树张量网络储层计算：具有不变相位边界的分层集成
Tree Tensor Network Reservoir Computing: Hierarchical Ensemble with Invariant Phase Boundaries
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中文总结 AI 辅助
提出树张量网络储层计算框架TTN-RC用于时间序列预测，引入分层集成方法，在NARMA基准测试中有竞争力。基于储层雅可比矩阵推导收缩率并进行平均场描述，确定渐近稳定性边界，为张量网络储层计算提供设计原则。
中文摘要 AI 辅助
我们提出树张量网络储层计算（TTN-RC），这是一种受量子启发的用于时间序列预测的储层计算框架，它将树张量网络的分层结构用作随机储层。为控制TTN输出的指数集中或发散，我们引入分层集成方法，将固定大小的储层划分为多个独立子储层。在测试的NARMA基准中，TTN-RC与传统回声状态网络相比具有竞争力或更优性能。我们还基于储层雅可比矩阵推导了预期收缩率，并对储层状态统计进行了平均场描述。这些分析确定了在大树规模极限下，σT = √2 处的渐近稳定性边界，多个理论指标在此收敛。我们的结果为基于张量网络的储层计算提供了设计原则，并阐明了分层储层拓扑如何控制稳定性和非线性信息处理。
英文摘要
We propose Tree Tensor Network Reservoir Computing (TTN-RC), a quantum-inspired reservoir computing framework for time-series prediction that uses the hierarchical structure of Tree Tensor Networks as a random reservoir. To control the exponential concentration or divergence of TTN outputs, we introduce a hierarchical ensemble method that partitions a fixed-size reservoir into multiple independent sub-reservoirs. In the tested NARMA benchmarks, TTN-RC achieves competitive or improved performance compared with conventional Echo State Networks, especially for tasks requiring higher-order nonlinear processing and longer contextual dependence. We also derive an expected contraction rate based on the reservoir Jacobian and develop a mean-field description of the reservoir-state statistics. These analyses identify an asymptotic stability boundary at $σ_{T}=\sqrt{2}$ in the large per-tree-size limit, where several theoretical indicators converge. Our results provide a design principle for tensor-network-based reservoir computing and clarify how hierarchical reservoir topology controls stability and nonlinear information processing.
