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Gabriel Peyré    @gabrielpeyre   ·   10/12/2021
Monge and Kantorovitch Optimal Transport are equivalent when the measures are supported on the same number of points. https://t.co/ZS3RjHc50g https://t.co/fEINE2gq3A
 
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Gabriel Peyré    @gabrielpeyre   ·   9/20/2021
Optimal computation of gradients is equivalent to optimal parenthesis problem. It is NP hard. Forward and backward (backprop aka adjoint state method) are two extreme cases. Backward is optimal for scalar-valued functions. https://t.co/UVMi13PXJm https://t.co/vPZopuNMyv
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Gabriel Peyré    @gabrielpeyre   ·   10/1/2021
Oldies but goldies: L Kantorovich, On translocation of masses, 1942. Nobel Prize in economy in 1975 for description of optimal transport as a linear program. Makes the transport problem formulated by Gaspard Monge tractable by allowing splitting of mass. https://t.co/4l9nWCNrCh
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Gabriel Peyré    @gabrielpeyre   ·   9/23/2021
Oldies but goldies: Martial Agueh and Guillaume Carlier, Barycenters in the Wasserstein Space, 2011. Defines a notion of averaging of probability distributions which is the solution of a convex program involving optimal transport distances. https://t.co/OKO27qL1Uj
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Gabriel Peyré    @gabrielpeyre   ·   9/20/2021
As pointed out by @vit_tucek, optimal parenthesis for matrix multiplication is not NP hard, it can be solved in O(n*log(n)). Deriving optimal automatic differentiation for purely feedforward graph is easy. https://t.co/vPZopuNMyv
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