Gabriel Peyré

gabrielpeyre.bsky.social

19 October 2026 11:47

If two maps are optimal transports, is their composition optimal? Not necessarily. A matrix example shows why monotonicity is weaker than being a convex gradient. https://www.gpeyre.com/blog/2026/10/19/composing-optimal-transport-maps/

Gabriel Peyré

gabrielpeyre.bsky.social

18 October 2026 10:30

The 1D heat flow ρ̇=ρ″ reads q̇=q″/(q′)² over quantiles which follow deterministic paths that never cross. www.gpeyre.com/blog/2026/10...

Gabriel Peyré

gabrielpeyre.bsky.social

16 October 2026 07:30

Approximating attention with fewer tokens is hard. In recent work with Léa Bohbot, we show how token amplitude affects convergence: a pointwise 1/√n rate can hide much slower global guarantees. www.gpeyre.com/blog/2026/10...

Gabriel Peyré

gabrielpeyre.bsky.social

14 October 2026 09:04

Costs of the form c(x,y)=h(x-y) are not the only ones for which Optimal Transport is equivariant ... www.gpeyre.com/blog/2026/10...

Gabriel Peyré

gabrielpeyre.bsky.social

13 October 2026 12:02

While studying the convergence of linear neural networks, I stumbled upon a nice conservation law that depends only on the distribution of neurons: a “mean-field” conservation law. www.gpeyre.com/blog/2026/10...