Learning to generate feasible graphs using graph grammars

TL;DR

This paper introduces a graph grammar-based generative method with domain-dependent coarsening to effectively model complex, long-range dependencies in graph generation, demonstrated on molecular and RNA structures.

Contribution

It proposes a novel graph grammar approach with coarsening to address message passing limitations in modeling long-range dependencies.

Findings

Outperforms existing methods on molecular graph benchmarks.

Generates valid large RNA secondary structure graphs.

Effective in modeling complex long-range dependencies.

Abstract

Generative methods for graphs need to be sufficiently flexible to model complex dependencies between sets of nodes. At the same time, the generated graphs need to satisfy domain-dependent feasibility conditions, that is, they should not violate certain constraints that would make their interpretation impossible within the given application domain (e.g. a molecular graph where an atom has a very large number of chemical bounds). Crucially, constraints can involve not only local but also long-range dependencies: for example, the maximal length of a cycle can be bounded. Currently, a large class of generative approaches for graphs, such as methods based on artificial neural networks, is based on message passing schemes. These approaches suffer from information 'dilution' issues that severely limit the maximal range of the dependencies that can be modeled. To address this problem, we propose a generative approach based on the notion of graph grammars. The key novel idea is to introduce a domain-dependent coarsening procedure to provide short-cuts for long-range dependencies. We show the effectiveness of our proposal in two domains: 1) small drugs and 2) RNA secondary structures. In the first case, we compare the quality of the generated molecular graphs via the Molecular Sets (MOSES) benchmark suite, which evaluates the distance between generated and real molecules, their lipophilicity, synthesizability, and drug-likeness. In the second case, we show that the approach can generate very large graphs (with hundreds of nodes) that are accepted as valid examples for a desired RNA family by the "Infernal" covariance model, a state-of-the-art RNA classifier. Our implementation is available on github: github.com/fabriziocosta/GraphLearn