# Euler State Networks: Non-dissipative Reservoir Computing

arXiv: https://arxiv.org/abs/2203.09382 · HTML: https://mlsanity.com/paper/2203.09382/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 83 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Stability](https://mlsanity.com/paper/1310.0150/) (2013)
- [AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks](https://mlsanity.com/paper/1902.09689/) (2019)
- [Reversible Architectures for Arbitrarily Deep Residual Neural Networks](https://mlsanity.com/paper/1709.03698/) (2017)
- [Mobile Sensor Data Anonymization](https://mlsanity.com/paper/1810.11546/) (2018)
- [Multi-level Residual Networks from Dynamical Systems View](https://mlsanity.com/paper/1710.10348/) (2017)
- [Recurrent Orthogonal Networks and Long-Memory Tasks](https://mlsanity.com/paper/1602.06662/) (2016)
- [Fast and Deep Graph Neural Networks](https://mlsanity.com/paper/1911.08941/) (2019)
- [Deep Randomized Neural Networks](https://mlsanity.com/paper/2002.12287/) (2020)
- [Dynamical Systems as Temporal Feature Spaces](https://mlsanity.com/paper/1907.06382/) (2019)
- [Learn to Synchronize, Synchronize to Learn](https://mlsanity.com/paper/2010.02860/) (2020)
- [Investigating echo state networks dynamics by means of recurrence analysis](https://mlsanity.com/paper/1601.07381/) (2016)
- [Input-to-State Representation in linear reservoirs dynamics](https://mlsanity.com/paper/2003.10585/) (2020)

## Built on by (most cited first, 1 of 1)

- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)

## Abstract (arXiv)

Inspired by the numerical solution of ordinary differential equations, in this paper we propose a novel Reservoir Computing (RC) model, called the Euler State Network (EuSN). The presented approach makes use of forward Euler discretization and antisymmetric recurrent matrices to design reservoir dynamics that are both stable and non-dissipative by construction. Our mathematical analysis shows that the resulting model is biased towards a unitary effective spectral radius and zero local Lyapunov exponents, intrinsically operating near to the edge of stability. Experiments on long-term memory tasks show the clear superiority of the proposed approach over standard RC models in problems requiring effective propagation of input information over multiple time-steps. Furthermore, results on time-series classification benchmarks indicate that EuSN is able to match (or even exceed) the accuracy of trainable Recurrent Neural Networks, while retaining the training efficiency of the RC family, resulting in up to ≈ 490-fold savings in computation time and ≈ 1750-fold savings in energy consumption.