Stability of the Monge Map in Semi-Dual Optimal Transport
This episode discusses 'Stability of the Monge Map in Semi-Dual Optimal Transport,' a paper addressing structural weaknesses in optimal transport. The authors identify a degenerate saddle-point problem and propose a new error metric to track convergence without requiring the dual potential. They also observe that the transport map evolves much faster than the potential function, providing practical insights for designing robust AI training loops.