Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders (1809.02630v2)

Abstract: Deep generative models have achieved remarkable success in various data domains, including images, time series, and natural languages. There remain, however, substantial challenges for combinatorial structures, including graphs. One of the key challenges lies in the difficulty of ensuring semantic validity in context. For examples, in molecular graphs, the number of bonding-electron pairs must not exceed the valence of an atom; whereas in protein interaction networks, two proteins may be connected only when they belong to the same or correlated gene ontology terms. These constraints are not easy to be incorporated into a generative model. In this work, we propose a regularization framework for variational autoencoders as a step toward semantic validity. We focus on the matrix representation of graphs and formulate penalty terms that regularize the output distribution of the decoder to encourage the satisfaction of validity constraints. Experimental results confirm a much higher likelihood of sampling valid graphs in our approach, compared with others reported in the literature.

Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders

Efforts to advance generative modeling have demonstrated significant achievements across various data modalities, yet the task of generating semantically valid combinatorial structures, such as graphs, remains challenging. This paper addresses the generation of semantically valid graphs by proposing a regularization framework for Variational Autoencoders (VAEs), particularly focusing on graph representations under constraints related to semantic validity.

Core Contributions and Methodology

The paper introduces a novel regularization framework for VAEs to enforce semantic validity in generated graphs. The proposed method adds penalty terms to the generative process, which ensure that constraints regarding graph properties, such as connectivity, node compatibility, and valence (in the context of molecular graphs), are respected. These constraints are formulated using the node-label matrix and edge-label tensor, forming the fundamental structure of probabilistic graph models in this paper.

By transforming the constrained optimization of graph semantic validity into a regularized, unconstrained problem, this paper constructs penalty terms that can be integrated into the VAE framework. This strategic regularization approach stands on the principle that the semantic constraints of graph generation can be represented as probability distributions of node and edge types, thereby ensuring the structural integrity and validity of generated graphs in accordance with specific applications.

Experimental Evaluation

The effectiveness of the proposed approach is demonstrated using both real-world and synthetic datasets, focusing on two primary tasks: the generation of molecular graphs and node-compatible graphs. The empirical results indicate a higher likelihood of generating valid graph samples. For instance, in experiments with the QM9 molecular dataset, the proposed model achieved a 96.6% validity rate for generated graphs, significantly outperforming baseline methods. This outcome is complemented by a strong novelty rate and competitive reconstruction capabilities, showcasing the practical applicability of the method in graph generation domains.

Implications and Future Directions

The implications of this work are twofold—practical and theoretical. Practically, the proposed regularization technique has potential applications in domains requiring valid graph generation, such as drug discovery where molecular graphs are pivotal. Theoretical implications pertain to the enhancement of the flexibility and expressivity of VAEs in handling complex, structure-constrained data, thereby advancing the methodologies for graph-based generative modeling.

Future developments may endeavor to optimize the balance between penalization strength and model expressive power further, alongside exploring the adaptation to more sophisticated graph types and constraints. Additionally, scaling the computational feasibility for larger and more diverse datasets represents an intriguing challenge for future research endeavors.

In conclusion, this paper provides a robust framework for addressing the generation of semantically valid combinatorial graphs. By embedding constraints directly into the generative model, it lays the groundwork for more advanced applications and interpretations across various scientific and industrial fields involving complex data structures.