# Learning to Learn Graph Topologies Source: [Learning to Learn Graph Topologies]() Collection index: [llms.txt]() Data updated: 2026-01-02T03:23:48.834Z Authors: Xingyue Pu, Tianyue Cao, Xiaoyun Zhang, Xiaowen Dong, Siheng Chen Published: 2021-10-19T08:42:38.000Z ## Abstract Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the problem can be formulated as a regularised convex optimisation over a positive semidefinite cone and solved by iterative algorithms. Classic methods require an explicit convex function to reflect generic topological priors, e.g. the $\\ell\_1$ penalty for enforcing sparsity, which limits the flexibility and expressiveness in learning rich topological structures. We propose to learn a mapping from node data to the graph structure based on the idea of learning to optimise (L2O). Specifically, our model first unrolls an iterative primal-dual splitting algorithm into a neural network. The key structural proximal projection is replaced with a variational autoencoder that refines the estimated graph with enhanced topological properties. The model is trained in an end-to-end fashion with pairs of node data and graph samples. Experiments on both synthetic and real-world data demonstrate that our model is more efficient than classic iterative algorithms in learning a graph with specific topological properties. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Graph Reconstruction on Scale-free BA (test)](): Graph Reconstruction; Scale-free BA (test); GMSE: 0.0594. - [Graph Reconstruction on Random sparse (ER) (test)](): Graph Reconstruction; Random sparse (ER) (test); GMSE: 0.0746. - [Graph Reconstruction on Community SBM (test)](): Graph Reconstruction; Community SBM (test); GMSE: 0.0735. - [Graph Reconstruction on Small-world (WS) (test)](): Graph Reconstruction; Small-world (WS) (test); GMSE: 0.0513. - [Brain functional connectivity estimation on Brain functional connectivity (Control Group)](): Brain functional connectivity estimation; Brain functional connectivity (Control Group); Mean Spearman Correlation: 0.76. - [Brain Functional Connectivity Estimation on Autistic Group Data](): Brain functional connectivity estimation; Brain functional connectivity (Autistic Group); Mean Spearman Correlation: 0.34. - [Binary Graph Structure Recovery on Scale-free BA (test)](): Binary graph structure recovery; Scale-free BA binary (test); KS Test Score: 96.15. - [Binary graph structure recovery on Community (SBM) binary (test)](): Binary graph structure recovery; Community (SBM) binary (test); Community Score: 47.9. - [Binary graph structure recovery on Small-world (WS) binary (test)](): Binary graph structure recovery; Small-world (WS) binary (test); Avg Shortest Path Length: 2.225. ## Original sources and implementation [Original paper]() [PDF]() [Implementation]()