# Learning Reservoir Dynamics with Temporal Self-Modulation

arXiv: https://arxiv.org/abs/2301.09235 · HTML: https://mlsanity.com/paper/2301.09235/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 75 references that are in the map.
- First posted on arXiv 23 Jan 2023.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [A Survey on Visual Transformer](https://mlsanity.com/paper/2012.12556/) (2020)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [The Computational Limits of Deep Learning](https://mlsanity.com/paper/2007.05558/) (2020)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Machine Learning at the Network Edge: A Survey](https://mlsanity.com/paper/1908.00080/) (2019)
- [Towards deep learning with segregated dendrites](https://mlsanity.com/paper/1610.00161/) (2016)
- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [Supervised Learning in Spiking Neural Networks with FORCE Training](https://mlsanity.com/paper/1609.02545/) (2016)
- [Designing spontaneous behavioral switching via chaotic itinerancy](https://mlsanity.com/paper/2002.08332/) (2020)
- [Real-time ultra-low power ECG anomaly detection using an event-driven neuromorphic processor](https://mlsanity.com/paper/1911.05521/) (2019)
- [A Review of Designs and Applications of Echo State Networks](https://mlsanity.com/paper/2012.02974/) (2020)
- [Transfer learning for nonlinear dynamics and its application to fluid turbulence](https://mlsanity.com/paper/2009.01407/) (2020)
- [Model-Size Reduction for Reservoir Computing by Concatenating Internal States Through Time](https://mlsanity.com/paper/2006.06218/) (2020)
- [Unveiling the role of plasticity rules in reservoir computing](https://mlsanity.com/paper/2101.05848/) (2021)
- [Local Dynamics in Trained Recurrent Neural Networks](https://mlsanity.com/paper/1511.05222/) (2015)
- [Efficient Design of Hardware-Enabled Reservoir Computing in FPGAs](https://mlsanity.com/paper/1805.03033/) (2018)
- [Investigation of Proper Orthogonal Decomposition for Echo State Networks](https://mlsanity.com/paper/2211.17179/) (2022)
- [The Expressivity and Training of Deep Neural Networks: toward the Edge of Chaos?](https://mlsanity.com/paper/1910.04970/) (2019)

## Built on by (most cited first, 4 of 4)

- [Chaos-based reinforcement learning with TD3](https://mlsanity.com/paper/2405.09086/) (2024)
- [Oscillations enhance time-series prediction in reservoir computing with feedback](https://mlsanity.com/paper/2406.02867/) (2024)
- [Boosting Reservoir Computing with Brain-inspired Adaptive Dynamics](https://mlsanity.com/paper/2504.12480/) (2025)
- [Enhancing Time-Series Anomaly Detection by Integrating Spectral-Residual Bottom-Up Attention with Reservoir Computing](https://mlsanity.com/paper/2510.14287/) (2025)

## Abstract (arXiv)

Reservoir computing (RC) can efficiently process time-series data by transferring the input signal to randomly connected recurrent neural networks (RNNs), which are referred to as a reservoir. The high-dimensional representation of time-series data in the reservoir significantly simplifies subsequent learning tasks. Although this simple architecture allows fast learning and facile physical implementation, the learning performance is inferior to that of other state-of-the-art RNN models. In this paper, to improve the learning ability of RC, we propose self-modulated RC (SM-RC), which extends RC by adding a self-modulation mechanism. The self-modulation mechanism is realized with two gating variables: an input gate and a reservoir gate. The input gate modulates the input signal, and the reservoir gate modulates the dynamical properties of the reservoir. We demonstrated that SM-RC can perform attention tasks where input information is retained or discarded depending on the input signal. We also found that a chaotic state emerged as a result of learning in SM-RC. This indicates that self-modulation mechanisms provide RC with qualitatively different information-processing capabilities. Furthermore, SM-RC outperformed RC in NARMA and Lorentz model tasks. In particular, SM-RC achieved a higher prediction accuracy than RC with a reservoir 10 times larger in the Lorentz model tasks. Because the SM-RC architecture only requires two additional gates, it is physically implementable as RC, providing a new direction for realizing edge AI.