Reservoir computation models form a subclass of recurrent neural networks with fixed non-trainable input and dynamic coupling weights. Only the static readout from the state space (reservoir) is trainable, thus avoiding the known problems with propagation of gradient information backwards through time. Reservoir models have been successfully applied in a variety of tasks and were shown to be universal approximators of time-invariant fading memory dynamic filters under various settings. Simple cycle reservoirs (SCR) have been suggested as severely restricted reservoir architecture, with equal weight ring connectivity of the reservoir units and input-to-reservoir weights of binary nature with the same absolute value. Such architectures are well suited for hardware implementations without performance degradation in many practical tasks. In this contribution, we rigorously study the expressive power of SCR in the complex domain and show that they are capable of universal approximation of any unrestricted linear reservoir system (with continuous readout) and hence any time-invariant fading memory filter over uniformly bounded input streams.

翻译：储层计算模型是递归神经网络的一个子类，其输入和动态耦合权重固定且不可训练，仅状态空间（储层）的静态读出层可训练，从而避免了梯度信息随时间反向传播的已知问题。储层模型已成功应用于多种任务，并被证明在不同设定下是时不变衰减记忆动态滤波器的普适逼近器。简单循环储层（SCR）是一种高度受限的储层架构，其储层单元采用等权重环状连接，输入到储层的权重具有相同的绝对值且为二元性质。此类架构非常适合硬件实现，且在诸多实际任务中性能无衰减。本文在复数域内严谨研究了SCR的表达能力，证明了其对任意无限制线性储层系统（含连续读出层）具有普适逼近能力，进而能逼近任意均匀有界输入流上的时不变衰减记忆滤波器。