Chern-Simons上下文储层计算的可实现性与记忆机制
Feasibility and Memory Mechanisms of Chern-Simons Context Reservoir Computation
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中文总结 AI 辅助
本文探究Chern-Simons上下文储层作为计算基质的可行性，通过对比四个模型，发现全耦合CS动力学在几何与顺序敏感任务上具有特定优势，但非普遍优越。
中文摘要 AI 辅助
我们研究了Chern-Simons（CS）上下文储层是否是一种可行的计算基质，以及演化其规范连接是否比更简单的机制带来额外益处。储层状态是二维上下文流形上的密度涨落，其漂移由密度源连接生成。为区分一般储层行为与规范特定效应，我们比较了四个匹配模型：互易输运、瞬时横向重构、局部非线性反馈以及全耦合守恒流CS动力学。在十个随机种子下，全耦合CS动力学将高斯定律传播至数值精度，在空间和时间细化下收敛，在约束兼容噪声下保持稳定，并且比瞬时控制更准确地满足空间CS方程。所有四个模型都表现出衰减标量记忆，并在密度中区分匹配的脉冲顺序历史，耦合CS没有解决出普遍优势。区别出现在流动几何中：耦合演化同时支持循环和纵向历史通道，在输入移除后短暂保留它们，并产生组合特征脉冲顺序精度\\(0.879\pm0.035\\)，而瞬时横向控制为\\(0.679\pm0.065\\)。演化连接也不能从瞬时密度快照中重建，或由拟合的局部乘子替代。因此，我们发现了针对几何和顺序敏感处理的任务特定优势，而非普遍储层优越性。这里“拓扑”指的是状态的规范组织；所报告的记忆和循环滞后度量不是拓扑不变量。
英文摘要
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.
发表机构
- Center for Philosophical and Cognitive Sciences, ISS Delhi（德里ISS哲学与认知科学中心）
- Indian Institute of Technology Mandi（曼迪印度理工学院）
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