arXiv:2608.04028cs.LGcs.AI2026-08

提出可独立调控记忆与混合的多时标储池,提升时间序列建模稳定性与性能。

Lindblad-Inspired Multi-Timescale Reservoir Computing with Separable Rotation and Dissipation

论文配图:Lindblad-Inspired Multi-Timescale Reservoir Computing with Separable Rotation and Dissipation
图 1 · 摘自论文原文
  • 基于林德布拉德原理设计旋转与衰减分离的递归算子
  • 在Lorenz-63上实现最低均方误差,NARMA-20表现最佳
  • 适合需要可解释性与稳定性的时序建模任务

回声状态网络通过固定递归动态并仅训练线性读出实现高效时序学习。然而传统储池通常将信号混合、记忆保持与稳定性集成于单一随机递归矩阵中。现有结构化设计虽改进拓扑、范数保持、泄漏或深度,但普遍无法独立控制可逆混合与不可逆遗忘,并缺乏全局稳定性保证。本文提出一类受林德布拉德启发的多时标储池,将递归算子构建为精确离散化的阻尼旋转模式,使旋转与衰减成为独立的设计变量,分别控制相位混合与记忆衰减。正交模式混合保持正规性,衰减谱直接决定回声态稳定性裕度,无需事后谱半径缩放。在十组对齐种子下,对比标准、漏失、深层、正交、循环及下一代储池,以及紧凑型门控循环单元,在线性记忆、非线性递归、混沌预测、延迟逻辑与真实传感器校准任务上进行评估。在基准测试集上,该方法在有界NARMA-20上达到最优固定储池性能,洛伦兹-63均方误差最低,线性记忆结果最强,并在多数任务上保持竞争力。消融实验表明,旋转提升状态多样性,衰减提供可控遗忘并改善预测条件。该框架提供一个可解释的递归架构,其中混合、记忆与稳定性均为显式且独立可调的设计变量。

原文摘要 · Abstract (English)

Echo-state networks enable efficient temporal learning by fixing the recurrent dynamics and training only a linear readout. However, conventional reservoirs typically accommodate signal mixing, memory retention, and stability within a single random recurrent matrix. Existing structured designs improve topology, norm preservation, leakage, or depth, but generally do not provide separate modal control of reversible mixing and irreversible forgetting together with a direct global stability guarantee. We introduce a classical Lindblad-inspired multi-timescale reservoir that bridges open-system dynamical principles with structured state-space modeling. The recurrent operator is assembled from exactly discretized damped rotational modes, so rotation and decay become independent design variables governing phase mixing and memory loss. Orthogonal mode mixing preserves normality, while the decay spectrum directly determines the echo-state stability margin without post-hoc spectral-radius rescaling. We evaluate the method over ten aligned seeds against standard, leaky, deep, orthogonal, cycle, and next-generation reservoirs, together with a compact trained gated recurrent unit, across linear memory, nonlinear recurrence, chaotic forecasting, delayed logic, and real sensor calibration. Across the benchmark suite, the proposed reservoir achieves the best fixed-reservoir performance on bounded NARMA-20 and the lowest mean error on Lorenz-63, matches the strongest linear-memory result, and remains broadly competitive across broad range of benchmarks. Ablation studies show that rotation increases state diversity, whereas dissipation provides controlled forgetting and improves predictive conditioning. The resulting framework offers an interpretable recurrent architecture in which mixing, memory, and stability are explicit and independently tunable design variables.

储池计算时序建模可解释性稳定性

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