Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning

TL;DR

This paper introduces a novel non-Euclidean Transformer model that operates on product of constant curvature spaces, enabling better representation of hierarchical and cyclical graph structures, with efficient attention mechanisms.

Contribution

It proposes the Fully Product-Stereographic Transformer, a generalization of Transformers to non-Euclidean geometries, capable of learning graph curvature end-to-end without extra tuning.

Findings

Improved graph reconstruction accuracy

Enhanced node classification performance

Linear time and memory complexity for non-Euclidean attention

Abstract

Real-world graphs naturally exhibit hierarchical or cyclical structures that are unfit for the typical Euclidean space. While there exist graph neural networks that leverage hyperbolic or spherical spaces to learn representations that embed such structures more accurately, these methods are confined under the message-passing paradigm, making the models vulnerable against side-effects such as oversmoothing and oversquashing. More recent work have proposed global attention-based graph Transformers that can easily model long-range interactions, but their extensions towards non-Euclidean geometry are yet unexplored. To bridge this gap, we propose Fully Product-Stereographic Transformer, a generalization of Transformers towards operating entirely on the product of constant curvature spaces. When combined with tokenized graph Transformers, our model can learn the curvature appropriate for the input graph in an end-to-end fashion, without the need of additional tuning on different curvature initializations. We also provide a kernelized approach to non-Euclidean attention, which enables our model to run in time and memory cost linear to the number of nodes and edges while respecting the underlying geometry. Experiments on graph reconstruction and node classification demonstrate the benefits of generalizing Transformers to the non-Euclidean domain.