Any2Graph: Deep End-To-End Supervised Graph Prediction With An Optimal Transport Loss

TL;DR

Any2graph, a generic framework for end-to-end Supervised Graph Prediction (SGP) i.e. a deep learning model that predicts an entire graph for any kind of input, is proposed and is designed to handle any-sized graphs.

Abstract

We propose Any2graph, a generic framework for end-to-end Supervised Graph Prediction (SGP) i.e. a deep learning model that predicts an entire graph for any kind of input. The framework is built on a novel Optimal Transport loss, the Partially-Masked Fused Gromov-Wasserstein, that exhibits all necessary properties (permutation invariance, differentiability and scalability) and is designed to handle any-sized graphs. Numerical experiments showcase the versatility of the approach that outperform existing competitors on a novel challenging synthetic dataset and a variety of real-world tasks such as map construction from satellite image (Sat2Graph) or molecule prediction from fingerprint (Fingerprint2Graph).

Figures (17)

• Figure 1: Illustration of the architecture for a target graph of size 3 and $M = 4$.
• Figure 2: Average number of solver iterations required for computing PMFGW loss.
• Figure 3: Effect of $M$ on test edit distance and number of active nodes for Coloring.
• Figure 4: Effect of $\boldsymbol\alpha$ on the test edit distance.
• Figure 5: (Left): a sample of predictions made by Any2Graph and Relationformer for a given input and ground truth target. Many more are provided in \ref{['appendix:qualitative']}. (Right): we truncate the train datasets to provide an overview of Any2Graph training curves (test performances against train set size).

Theorems & Definitions (23)

• Proposition 1: Complexity
• Proposition 2: GI Invariance
• Proposition 3: Positivity
• Proposition 4
• Remark 1
• Proposition 5
• proof
• Remark 2: Computational cost
• Remark 3: Kullback-Leibler divergence decomposition
• Remark 4