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.

翻译：本文利用模拟电子电路的基本原理——基尔霍夫电流定律，提出了一类独特的神经网络模型，我们称之为KirchhoffNet。KirchhoffNet与消息传递神经网络和连续深度网络建立了紧密联系。我们证明，即便在没有任何传统层（如卷积层、池化层或线性层）的情况下，KirchhoffNet在MNIST数据集上仍能达到98.86%的测试准确率，与最先进（SOTA）结果相当。更令人关注的是KirchhoffNet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则可通过模拟电子电路物理实现。此外，我们论证了无论KirchhoffNet中的参数数量如何，其前向计算始终可以在1/f秒内完成，其中f表示硬件的时钟频率。这一特性为实现超大规模神经网络提供了一种极具前景的技术。