Entanglement asymmetry and quantum Mpemba effect for Kramers-Wannier duality

What the math gives to ML

The paper identifies a quantum Mpemba mechanism: an initially more asymmetric state can restore Kramers-Wannier symmetry faster than a state that starts closer to symmetry because its overlap with the slowest relaxing mode is smaller. The transferable asset is not the specific duality, but a computable asymmetry functional together with spectral mode-selection diagnostics for nonequilibrium relaxation. In neural-network training or inference, one can define a transformation or channel symmetry, measure asymmetry of representations or predictions, estimate decay modes from short trajectories, and deliberately suppress the slow mode. The key falsifiable signature is a crossing of asymmetry curves and a late-time decay rate controlled by the first nonzero mode with nonvanishing projection, rather than by initial asymmetry.