Bridging Graph Position Encodings for Transformers with Weighted Graph-Walking Automata

TL;DR

This paper introduces GAPE, a new graph positional encoding based on weighted graph-walking automata, improving transformer performance on graph tasks and providing a comprehensive comparison of existing PEs.

Contribution

It presents GAPE, a novel graph PE derived from weighted graph-walking automata, and offers a thorough comparison of recent PEs in graph transformers.

Findings

GAPE generalizes several existing positional encodings.

GAPE improves transformer performance on graph tasks.

The study provides a detailed comparison of PEs independent of edge features.

Abstract

A current goal in the graph neural network literature is to enable transformers to operate on graph-structured data, given their success on language and vision tasks. Since the transformer's original sinusoidal positional encodings (PEs) are not applicable to graphs, recent work has focused on developing graph PEs, rooted in spectral graph theory or various spatial features of a graph. In this work, we introduce a new graph PE, Graph Automaton PE (GAPE), based on weighted graph-walking automata (a novel extension of graph-walking automata). We compare the performance of GAPE with other PE schemes on both machine translation and graph-structured tasks, and we show that it generalizes several other PEs. An additional contribution of this study is a theoretical and controlled experimental comparison of many recent PEs in graph transformers, independent of the use of edge features.