Let There Be Order: Rethinking Ordering in Autoregressive Graph Generation

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Conditional graph generation tasks involve training a model to generate a graph given a set of input conditions. Many previous studies employ autoregressive models to incrementally generate graph components such as nodes and edges. However, as graphs typically lack a natural ordering among their components, converting a graph into a sequence of tokens is not straightforward. While prior works mostly rely on conventional heuristics or graph traversal methods like breadth-first search (BFS) or depth-first search (DFS) to convert graphs to sequences, the impact of ordering on graph generation has largely been unexplored. This paper contributes to this problem by: (1) highlighting the crucial role of ordering in autoregressive graph generation models, (2) proposing a novel theoretical framework that perceives ordering as a dimensionality reduction problem, thereby facilitating a deeper understanding of the relationship between orderings and generated graph accuracy, and (3) introducing "latent sort," a learning-based ordering scheme to perform dimensionality reduction of graph tokens. Our experimental results showcase the effectiveness of latent sort across a wide range of graph generation tasks, encouraging future works to further explore and develop learning-based ordering schemes for autoregressive graph generation.