# KCLNet: Electrically Equivalence-Oriented Graph Representation Learning for Analog Circuits

arXiv: https://arxiv.org/abs/2603.24101 · HTML: https://mlsanity.com/paper/2603.24101/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [GCN-RL Circuit Designer: Transferable Transistor Sizing with Graph Neural Networks and Reinforcement Learning](https://mlsanity.com/paper/2005.00406/) (2020)
- [CktGNN: Circuit Graph Neural Network for Electronic Design Automation](https://mlsanity.com/paper/2308.16406/) (2023)
- [AutoCkt: Deep Reinforcement Learning of Analog Circuit Designs](https://mlsanity.com/paper/2001.01808/) (2020)
- [DeepGate: Learning Neural Representations of Logic Gates](https://mlsanity.com/paper/2111.14616/) (2021)
- [DeepGate3: Towards Scalable Circuit Representation Learning](https://mlsanity.com/paper/2407.11095/) (2024)
- [Unsupervised Visual Representation Learning by Synchronous Momentum Grouping](https://mlsanity.com/paper/2207.06167/) (2022)
- [DeepGate4: Efficient and Effective Representation Learning for Circuit Design at Scale](https://mlsanity.com/paper/2502.01681/) (2025)
- [TAG: Learning Circuit Spatial Embedding From Layouts](https://mlsanity.com/paper/2209.03465/) (2022)
- [Circuit Representation Learning with Masked Gate Modeling and Verilog-AIG Alignment](https://mlsanity.com/paper/2502.12732/) (2025)

## Abstract (arXiv)

Digital circuits representation learning has made remarkable progress in the electronic design automation domain, effectively supporting critical tasks such as testability analysis and logic reasoning. However, representation learning for analog circuits remains challenging due to their continuous electrical characteristics compared to the discrete states of digital circuits. This paper presents a direct current (DC) electrically equivalent-oriented analog representation learning framework, named KCLNet. It comprises an asynchronous graph neural network structure with electrically-simulated message passing and a representation learning method inspired by Kirchhoff's Current Law (KCL). This method maintains the orderliness of the circuit embedding space by enforcing the equality of the sum of outgoing and incoming current embeddings at each depth, which significantly enhances the generalization ability of circuit embeddings. KCLNet offers a novel and effective solution for analog circuit representation learning with electrical constraints preserved. Experimental results demonstrate that our method achieves significant performance in a variety of downstream tasks, e.g., analog circuit classification, subcircuit detection, and circuit edit distance prediction.