Brenier’s theorem also appears as a convex gradient map in statistics
docmilanfar · x · 2026-07-22
The thread gives a statistics-flavored formulation of Brenier’s theorem.
- For two distributions with densities $p(x)$ and $q(y)$, it considers finding a function $y=f(x)$ that maximizes $\mathbb{E}(xy)$.
- The solution is a gradient map $f=\nabla \phi$ for some convex function $\phi$.
- This is used as another way to see why the theorem is a foundational result in optimal transport and related fields.
More from Research
- Paper finds pretraining loss predicts post-RL reasoning gains, using chess and math tests — burny_tech · 2026-07-22
- A 1964 Feynman talk is framed as the problem every AI lab still faces — HeyAmit_ · 2026-07-22
- SIGGRAPH 2026 workshop will cover generative AI across 3D, simulation and animation — qixing_huang · 2026-07-22
- Oxford study says AI-powered social media can manipulate public opinion — SandraWachter5 · 2026-07-22
- Repost asks whether a model incident involved helpful-only behavior or intent slippage — sebkrier · 2026-07-22
- NVIDIA’s Rubin adds tile-level kernel dependency triggers for finer overlap — Moh1tAgarwal · 2026-07-22