# Feasibility and Memory Mechanisms of Chern-Simons Context Reservoir Computation

arXiv: https://arxiv.org/abs/2609.13315 · HTML: https://mlsanity.com/paper/2609.13315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [Separation of Chaotic Signals by Reservoir Computing](https://mlsanity.com/paper/1910.10080/) (2019)
- [Adding Filters to Improve Reservoir Computer Performance](https://mlsanity.com/paper/2008.10633/) (2020)
- [Transport in reservoir computing](https://mlsanity.com/paper/2209.07946/) (2022)

## Abstract (arXiv)

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±0.035), compared with (0.679±0.065) 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.