In this paper, we leverage a foundational principle of analog electronic circuitry, Kirchhoff's current and voltage laws, to introduce a distinctive class of neural network models termed KirchhoffNet. Essentially, KirchhoffNet is an analog circuit that can function as a neural network, utilizing its initial node voltages as the neural network input and the node voltages at a specific time point as the output. The evolution of node voltages within the specified time is dictated by learnable parameters on the edges connecting nodes. We demonstrate that KirchhoffNet is governed by a set of ordinary differential equations (ODEs), and notably, even in the absence of traditional layers (such as convolution layers), it attains state-of-the-art performances across diverse and complex machine learning tasks. Most importantly, KirchhoffNet can be potentially implemented as a low-power analog integrated circuit, leading to an appealing property -- irrespective of the number of parameters within a KirchhoffNet, its on-chip forward calculation can always be completed within a short time. This characteristic makes KirchhoffNet a promising and fundamental paradigm for implementing large-scale neural networks, opening a new avenue in analog neural networks for AI.

翻译：本文借鉴模拟电子电路的基本原理——基尔霍夫电流定律和电压定律，提出了一类独特的神经网络模型，称为KirchhoffNet。本质上，KirchhoffNet是一种可作为神经网络运行的模拟电路，利用其初始节点电压作为神经网络输入，并将特定时间点的节点电压作为输出。指定时间内节点电压的演化由连接节点的边上的可学习参数决定。我们证明，KirchhoffNet由一组常微分方程（ODEs）控制，值得注意的是，即使没有传统层（如卷积层），它也能在多种复杂机器学习任务上达到最先进的性能。最重要的是，KirchhoffNet有望实现为低功耗模拟集成电路，从而带来一个引人注目的特性——无论KirchhoffNet内部参数数量如何，其片上前向计算始终能在短时间内完成。这一特性使KirchhoffNet成为实现大规模神经网络的一种有前景的基础范式，为人工智能领域的模拟神经网络开辟了新途径。