Leveraging Manifold Embeddings for Enhanced Graph Transformer Representations and Learning

TL;DR

This paper introduces a Riemannian mixture-of-experts layer for graph transformers, enabling adaptive manifold embeddings that improve accuracy and interpretability by capturing heterogeneous local structures.

Contribution

It proposes a novel geometry-aware projection layer that dynamically routes nodes to different manifolds, enhancing graph transformer representations.

Findings

Up to 3% accuracy improvement on node classification benchmarks

Ensemble of Euclidean and non-Euclidean features enhances performance

Provides intrinsic geometric explanations for latent space representations

Abstract

Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of spherical, flat, hyperbolic - best matching its local structure. These projections provide intrinsic geometric explanations to the latent space. Inserted into a state-of-the-art ensemble graph transformer, this projector lifts accuracy by up to 3% on four node-classification benchmarks. The ensemble makes sure that both euclidean and non-euclidean features are captured. Explicit, geometry-aware projection thus sharpens predictive power while making graph representations more interpretable.