Directed Graph Grammars for Sequence-based Learning

TL;DR

This paper introduces a grammar-based method to convert directed acyclic graphs into unique sequential representations, enabling principled decoding, compression, and various applications like graph generation and property prediction.

Contribution

It proposes a novel grammar-based approach to represent DAGs as unique sequences, facilitating decoding, compression, and downstream tasks in a principled manner.

Findings

Provides a lossless, compact DAG representation as sequences.

Enables generative modeling and property prediction for graphs.

Supports Bayesian Optimization over structured graph data.

Abstract

Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains challenging to decode them in a principled manner, because the nodes of a DAG can have many different topological orders. In this work, we propose a grammar-based approach to constructing a principled, compact and equivalent sequential representation of a DAG. Specifically, we view a graph as derivations over an unambiguous grammar, where the DAG corresponds to a unique sequence of production rules. Equivalently, the procedure to construct such a description can be viewed as a lossless compression of the data. Such a representation has many uses, including building a generative model for graph generation, learning a latent space for property prediction, and leveraging the sequence representational continuity for Bayesian Optimization over structured data. Code is available at https://github.com/shiningsunnyday/induction.