Learning to generate feasible graphs using graph grammars

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

• The paper introduces a novel graph generative framework using graph grammars integrated with MCMC to handle complex domain-specific constraints and long-range dependencies.
• Empirical tests on drug molecules and RNA structures show the method effectively generates graphs adhering to domain constraints, demonstrating comparable performance to domain-specific tools while capturing long-range structures.
• The work highlights the utility of graph grammars for generating constrained graphs and offers flexibility through user-defined coarsening, paving the way for applications in various domains requiring structural fidelity.

Learning to Generate Feasible Graphs Using Graph Grammars

The paper "Learning to Generate Feasible Graphs Using Graph Grammars" by Stefan Mautner, Rolf Backofen, and Fabrizio Costa presents an innovative approach to graph generation by leveraging graph grammars. This methodology addresses the key challenge of maintaining feasibility with respect to domain-specific constraints, especially when dealing with both local and long-range dependencies.

Methodological Approach

The authors propose a novel graph generative framework that harnesses graph grammars, primarily to avoid the pitfalls of existing methods, such as those based on message passing neural networks. The inherent challenge with neural methods is the dilution of information, which severely constrains their ability to capture long-range dependencies effectively. In contrast, the method presented in this work introduces a domain-dependent coarsening procedure. This procedure helps in forming shortcuts for modeling long-range dependencies by operating at multiple levels of abstraction within the graph.

Key to the authors' approach is the integration of the Metropolis Hastings (MH) Markov Chain Monte Carlo (MCMC) method. This method effectively balances the complexity of local constraints using a context-sensitive graph grammar while addressing global constraints through a regularized statistical model. The core/interfaces graph grammar is employed, which allows for decomposing graph transformations into manageable pieces, thus allowing efficient sampling of feasible graph structures from a given probability distribution.

Empirical Demonstration and Results

The effectiveness of the proposed generative model is examined in two distinct domains: small-molecule drug graphs and RNA secondary structures. In the chemical domain, the framework is benchmarked against the Molecular Sets (MOSES), demonstrating comparable performance metrics, including lipophilicity, synthesizability, and drug-likeness against domain-specific methods, but with the notable advantage of covering complex long-range constraints inherently defined in the graph grammar structure.

For RNA secondary structures, the ability of the method to generate graphs with hundreds of nodes is showcased. The generative process is validated by ensuring that the output adheres to the constraints delineated by the "Infernal" covariance model. This model is used to verify the biological viability of synthesized sequences, ensuring adherence to known RNA families. The experimental outcomes signal that the method can sustain the balance between graph novelty and adherence to domain-specific global structure constraints.

Implications and Future Outlook

The broader implications of this work emphasize the applicability of graph grammars for domains requiring stringent constraint satisfaction and the capacity to generalize over diverse structural motifs. Notably, the capacity for user-defined graph coarsening procedures offers valuable flexibility, permitting the model to be tailored to specific structural nuances of varied graph-based domains.

The paper hints at future directions, notably the automated learning of coarsening procedures via machine learning techniques. This could drastically enhance the scalability and adaptability of the model across various domains. Furthermore, optimizing the computational performance while handling extensive long-range dependencies remains a focal point for ongoing research.

Consequently, this paper offers an insightful contribution to the field of graph generation, especially by introducing a method capable of structural fidelity and flexibility across domains characterized by diverse dependency complexities. The integration of graph grammars with modern computational techniques effectively broadens the horizon for feasible graph synthesis in computational and biological settings.