# SGL: Spectral Graph Learning from Measurements

arXiv: https://arxiv.org/abs/2104.07867 · HTML: https://mlsanity.com/paper/2104.07867/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 16 references that are in the map.
- First posted on arXiv 16 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [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)
- [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)
- [Nearly-Linear Time Spectral Graph Reduction for Scalable Graph Partitioning and Data Visualization](https://mlsanity.com/paper/1812.08942/) (2018)

## Built on by (most cited first, 5 of 5)

- [GARNET: Reduced-Rank Topology Learning for Robust and Scalable Graph Neural Networks](https://mlsanity.com/paper/2201.12741/) (2022)
- [SAGMAN: Stability Analysis of Graph Neural Networks on the Manifolds](https://mlsanity.com/paper/2402.08653/) (2024)
- [SALMAN: Stability Analysis of Language Models Through the Maps Between Graph-based Manifolds](https://mlsanity.com/paper/2508.18306/) (2025)
- [SF-SGL: Solver-Free Spectral Graph Learning from Linear Measurements](https://mlsanity.com/paper/2302.04384/) (2023)
- [A Spectral Framework for Evaluating Geodesic Distances Between Graphs](https://mlsanity.com/paper/2406.10500/) (2024)

## Abstract (arXiv)

This work introduces a highly scalable spectral graph densification framework for learning resistor networks with linear measurements, such as node voltages and currents. We prove that given O(log N) pairs of voltage and current measurements, it is possible to recover ultra-sparse N-node resistor networks which can well preserve the effective resistance distances on the graph. Also, the learned graphs preserve the structural (spectral) properties of the original graph, which can potentially be leveraged in many circuit design and optimization tasks. We show that the proposed graph learning approach is equivalent to solving the classical graphical Lasso problems with Laplacian-like precision matrices. Through extensive experiments for a variety of real-world test cases, we show that the proposed approach is highly scalable for learning ultra-sparse resistor networks without sacrificing solution quality.