Tree Tensor Network Reservoir Computing: Hierarchical Ensemble with Invariant Phase Boundaries

2026/07/27 by Daiki Sasaki, Chih-Chieh Chen, Tomah Sogabe
#quant-ph

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Abstract

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=√(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.

Citations

• Optuna: A Next-generation Hyperparameter Optimization Framework
• Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach
• Exponential expressivity in deep neural networks through transient chaos
• Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation

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