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 introduced 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 unitary effective spectral radius and zero local Lyapunov exponents, intrinsically operating at the edge of stability. Experiments on synthetic tasks indicate the marked superiority of the proposed approach, compared to standard RC models, in tasks requiring long-term memorization skills. Furthermore, results on real-world time series classification benchmarks point out that EuSN is capable of matching (or even surpassing) the level of accuracy of trainable Recurrent Neural Networks, while allowing up to 100-fold savings in computation time and energy consumption.

翻译：受常微分方程数值解的启发，本文提出一种新型水库计算（RC）模型——欧拉状态网络（EuSN）。该方法利用前向欧拉离散化和反对称循环矩阵，设计出具有内在稳定且非耗散特性的水库动力学。理论分析表明，该模型偏向于具有单位有效谱半径和零局部李雅普诺夫指数，本质上在稳定性边缘运行。合成任务实验表明，在需要长期记忆能力的任务中，所提方法相较于标准RC模型具有显著优势。此外，在真实世界时间序列分类基准上的结果表明，EuSN能够匹配（甚至超越）可训练递归神经网络的精度水平，同时实现计算时间和能耗降低高达100倍。