Gromov-Wasserstein Distillation for Inductive Multi-View Embedding
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.
Related
- Gromov-compactifiability of Wasserstein spaces
- An isometric embedding of the space of non-increasing sequences with non-negative terms into the Gromov-Hausdorff space
- Quantitative Stability and Sample Complexity for Regularized Gromov-Wasserstein Distance
- Dynamic Generalized Gromov-Wasserstein Optimal Transport
- A Provably Convergent and Practical Algorithm for Gromov--Wasserstein Optimal Transport
BibTeX
@misc{eufrazio2026gromovwasserstein,
title = {{Gromov-Wasserstein Distillation for Inductive Multi-View Embedding}},
author = {Rafael Pereira Eufrazio and Eduardo Fernandes Montesuma and Charles Casimiro Cavalcante},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40047},
eprint = {2609.40047},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40047},
}
RIS
TY - UNPB
TI - Gromov-Wasserstein Distillation for Inductive Multi-View Embedding
AU - Rafael Pereira Eufrazio
AU - Eduardo Fernandes Montesuma
AU - Charles Casimiro Cavalcante
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40047
UR - https://arxiv.org/abs/2609.40047
AB - 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.
ER -