Krasnosel'skii-Mann iterations beyond asymptotics: a combinatorial analysis

What the math gives to ML

The paper turns finite-horizon Krasnosel'skii–Mann behavior into an explicit combinatorial and transport problem rather than relying only on asymptotic fixed-point convergence. Its transferable asset is the construction of couplings between the distributions of computational paths at two iteration depths, with a closed-form nested transport plan for alpha >= 1/2. This suggests a depth-consistency regularizer for recurrent, equilibrium, diffusion, or iterative transformer blocks that couples intermediate states according to mathematically justified path mass instead of matching all depths uniformly. The same machinery can support adaptive early exit, because the transport cost provides a finite-depth discrepancy signal between short and long unrolls.