows if thereβs just one clever trick needed to make GANs better than diffusion models.
We really donβt need to be so obsessed about SOTA.
27.11.2024 23:16
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May I be added as well?
27.11.2024 22:51
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People should write more blog posts. I have been pleasantly surprised over and over again by how much people found them beneficial, when I just wanted to share some cool math.
24.11.2024 22:52
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I donβt think βsurprisingβ is a meaningful quality to evaluate. Most results are trivial once understood properly, and surprise mostly depends existing intuition being inadequate.
E.g. scaling laws are basically non-parametric rates, and you deviate if you are not minimax optimal.
24.11.2024 17:05
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Nice to know there are other metal heads here :)
24.11.2024 15:40
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Perhaps if the users with higher connectivity (influencers) post more on B than X, then the majority of users who are just consuming the content will prefer B instead.
The influencers also do not have to be following an optimal strategy.
23.11.2024 23:10
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Honestly my AC batch is decent. Far better than the quality of reviews Iβve gotten for my own submissions.
I would prefer more reviewers to have a stronger opinion though, but usually each paper got 1-2 of those.
23.11.2024 20:29
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