Numerical experimentation

Let the samples and features learn one another’s geometry

Each displayed iteration is a complete pair of exact discrete transport transforms, normalized to maximum one. The worker computes 16 cycles; the slider then explores their actual history.

Data familyBump width Regularization τ

Displayed cycle 0Location–scale comparison

Input row histograms

Feature cost versus circular displacement

learned costcircular distancesquared circular distance

Learned feature costs C

Learned sample costs D

Successive-iterate projective change — log₁₀ scale

Preparing the transport problems…

No entropy is used. The additive term is τ‖C‖∞‖a−a′‖₁. The displayed projective change is a fixed-point diagnostic, not a certified distance to an unknown limit. Every coupling’s marginal residual is checked. Location–scale references are continuous Gaussian benchmarks; truncated grid histograms introduce discretization error, and the learned metric is not assumed to equal either benchmark.