A delay dynamical system can fold a feedforward neural network into one nonlinear neuron and multiple delay loops under the non-Von Neumann structure, greatly decreasing the hardware requirements. In this paper, we transform the folded-in-time DNN (Fit-DNN) into a folded-in-time RNN (Fit-RNN) and derive the backpropagation algorithm for it. The performance of the folded reservoir computing (DRC), Fit-DNN, and Fit-RNN is compared on time-series prediction and classification tasks, respectively. The impact of virtual node separation on the performance of Fit-RNN is analyzed. The limits of Fit-RNN's capabilities in conducting effective time-series predictions were determined based on the NARMA-X series tasks. We calculate the 5-order information processing capacity (IPC) of DRC and Fit-RNN on NARMA10. The results indicate that Fit-RNN has almost the necessary information transformation ability for the task. In the recognition tasks conducted separately on spoken digits and speakers, we investigate the impact of the number and separation of virtual nodes on the recognition capability of the three folded networks. The results demonstrate that Fit-RNN shows more promise in handling long sequences and large-scale recognition tasks. The recognition accuracy is further enhanced by increasing the number of virtual nodes and node separation. Furthermore, the introduction of two common types of noise in the speaker recognition task environment further highlights the potential of Fit-RNN in practical applications. Furthermore, two common types of noise are introduced into the speaker recognition task, further highlighting the potential of Fit-RNN in practical applications.

中文翻译：

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非冯·诺依曼架构下用于时间序列预测和分类的单层折叠 RNN

延迟动力系统可以将前馈神经网络折叠成非冯诺依曼结构下的一个非线性神经元和多个延迟环，大大降低了硬件要求。在本文中，我们将时间折叠 DNN (Fit-DNN) 转换为时间折叠 RNN (Fit-RNN)，并推导了其反向传播算法。分别在时间序列预测和分类任务上比较折叠水库计算 (DRC)、Fit-DNN 和 Fit-RNN 的性能。分析了虚拟节点分离对Fit-RNN性能的影响。Fit-RNN 进行有效时间序列预测的能力限制是根据 NARMA-X 系列任务确定的。我们计算了 DRC 和 Fit-RNN 在 NARMA10 上的 5 阶信息处理能力（IPC）。结果表明Fit-RNN几乎具备了该任务所需的信息转换能力。在分别对口语数字和说话人进行的识别任务中，我们研究了虚拟节点的数量和分离对三折叠网络识别能力的影响。结果表明，Fit-RNN 在处理长序列和大规模识别任务方面表现出更大的前景。通过增加虚拟节点数量和节点分离度进一步提高识别精度。此外，在说话人识别任务环境中引入两种常见类型的噪声进一步凸显了 Fit-RNN 在实际应用中的潜力。此外，两种常见类型的噪声被引入到说话人识别任务中，进一步凸显了 Fit-RNN 在实际应用中的潜力。