Comparative Analysis of Graph Isomorphism and Graph Neural Networks for Analog Hierarchy Labeling

Automated synthesis of analog ICs requires recognition of circuit hierarchies at both the device level and system level. The capability of a model to distinguish between circuit structures allows for the automated synthesis of a topology given a set of specifications. The device groupings also provide symmetry and matching constraints for layout optimization. Traditional methods based on graph isomorphism matching require a manual setup of a library of primitives. While learning-based approaches have been proposed that do not require a library, the categorical specification of a detected group is not returned by prior algorithms. In addition, device sizes are utilized as features, which render the models technology-dependent and infeasible for use before device sizing is performed. To address such limitations, a relational GraphSAGE (R-SAGE) model is proposed that performs multi-class link prediction instead of binary prediction for the labeling of analog functional pairs. The R-SAGE model is characterized and compared with the subgraph isomorphism algorithm VF2 on a dataset that consists of 14 analog circuits with a total of 219 transistors and 120 functional pairs that span seven primitive categories. The R-SAGE model achieves an average macro F1-score of 0.864 and exhibits an average testing time of 80.3 ms across 10 executed runs, outperforming VF2 that provides an average F1-score of 0.841 and an average test time of 594 ms. The proposed R-SAGE model advances machine learning based reasoning of circuit topology. The learned hierarchies provide utility for downstream tasks in the modeling and design of analog circuits.