  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.
