发表机构
IKS Research Centre; ISS; Indian Institute of Technology Mandi（IKS研究中心; 印度统计研究所; 印度理工学院曼迪分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出受林德布拉德启发的多时间尺度储备池计算方法，通过分离旋转与耗散实现模态控制与稳定性保证，在多项时序任务基准测试中表现优异，为可解释循环架构提供了新方案。
AI 中文摘要
回声状态网络通过固定循环动力学、仅训练线性读出层实现高效时序学习，但传统储备池通常在单个随机循环矩阵中同时处理信号混合、记忆保留与稳定性。现有结构化设计虽在拓扑、范数保持、泄漏或深度上有所改进，但通常无法同时对可逆混合与不可逆遗忘提供独立模态控制，也缺乏直接的全局稳定性保证。我们提出一种受经典林德布拉德（Lindblad）启发的多时间尺度储备池，将开放系统动力学原理与结构化状态空间建模相结合。循环算子由精确离散化的阻尼旋转模态组装而成，因此旋转与衰减成为控制相位混合和记忆丢失的独立设计变量。正交模态混合保持正态性，衰减谱直接决定回声状态稳定性裕度，无需事后谱半径缩放。我们在10个对齐种子上，针对线性记忆、非线性循环、混沌预测、延迟逻辑及真实传感器校准任务，将该方法与标准储备池、泄漏储备池、深度储备池、正交储备池、循环储备池及下一代储备池，以及紧凑训练的门控循环单元进行对比评估。在基准测试集上，所提储备池在有界NARMA-20任务上取得最佳固定储备池性能，在Lorenz-63任务上实现最低平均误差，达到最强线性记忆结果，并在广泛基准测试中保持整体竞争力。消融研究表明，旋转可增加状态多样性，而耗散提供可控遗忘并改善预测条件。该框架提供了一种可解释的循环架构，其中混合、记忆与稳定性为明确且可独立调优的设计变量。
英文摘要
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.
CommentsUnder Review at IEEE Transactions on Artificial Intelligence
