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

arXiv: https://arxiv.org/abs/2302.04384 · HTML: https://mlsanity.com/paper/2302.04384/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [GCN-RL Circuit Designer: Transferable Transistor Sizing with Graph Neural Networks and Reinforcement Learning](https://mlsanity.com/paper/2005.00406/) (2020)
- [GraphZoom: A multi-level spectral approach for accurate and scalable graph embedding](https://mlsanity.com/paper/1910.02370/) (2019)
- [Learning continuous-time PDEs from sparse data with graph neural networks](https://mlsanity.com/paper/2006.08956/) (2020)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [Learning to Learn Graph Topologies](https://mlsanity.com/paper/2110.09807/) (2021)
- [GLAD: Learning Sparse Graph Recovery](https://mlsanity.com/paper/1906.00271/) (2019)
- [Structured Graph Learning Via Laplacian Spectral Constraints](https://mlsanity.com/paper/1909.11594/) (2019)
- [Estimation of positive definite M-matrices and structure learning for attractive Gaussian Markov Random fields](https://mlsanity.com/paper/1404.6640/) (2014)
- [A General Framework for Fast Stagewise Algorithms](https://mlsanity.com/paper/1408.5801/) (2014)
- [GRASS: Graph Spectral Sparsification Leveraging Scalable Spectral Perturbation Analysis](https://mlsanity.com/paper/1911.04382/) (2019)
- [SGL: Spectral Graph Learning from Measurements](https://mlsanity.com/paper/2104.07867/) (2021)
- [SF-GRASS: Solver-Free Graph Spectral Sparsification](https://mlsanity.com/paper/2008.07633/) (2020)

## Built on by (most cited first, 1 of 1)

- [SAGMAN: Stability Analysis of Graph Neural Networks on the Manifolds](https://mlsanity.com/paper/2402.08653/) (2024)

## Abstract (arXiv)

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.