A Non-Asymptotic Convergent Analysis for Scored-Based Graph Generative Model via a System of Stochastic Differential Equations

Junwei Su, Chuan Wu

TL;DR: This paper provides a non-asymptotic convergent analysis for score-based graph generative models.

Abstract: This paper investigates the convergence behavior of score-based graph generative models (SGGMs). Unlike common score-based generative models (SGMs) that are governed by a single stochastic differential equation (SDE), SGGMs utilize a system of dependent SDEs, where the graph structure and node features are modeled separately, while accounting for their inherent dependencies. This distinction makes existing convergence analyses from SGMs inapplicable for SGGMs. In this work, we present the first convergence analysis for SGGMs, focusing on the convergence bound (the risk of generative error) across three key graph generation paradigms: (1) feature generation with a fixed graph structure, (2) graph structure generation with fixed node features, and (3) joint generation of both graph structure and node features. Our analysis reveals several unique factors specific to SGGMs (e.g., the topological properties of the graph structure) which significantly affect the convergence bound. Additionally, we offer theoretical insights into the selection of hyperparameters (e.g., sampling steps and diffusion length) and advocate for techniques like normalization to improve convergence. To validate our theoretical findings, we conduct a controlled empirical study using a synthetic graph model. The results in this paper contribute to a deeper theoretical understanding of SGGMs and offer practical guidance for designing more efficient and effective SGGMs.

Lay Summary: This paper examines how accurately score-based graph generative models (SGGMs) can create realistic graph data, such as social networks or molecular structures. Unlike traditional methods, SGGMs handle graph connections and node features separately while still accounting for their interactions, making existing analysis methods unsuitable. The authors provide the first theoretical analysis of these models, evaluating their accuracy in different graph-generation tasks: creating node features for existing graph structures, generating graph structures based on given features, and simultaneously generating both. The study highlights critical factors—such as network shape and connectivity—that influence model performance. Additionally, the paper offers practical recommendations for selecting model parameters, helping improve the effectiveness of these generative models.

Primary Area: Social Aspects->Accountability, Transparency, and Interpretability

Keywords: graph generation, score-based generative model, convergence analysis

Submission Number: 3303