Beyond density snapshots: Dynamical memory in Chern-Simons reservoirs

Abstract

How a reservoir encodes input history jointly in density and geometric degrees of freedom remains insufficiently understood. We address this mechanistic gap with a continuous density on an internal manifold coupled to an independently evolving Chern-Simons (CS) connection through a conserved current. On the same internal manifold, we compare reciprocal transport, instantaneous transverse reconstruction, local nonlinear feedback, and coupled CS evolution. These controls isolate how transport and independent connection evolution contribute to memory. We identify a current-generated exact connection component that the tested instantaneous reconstruction and scalar local closure miss. Resetting this component at fixed density and Gauss-law curl changes the future density response within the chosen gauge and drift law and the small effect persists under numerical refinement. We then distinguish dynamical memory from its readout accessibility. Although the four models have similar scalar-memory scores and density traces of pulse order, their circulating and longitudinal traces differ. With all measured features, coupled CS improves pulse-order decoding by \(6.5\pm1.9\) percentage points over the instantaneous-transverse control in paired seedwise comparisons, while remaining comparable to local feedback. Coupled CS shows less lag than the instantaneous and local-feedback controls on the first cycle, but more on subsequent cycles, revealing a dependence on preparation. We thus connect a field-theoretic mechanism of history retention to controlled tests of its dynamical role and computational use. The four-model framework provides a way to determine what an evolving transport field contributes when density snapshots and aggregate performance alone leave the memory mechanism unresolved.