# Gromov-Wasserstein Distillation for Inductive Multi-View Embedding

arXiv: https://arxiv.org/abs/2609.40047 · HTML: https://mlsanity.com/paper/2609.40047/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 10 of 10)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Learning Generative Models across Incomparable Spaces](https://mlsanity.com/paper/1905.05461/) (2019)
- [Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance](https://mlsanity.com/paper/2405.15959/) (2024)
- [Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein](https://mlsanity.com/paper/2402.02239/) (2024)
- [A dimensionality reduction technique based on the Gromov-Wasserstein distance](https://mlsanity.com/paper/2501.13732/) (2025)
- [Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport](https://mlsanity.com/paper/2604.02610/) (2026)
- [Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering](https://mlsanity.com/paper/2604.23912/) (2026)

## Abstract (arXiv)

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.