Non-Reciprocal yet Equilibrium Critical Dynamics

What the math gives to ML

The paper shows that non-reciprocal complex couplings can produce non-equilibrium dynamics while remaining renormalization-group irrelevant near the critical point. Under coarse-graining, the dynamics flows toward an equilibrium Model-A fixed point with 2n components, so non-reciprocity changes transients but not the asymptotic universality class. A transferable neural-network construction is to add skew-symmetric cross-stream couplings to residual or state-space blocks, while decaying their strength with depth so that expressive rotational mixing is strongest early and the deep network approaches a stable reciprocal backbone. The key falsifiable signature is a power-law decrease in measured non-reciprocal influence and convergence of deep-layer statistics toward those of the reciprocal model.