Gromov-Wasserstein Distillation for Inductive Multi-View Embedding

2026-09-30

AI Summary

This study addresses the limitation of Gromov-Wasserstein multidimensional scaling (GW-MDS), which is inherently transductive and cannot generalize to unseen samples. To overcome this, we propose an inductive learning framework based on barycentric distillation. This method establishes, for the first time, a bridge between transductive GW embeddings and inductive neural networks via barycentric projection. Specifically, a teacher model generates target-space representations, and knowledge distillation is employed to train a student network that learns an explicit out-of-sample mapping while supporting multi-view consensus learning. Experiments on both synthetic and real-world datasets demonstrate that the proposed framework effectively preserves data geometric structures, achieving significantly superior performance compared to direct neural GW training baselines.

Abstract

Gromov-Wasserstein multidimensional scaling (GW-MDS) learns low-dimensional representations from relational data but remains transductive, providing no explicit mapping for unseen samples. We introduce an inductive framework based on barycentric distillation. A GW-MDS teacher learns a latent support and an optimal transport plan from the training data, and barycentric projection converts the resulting coupling into sample-aligned targets. A neural student then learns an explicit out-of-sample mapping, avoiding additional relational-matrix construction and GW optimization at inference. We formulate the approach for single-view data and extend it to Mean-GWMDS and Multi-GWMDS teachers through consensus and selected-projection targets learned by a multi-view student with view-specific encoders. We also investigate a direct neural baseline trained solely with a GW objective. Experiments on synthetic and real-world data using Euclidean, geodesic, and cosine relations show that the distilled models preserve the teacher geometry on unseen samples and consistently outperform direct neural GW training in sample-indexed relational preservation. These results establish barycentric projection as an effective bridge between transductive GW embeddings and inductive neural mappings.

Problem

• Gromov-Wasserstein
• inductive embedding
• multi-view learning
• out-of-sample mapping
• distillation

Innovation

• Gromov-Wasserstein Distillation
• Barycentric Projection
• Inductive Multi-View Embedding
• Optimal Transport
• Teacher-Student Framework