SF-SGL: Solver-Free Spectral Graph Learning From Linear Measurements

Zhang, Ying; Zhao, Zhiqiang; Feng, Zhuo

doi:10.1109/tcad.2022.3198513

Cited by 1 publication

(1 citation statement)

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“…A spectrum decomposition perspective. As shown in [51], the spectrally-coarsened graphs will carry different (spectrum) bandwidths of the original graph G. For example, the coarsest graph Laplacian L G l f will only preserve the key spectral properties of G 0 , such as the first few Laplacian eigenvalues and eigenvectors, whereas the Laplacians of the increasingly finer graphs will match the lower to moderate eigenvalues of L G0 . Consequently, the coarsened graphs can be considered as a cascade of low-pass graph filters with gradually decreasing bandwidths: the finest graph retains the highest bandwidth, whereas the coarsest graph retains the lowest bandwidth.…”

Section: B Graph Topology Learning Via a Bottom-up Approachmentioning

confidence: 99%

SF-SGL: Solver-Free Spectral Graph Learning from Linear Measurements

Zhang,

Zhao,

Feng

2023

Preprint

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This work introduces a highly-scalable spectral graph densification framework (SGL) for learning resistor networks with linear measurements, such as node voltages and currents. We show that the proposed graph learning approach is equivalent to solving the classical graphical Lasso problems with Laplacian-like precision matrices. We prove that given O(log N ) pairs of voltage and current measurements, it is possible to recover sparse N -node resistor networks that can well preserve the effective resistance distances on the original graph. In addition, the learned graphs also preserve the structural (spectral) properties of the original graph, which can potentially be leveraged in many circuit design and optimization tasks.To achieve more scalable performance, we also introduce a solver-free method (SF-SGL) that exploits multilevel spectral approximation of the graphs and allows for a scalable and flexible decomposition of the entire graph spectrum (to be learned) into multiple different eigenvalue clusters (frequency bands). Such a solver-free approach allows us to more efficiently identify the most spectrally-critical edges for reducing various ranges of spectral embedding distortions. Through extensive experiments for a variety of real-world test cases, we show that the proposed approach is highly scalable for learning sparse resistor networks without sacrificing solution quality. We also introduce a datadriven EDA algorithm for vectorless power/thermal integrity verifications to allow estimating worst-case voltage/temperature (gradient) distributions across the entire chip by leveraging a few voltage/temperature measurements.

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Section: B Graph Topology Learning Via a Bottom-up Approachmentioning

confidence: 99%