Beyond Autoregression: Permutation-Invariant Graph Generation with Scalable Edge Construction

Resul Tugay, Eren Olug, Elif Ak, Şule Gündüz Öğüdücü

Keywords: Graph Generation, Maximum Likelihood Estimation, Link Prediction, KDTree

TL;DR: We propose a non-autoregressive graph generation method that allows flexible control over graph size and structure using node sampling and neighborhood-based edge construction.

Abstract: Graph generation models have advanced significantly with deep learning, yet they remain limited in scalability, flexibility, and their ability to model underlying structures. We present GraphK, a novel encoder-sampler-decoder framework for graph generation that overcomes these challenges through structural flexibility and computational efficiency. Unlike autoregressive approaches constrained by vocabulary size (i.e. number of nodes in graph generation), GraphK enables both upsampling (generating graphs with more nodes than the input) and downsampling, providing fine-grained control over output graph size. By learning permutation-invariant latent representations and sampling new node embeddings via maximum likelihood estimation, GraphK generalizes across graph sizes and structures. For edge generation, we employ link prediction with a KDTree-based top-k neighbour search in the latent space, reducing computational cost. Based on the manifold smoothness assumption, our method effectively captures graph properties. Experiments on synthetic and real-world datasets show that GraphK outperforms existing methods, accurately learns graph structures, and generates synthetic graphs without requiring explicit definitions.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 24581