Directed Graph Grammars for Sequence-based Learning

2025-05-29

AI Summary

To address the ambiguity and redundancy in DAG serialization arising from non-unique topological orders, this paper proposes a reversible generative framework based on an unambiguous context-free graph grammar: it uniquely maps each DAG to a deterministic sequence of production rules, eliminating reliance on topological sorting while ensuring representation compactness, uniqueness, and invertibility. Methodologically, we formulate DAG generation as an unambiguous syntactic derivation process—the first such formulation—and introduce a normalized traversal strategy coupled with a rule-serialization mechanism. The framework enables lossless DAG compression, differentiable graph generation, continuous latent-space learning for attribute prediction, and efficient Bayesian optimization over structured data. It combines theoretical rigor—guaranteeing bijective mapping—with interpretable, syntax-driven generation.

Technology Category

• Natural Language Processing: Generation
• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Decoding DAGs with multiple topological orders
• Constructing sequential representations using grammars
• Enabling generative models and property prediction

Innovation

• Grammar-based approach for DAG sequential representation
• Unique sequence of production rules for DAGs
• Lossless compression of structured data