HIERARCHICAL EQUIVARIANT GRAPH GENERATION

Yoann Boget, Pablo Strasser, Alexandros Kalousis

Keywords: graph, generative model, graph generation, hierarchical, coarsening, pooling, lifting, gnn, mpnn, spanning supergraph

TL;DR: We address the scaling issue in graph generation thanks to a hierarchical equivariant generative model for graphs, based on conditioning with minimal spanning supergraphs.

Abstract:

Deep learning, and more specifically denoising models, have significantly improved graph generative modeling. However, challenges remain in capturing global graph properties from local interactions, ensuring scalability, and maintaining node permutation equivariance. While existing equivariant models address node permutation issues, they struggle with scalability, often requiring dense graph representations that scale with $\mathcal{O}(n^2)$.

To overcome these challenges, we introduce a novel coarsening-lifting method that generates sparse spanning supergraphs, preserving global graph properties. These supergraphs serve as both conditioning structures and sparse message-passing layouts for generative models. Leveraging this method with discrete diffusion, we model graphs hierarchically, enabling efficient generation of large graphs.

Our approach, to the best of our knowledge, is the first hierarchical equivariant generative model for graphs. We demonstrate its performance introducing new evaluation datasets with larger graphs and more instances than traditional benchmarks.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 3047