Echo Flow Networks

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arXiv:2509.24122v3 Announce Type: replace Abstract: At the heart of time-series forecasting (TSF) lies a fundamental challenge: how can models efficiently and effectively capture long-range temporal dependencies across ever-growing sequences? While deep learning has brought notable progress, conventional architectures often face a trade-off between computational complexity and their ability to retain accumulative information over extended horizons. Echo State Networks (ESNs), a class of reservoir computing models, have recently regained attention for their exceptional efficiency, offering constant memory usage and per-step training complexity regardless of input length. This makes them particularly attractive for modeling extremely long-term event history in TSF. However, traditional ESNs fall short of state-of-the-art performance due to their limited nonlinear capacity, which constrains both their expressiveness and stability. We introduce Echo Flow Networks (EFNs), a framework composed of a group of extended Echo State Networks (X-ESNs) with MLP readouts, enhanced by our novel Matrix-Gated Composite Random Activation (MCRA), which enables complex, neuron-specific temporal dynamics, significantly expanding the network's representational capacity without compromising computational efficiency. In addition, we propose a dual-stream architecture in which recent input history dynamically selects signature reservoir features from an infinite-horizon memory, leading to improved prediction accuracy and long-term stability. Extensive evaluations on five benchmarks demonstrate …

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