# KirchhoffNet: A Scalable Ultra Fast Analog Neural Network

arXiv: https://arxiv.org/abs/2310.15872 · HTML: https://mlsanity.com/paper/2310.15872/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 24 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [A Survey of Neuromorphic Computing and Neural Networks in Hardware](https://mlsanity.com/paper/1705.06963/) (2017)
- [Training End-to-End Analog Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2006.01981/) (2020)
- [Quantum Deep Learning](https://mlsanity.com/paper/1412.3489/) (2014)
- [Learning Discrete Energy-based Models via Auxiliary-variable Local Exploration](https://mlsanity.com/paper/2011.05363/) (2020)
- [A deep learning theory for neural networks grounded in physics](https://mlsanity.com/paper/2103.09985/) (2021)
- [Advances in Quantum Deep Learning: An Overview](https://mlsanity.com/paper/2005.04316/) (2020)
- [Spiking Neural Networks Hardware Implementations and Challenges: a Survey](https://mlsanity.com/paper/2005.01467/) (2020)
- [DLAU: A Scalable Deep Learning Accelerator Unit on FPGA](https://mlsanity.com/paper/1605.06894/) (2016)
- [On the Forward Invariance of Neural ODEs](https://mlsanity.com/paper/2210.04763/) (2022)
- [When Machine Learning Meets Quantum Computers: A Case Study](https://mlsanity.com/paper/2012.10360/) (2020)
- [SC-DCNN: Highly-Scalable Deep Convolutional Neural Network using Stochastic Computing](https://mlsanity.com/paper/1611.05939/) (2016)
- [A Study of Complex Deep Learning Networks on High Performance, Neuromorphic, and Quantum Computers](https://mlsanity.com/paper/1703.05364/) (2017)
- [A Gradient Estimator for Time-Varying Electrical Networks with Non-Linear Dissipation](https://mlsanity.com/paper/2103.05636/) (2021)
- [Spintronics based Stochastic Computing for Efficient Bayesian Inference System](https://mlsanity.com/paper/1711.01125/) (2017)

## Built on by (most cited first, 1 of 1)

- [Circuit realization and hardware linearization of monotone operator equilibrium networks](https://mlsanity.com/paper/2509.13793/) (2025)

## Abstract (arXiv)

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.