cs.LGMar 25, 2026

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

Authors: Peng Xu, Yapeng Li, Tinghuan Chen, Tsung-Yi Ho, Bei Yu

Organizations: Department of Computer Science & Engineering, The Chinese University of Hong Kong · School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen)

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Abstract

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.

Figures & tables

Figure 1: ΔΣ\Delta\Sigma analog-to-digital converter (ADC), a typical analog circuit type.
DeviceNumber of PinsPin types
NMOSnd+ng+ns+nbn_{d}+n_{g}+n_{s}+n_{b}nd, ng, ns, nb
PMOSnd+ng+ns+nbn_{d}+n_{g}+n_{s}+n_{b}pd, pg, ps, pb
NPNnb+nc+nen_{b}+n_{c}+n_{e}nb, nc, ne
PNPnb+nc+nen_{b}+n_{c}+n_{e}nb, nc, ne
Diode2n+, n-
Resistor2n+, n-
Table 1: Typical Analog Device Types
Figure 2: Directed acyclic circuit graph representation: (1) analog circuit; (2) convert bipartite graph representation (left) to DAG via topology sorting (right); (3) electrically-simulated asynchronous message passing scheme.
Figure 3: The framework of the physics-guided contrastive learning scheme, named the KCL Loss
Figure 4: The illustration of the downstream tasks: (1) Analog circuit classification ; (2) Analog subcircuit detection ; (3) Analog GED preidction .
MethodAcc@1 ↑\uparrowAcc@2 ↑\uparrowAcc@5 ↑\uparrowRecall ↑\uparrowF1 Score ↑\uparrow
Base Models
GCN0.561 ±0.061{}_{\pm{\text{0.061}}}0.784 ±0.040{}_{\pm{\text{0.040}}}0.913 ±0.014{}_{\pm{\text{0.014}}}0.405 ±0.087{}_{\pm{\text{0.087}}}0.404 ±0.121{}_{\pm{\text{0.121}}}
GAT0.479 ±0.105{}_{\pm{\text{0.105}}}0.681 ±0.148{}_{\pm{\text{0.148}}}0.794 ±0.118{}_{\pm{\text{0.118}}}0.327 ±0.060{}_{\pm{\text{0.060}}}0.275 ±0.069{}_{\pm{\text{0.069}}}
GATv20.498 ±0.100{}_{\pm{\text{0.100}}}0.694 ±0.139{}_{\pm{\text{0.139}}}0.799 ±0.133{}_{\pm{\text{0.133}}}0.322 ±0.051{}_{\pm{\text{0.051}}}0.270 ±0.075{}_{\pm{\text{0.075}}}
GIN0.786 ±0.077{}_{\pm{\text{0.077}}}0.883 ±0.058{}_{\pm{\text{0.058}}}0.931 ±0.039{}_{\pm{\text{0.039}}}0.648 ±0.101{}_{\pm{\text{0.101}}}0.669 ±0.118{}_{\pm{\text{0.118}}}
SAGE0.774 ±0.019{}_{\pm{\text{0.019}}}0.927 ±0.023{}_{\pm{\text{0.023}}}0.938 ±0.004{}_{\pm{\text{0.004}}}0.626 ±0.028{}_{\pm{\text{0.028}}}0.638 ±0.055{}_{\pm{\text{0.055}}}
Table 2: Performance comparison on analog circuit classification. Top performers in each category are bold.
MethodmAP ↑\uparrowRecall ↑\uparrowF1 Score ↑\uparrowAUC ↑\uparrowIoU ↑\uparrow
Base Models
GCN0.368 ±0.002{}_{\pm{\text{0.002}}}0.260 ±0.004{}_{\pm{\text{0.004}}}0.225 ±0.003{}_{\pm{\text{0.003}}}0.796 ±0.002{}_{\pm{\text{0.002}}}0.144 ±0.002{}_{\pm{\text{0.002}}}
GAT0.383 ±0.013{}_{\pm{\text{0.013}}}0.290 ±0.033{}_{\pm{\text{0.033}}}0.262 ±0.038{}_{\pm{\text{0.038}}}0.808 ±0.012{}_{\pm{\text{0.012}}}0.170 ±0.032{}_{\pm{\text{0.032}}}
GATv20.382 ±0.017{}_{\pm{\text{0.017}}}0.303 ±0.059{}_{\pm{\text{0.059}}}0.279 ±0.072{}_{\pm{\text{0.072}}}0.807 ±0.022{}_{\pm{\text{0.022}}}0.183 ±0.051{}_{\pm{\text{0.051}}}
GIN0.553 ±0.029{}_{\pm{\text{0.029}}}0.667 ±0.019{}_{\pm{\text{0.019}}}0.695 ±0.020{}_{\pm{\text{0.020}}}0.932 ±0.005{}_{\pm{\text{0.005}}}0.565 ±0.021{}_{\pm{\text{0.021}}}
SAGE0.355 ±0.004{}_{\pm{\text{0.004}}}0.255 ±0.002{}_{\pm{\text{0.002}}}0.211 ±0.002{}_{\pm{\text{0.002}}}0.785 ±0.001{}_{\pm{\text{0.001}}}0.133 ±0.001{}_{\pm{\text{0.001}}}
Table 3: Performance comparison on subcircuit detection task.
Figure 5: The averaged and normalized performance comparison on the analog circuit GED prediction task.
Figure 6: Comparison between KCLNet with different variants of KCL Loss.
Figure 7: The pre-training epochs impact of KCLNet on classification, which outperforms general graph pretraining at earlier epochs.
 ClassificationDetection
 Acc@1 ↑\uparrowF1-Score ↑\uparrowmAP ↑\uparrowIoU ↑\uparrow
GCN0.561 ±0.061{}_{\pm{\text{0.061}}}0.404 ±0.121{}_{\pm{\text{0.121}}}0.368 ±0.002{}_{\pm{\text{0.002}}}0.144 ±0.002{}_{\pm{\text{0.002}}}
GAT0.496 ±0.127{}_{\pm{\text{0.127}}}0.306 ±0.101{}_{\pm{\text{0.101}}}0.383 ±0.013{}_{\pm{\text{0.013}}}0.170 ±0.032{}_{\pm{\text{0.032}}}
GATv20.498 ±0.100{}_{\pm{\text{0.100}}}0.270 ±0.075{}_{\pm{\text{0.075}}}0.382 ±0.017{}_{\pm{\text{0.017}}}0.183 ±0.051{}_{\pm{\text{0.051}}}
GIN0.786 ±0.077{}_{\pm{\text{0.077}}}0.669 ±0.118{}_{\pm{\text{0.118}}}0.553 ±0.029{}_{\pm{\text{0.029}}}0.565 ±0.021{}_{\pm{\text{0.021}}}
SAGE0.774 ±0.019{}_{\pm{\text{0.019}}}0.638 ±0.055{}_{\pm{\text{0.055}}}0.355 ±0.004{}_{\pm{\text{0.004}}}0.133 ±0.001{}_{\pm{\text{0.001}}}
Table 4: Performance comparison between synchronous and asynchronous message passing (AGNN).

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