Interacting hydrodynamic modes in spinless fermions with dephasing noise

What the math gives to ML

The paper provides a nonstandard hydrodynamic mechanism: quartic observables acquire late-time diffusive tails because their hydrodynamic eigenoperators are interacting pairs of bilinear modes, even when translationally invariant bilinears have no corresponding tail. The transferable asset is a hierarchy of latent modes whose spatial support and operator size determine which slow components survive projection. A neural sequence model could implement this as a structured long-memory state-space model with diffusive single modes and pair-product modes, rather than forcing every observable to couple directly to one-particle modes. The key falsifiable prediction is an algebraic residual-memory tail whose exponent and amplitude depend on the retained pair modes.