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Flowette: Flow Matching with Graphette Priors for Graph Generation

Asiri Wijesinghe, Sevvandi Kandanaarachchi, Daniel M. Steinberg, Cheng Soon Ong

TL;DR

This work proposes Flowette, a continuous flow matching framework, that employs a graph neural network based transformer to learn a velocity field defined over graph representations with node and edge attributes, and introduces graphettes, a new probabilistic family of graph structure models that generalize graphons via controlled structural edits for motifs like rings, stars and trees.

Abstract

We study generative modeling of graphs with recurring subgraph motifs. We propose Flowette, a continuous flow matching framework, that employs a graph neural network based transformer to learn a velocity field defined over graph representations with node and edge attributes. Our model preserves topology through optimal transport based coupling, and long-range structural dependencies through regularisation. To incorporate domain driven structural priors, we introduce graphettes, a new probabilistic family of graph structure models that generalize graphons via controlled structural edits for motifs like rings, stars and trees. We theoretically analyze the coupling, invariance, and structural properties of the proposed framework, and empirically evaluate it on synthetic and small-molecule graph generation tasks. Flowette demonstrates consistent improvements, highlighting the effectiveness of combining structural priors with flow-based training for modeling complex graph distributions.

Flowette: Flow Matching with Graphette Priors for Graph Generation

TL;DR

This work proposes Flowette, a continuous flow matching framework, that employs a graph neural network based transformer to learn a velocity field defined over graph representations with node and edge attributes, and introduces graphettes, a new probabilistic family of graph structure models that generalize graphons via controlled structural edits for motifs like rings, stars and trees.

Abstract

We study generative modeling of graphs with recurring subgraph motifs. We propose Flowette, a continuous flow matching framework, that employs a graph neural network based transformer to learn a velocity field defined over graph representations with node and edge attributes. Our model preserves topology through optimal transport based coupling, and long-range structural dependencies through regularisation. To incorporate domain driven structural priors, we introduce graphettes, a new probabilistic family of graph structure models that generalize graphons via controlled structural edits for motifs like rings, stars and trees. We theoretically analyze the coupling, invariance, and structural properties of the proposed framework, and empirically evaluate it on synthetic and small-molecule graph generation tasks. Flowette demonstrates consistent improvements, highlighting the effectiveness of combining structural priors with flow-based training for modeling complex graph distributions.
Paper Structure (66 sections, 18 theorems, 103 equations, 8 figures, 9 tables, 9 algorithms)

This paper contains 66 sections, 18 theorems, 103 equations, 8 figures, 9 tables, 9 algorithms.

Table of Contents

  1. Introduction
  2. Background and setting
  3. Flow Matching on Graphs
  4. Related Work.
  5. Flow matching
  6. Structural priors
  7. Structure Preserving Flows
  8. Graph Structure Coupling, $(G_0, G_1)$
  9. FGW-Distance Computation.
  10. Batch-Level Coupling via Hungarian Matching.
  11. Flow Matching on FGW-Coupled Graphs.
  12. Flow Matching Learning Objective
  13. Local Velocity Matching Loss.
  14. Endpoint Consistency Loss.
  15. Chemistry-Aware Regularization.
  16. ...and 51 more sections

Key Result

Theorem 4.5

Let $\mathcal{W} = (W, \rho_n, f)$ denote a graphette and let $G' \sim \mathsf{G}(n, W, \rho_n)$ and $G \sim f(G')$ where $f \in \{R, S\}$ (GEF motif:ring3, motif:star) with ring size $c > 3$ for $R$. Suppose $|V(G')| = n$ and $|V(G)| = n + m$. Then for any triangle-covered $F \in \mathcal{F}$, $\ho

Figures (8)

  • Figure 1: Flowette training scheme. FGW optimal transport with Hungarian matching discussed in Sec. \ref{['sec:fgw_fm']}, GNN Transformer in App. \ref{['sec:gnn_transformer']}, Topology-aware loss and regularisation in Sec. \ref{['sec:learning_objective']} and graphettes in Sec. \ref{['sec:Graphettes']}. See Algorithm \ref{['alg:fgw_fm_training']} for details.
  • Figure 2: Graphs generated by Flowette for the Tree synthetic datasets.
  • Figure 3: Graphs generated by Flowette for the SBM synthetic datasets.
  • Figure 4: Graphs generated by Flowette for the Ego-small synthetic datasets.
  • Figure 5: Graphs generated by Flowette for the ZINC250k molecular datasets.
  • ...and 3 more figures

Theorems & Definitions (40)

  • Definition 2.1
  • Definition 2.2
  • Definition 4.1
  • Remark 4.2
  • Definition 4.3
  • Definition 4.4
  • Theorem 4.5
  • Proposition 2.0
  • Lemma 3.0
  • proof
  • ...and 30 more