ReLU Networks for Exact Generation of Similar Graphs
Summary: arXiv:2604.05929v1 Announce Type: cross
Abstract
The generation of graphs constrained by a specified graph edit distance from a source graph is increasingly important in various fields, including cheminformatics, network anomaly synthesis, and structured data augmentation. As the demand for constrained generative models rises, particularly in molecule design and network perturbation analysis, the neural architectures needed to reliably generate graphs within a bounded graph edit distance remain largely unexplored. Existing graph generative models are primarily data-driven, heavily relying on the availability and quality of training data. This dependency often leads to generated graphs that fail to meet the desired edit distance constraints.
Introduction
In this paper, we address these challenges by theoretically characterizing ReLU neural networks capable of generating graphs within a prescribed graph edit distance from a given graph. Our research demonstrates the existence of constant depth and O(n2 d) size ReLU networks that can deterministically generate graphs within an edit distance d from a given input graph with n vertices. This approach eliminates the reliance on training data while guaranteeing the validity of the generated graphs.
Key Findings
- Theoretical characterization of ReLU networks for graph generation.
- Constant depth and O(n2 d) size networks can deterministically generate valid graphs.
- Elimination of reliance on training data ensures validity and adherence to edit distance constraints.
- Experimental evaluations show success in generating valid graphs for instances with up to 1400 vertices.
- Baseline generative models often fail to meet desired edit distance parameters.
Experimental Evaluations
Our experiments indicate that the proposed ReLU network successfully generates valid graphs for instances with a significant number of vertices while maintaining edit distance bounds. In particular, we tested our model on graphs with up to 1400 vertices and found it capable of adhering to edit distance limits of up to 140.
Conclusion
The results presented in this study provide a theoretical foundation for constructing compact generative models that guarantee validity in graph generation. By focusing on ReLU networks, we bridge the gap between the need for constrained graph generation and the limitations imposed by traditional data-driven approaches. This research opens up new avenues for practical applications in various domains, such as drug discovery, where precise graph generation is crucial.
Future Work
Moving forward, additional research is necessary to refine these neural architectures and explore their applicability to more complex graph structures. The potential integration of other neural network types could further enhance our ability to generate graphs with even more intricate constraints.