Directed Graph Grammars for Sequence-based Learning
This addresses a bottleneck in sequence-based learning for DAGs, offering a novel method for structured data representation.
The authors tackled the challenge of decoding directed acyclic graphs (DAGs) by proposing a grammar-based approach that constructs a principled, compact sequential representation, enabling applications like generative modeling and Bayesian optimization.
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.