In this paper, we exploit a fundamental principle of analog electronic circuitry, Kirchhoff's current law, to introduce a unique class of neural network models that we refer to as KirchhoffNet. KirchhoffNet establishes close connections with message passing neural networks and continuous-depth networks. We demonstrate that even in the absence of any traditional layers (such as convolution, pooling, or linear layers), KirchhoffNet attains 98.86% test accuracy on the MNIST dataset, comparable with state of the art (SOTA) results. What makes KirchhoffNet more intriguing is its potential in the realm of hardware. Contemporary deep neural networks are conventionally deployed on GPUs. In contrast, KirchhoffNet can be physically realized by an analog electronic circuit. Moreover, we justify that irrespective of the number of parameters within a KirchhoffNet, its forward calculation can always be completed within 1/f seconds, with f representing the hardware's clock frequency. This characteristic introduces a promising technology for implementing ultra-large-scale neural networks.

利用模拟电子电路的基本原理――基尔霍夫电流定律，引入一种称为KirchhoffNet的独特类神经网络模型，与消息传递神经网络和连续深度网络密切相关。我们证明即使在没有传统层（如卷积、池化或线性层）的情况下，KirchhoffNet在MNIST数据集上达到了98.86%的测试准确率，与最新成果相媲美。KirchhoffNet更引人注目的是其在硬件领域的潜力。当代深度神经网络通常部署在GPU上，而KirchhoffNet可以通过模拟电子电路实现。此外，我们证明了无论KirchhoffNet中有多少参数，其正向计算始终可以在1/f秒内完成，其中f表示硬件的时钟频率。这一特征为实现超大规模神经网络提供了有希望的技术。

KirchhoffNet: 电路桥接的消息传递和连续深度模型