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

TL;DR

This paper presents a scalable spectral graph learning framework for resistor networks using linear measurements, combining classical graphical Lasso equivalence with a novel solver-free spectral approximation method for efficient graph reconstruction.

Contribution

It introduces SF-SGL, a solver-free spectral graph densification method that improves scalability and efficiency in learning resistor networks from limited measurements.

Findings

Achieves accurate resistor network recovery with O(log N) measurements.

Preserves spectral and structural properties of the original graph.

Demonstrates high scalability and solution quality in real-world tests.

Abstract

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 data-driven 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.