Feasibility and Memory Mechanisms of Chern-Simons Context Reservoir Computation

Abstract:We investigate whether a Chern-Simons (CS) context reservoir is a viable computational substrate and whether evolving its gauge connection provides a benefit beyond simpler mechanisms. The reservoir state is a density fluctuation on a two-dimensional context manifold, whose drift is generated by a density-sourced connection. To separate generic reservoir behavior from gauge-specific effects, we compare four matched models: reciprocal transport, instantaneous transverse reconstruction, local nonlinear feedback, and fully coupled conserved-current CS dynamics. Across ten random seeds, the fully coupled CS dynamics propagates Gauss law to numerical precision, converges under spatial and temporal refinement, remains stable under constraint-compatible noise, and satisfies the spatial CS equation more accurately than the instantaneous controls. All four models exhibit fading scalar memory and distinguish matched pulse-order histories in density, with no resolved general advantage for coupled CS. The distinction appears in the flow geometry: coupled evolution supports circulating and longitudinal history channels simultaneously, retains them briefly after input removal, and yields a combined-feature pulse-order accuracy of \(0.879\pm0.035\), compared with \(0.679\pm0.065\) for the instantaneous-transverse control. The evolved connection also cannot be reconstructed from an instantaneous density snapshot or replaced by a fitted local multiplier. We therefore find a task-specific advantage for geometry- and order-sensitive processing, rather than generic reservoir superiority. Here ``topological'' refers to the gauge organization of the state; the reported memory and cyclic-lag measures are not topological invariants.

Emerging Technologies (cs.ET); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE)

arXiv:2609.13315 [cs.ET]

(or arXiv:2609.13315v1 [cs.ET] for this version)

https://doi.org/10.48550/arXiv.2609.13315 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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