arXiv:2603.15155nlin.CDcs.LG2026-03

小规模确定性网络可存多混沌吸引子,但难凭外部信号切换

Storage and selection of multiple chaotic attractors in minimal reservoir computers

  • 用最小化确定性网络存储多个混沌系统吸引子
  • 在28组系统对中,存储成功率高但切换任务表现不稳
  • 适合研究极简动态系统建模与记忆机制的学者

现代预测建模越来越需要单一学习动力学底座在多种模式下运行。从动力系统视角看,这能力分解为多吸引子存储与响应上下文线索的吸引子选择。在回声状态机(RC)中,多吸引子学习主要依赖大规模随机连接的储池,认为随机连通是产生丰富内部动力学的必要条件。然而近期研究表明,最小化确定性储池在单系统混沌预测上可媲美随机设计。本论文探讨:最小拓扑能否学习多个混沌吸引子?我们发现最小架构能成功存储多个混沌吸引子,但对任务切换(即根据外部信号在吸引子间转换)表现不佳。我们在8个三维混沌系统中测试了所有28个无序系统对的存储与选择任务。10种拓扑结构中,无一在存储或提示依赖选择上始终优于其他。结果表明,尽管最小基底具备建模共存吸引子的表征能力,但可能缺乏实现提示驱动转换所需的鲁棒时序记忆。

原文摘要 · Abstract (English)

Modern predictive modeling increasingly calls for a single learned dynamical substrate to operate across multiple regimes. From a dynamical-systems viewpoint, this capability decomposes into the storage of multiple attractors and the selection of the appropriate attractor in response to contextual cues. In reservoir computing (RC), multi-attractor learning has largely been pursued using large, randomly wired reservoirs, on the assumption that stochastic connectivity is required to generate sufficiently rich internal dynamics. At the same time, recent work shows that minimal deterministic reservoirs can match random designs for single-system chaotic forecasting. Under which conditions can minimal topologies learn multiple chaotic attractors? In this paper, we find that minimal architectures can successfully store multiple chaotic attractors. However, these same architectures struggle with task switching, in which the system must transition between attractors in response to external cues. We test storage and selection on all 28 unordered system pairs formed from eight three-dimensional chaotic systems. We do not observe a robust dependence of multi-attractor performance on reservoir topology. Over the ten topologies investigated, we find that no single one consistently outperforms the others for either storage or cue-dependent selection. Our results suggest that while minimal substrates possess the representational capacity to model coexisting attractors, they may lack the robust temporal memory required for cued transitions.

混沌系统回声状态机记忆机制

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