TopoFormer: Topology Meets Attention for Graph Learning

2026-07-30

AI Summary

This work addresses the challenge of effectively integrating multi-scale topological structures to enhance graph representation learning. The authors propose TopoFormer, a novel framework featuring a parallelizable and persistence-free Topo-Scan module that converts graph structures into ordered topological sequences, which are then seamlessly integrated into a Transformer architecture. This design enables unified modeling of topological patterns ranging from local to global scales. By synergistically combining topological data analysis, node/edge filtering, and sequential encoding, TopoFormer achieves competitive or superior performance compared to existing graph neural networks and topological methods on graph classification and molecular property prediction tasks, while maintaining efficient and predictable computational overhead.

Abstract

We introduce Topoformer, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences. At the core of our method is Topo-Scan, a novel module that decomposes a graph into a short, ordered sequence of topological tokens by slicing over node or edge filtrations. These sequences capture multi-scale structural patterns, from local motifs to global organization, and are processed by a Transformer to produce expressive graph-level embeddings. Unlike traditional persistent homology pipelines, Topo-Scan is parallelizable, avoids costly diagram computations, and integrates seamlessly with standard deep learning architectures. We provide theoretical guarantees on the stability of our topological encodings and demonstrate state-of-the-art performance across graph classification and molecular property prediction benchmarks. Our results show that Topoformer matches or exceeds strong GNN and topology-based baselines while offering predictable and efficient compute. This work opens a new path for parallelizable and unifying approaches to graph representation learning that integrate topological inductive biases into attention frameworks.

Problem

• graph representation learning
• topological structure
• attention mechanism
• persistent homology
• graph-level embeddings

Innovation

• TopoFormer
• Topo-Scan
• topological representation learning
• graph attention
• parallelizable topology