Graph neural networks gain wider pattern recognition with new topological tools
Repurposing Unified Topological Signatures for Graph Representation Learning
Machine LearningArtificial Intelligence
Summary
Graph neural networks (GNNs) learn by passing messages between connected nodes but can miss differences in graphs that look similar locally. The authors use special topological summaries called Unified Topological Signatures (UTS) to capture more global and multi-scale features of graphs. They add UTS into GNN training in several ways, improving the networks' ability to tell apart complex graph structures and boosting classification accuracy on different tasks. This approach goes beyond previous GNN limits defined by a known graph comparison test.
What this means in practice
- •For machine learning engineers: Improve graph-based classification models by incorporating topological features that enhance structural distinction and reduce embedding collapse.
- •For bioinformatics teams: Enhance molecular graph analysis with topological signatures to better distinguish complex structural patterns in biological data.
Authors
Sanyam Sanjay Jain, Anshika Krishnatray, Aditya Sharma, Vinti Agarwal
Abstract
Message-passing Graph Neural Networks (GNNs) iteratively propagate and aggregate local neighborhood information followed by global readout to learn graph representations. However, their discriminative power is upper-bounded by the Weisfeiler--Lehman (1-WL) graph isomorphism test. This prevents GNNs from distinguishing certain non-isomorphic graphs with identical local neighborhood structures, often leading to similar graph representations. Unified Topological Signatures (UTS) capture compact, multi-scale representation of global graph topology derived from persistent homology. We introduce two complementary UTS signatures: Graph_UTS- a static signature of the input graph topology, and Embedding_UTS- a dynamic signature of the evolving embedding topology. They encode structural information inaccessible to 1-WL-based message-passing GNNs, yet their capabilities are explored solely for post-hoc embedding-space analysis. We integrate UTS into GNN training across three architectural interventions: (i) UTS-Aug: augmenting with standard readout feature that encodes graph's true topology; (ii) UTS-Reg: topological regularizer that constrains representation collapse; (iii) UTS-Pool: topology-guided pooling that retains structurally critical nodes. We further leverage UTS as a layer-wise diagnostic to quantify oversmoothing during GNN training. Theoretically, we show that integrating UTS into GNN optimization strictly extends GNN expressivity beyond the 1-WL hierarchy. Experiments on three graph classification benchmarks show consistent benefits: Graph-UTS, Dual-UTS, and UTS-Pool improve accuracy across all three datasets, Embedding-UTS provides smaller but similarly consistent gains, and UTS-Reg's benefit varies across graph domains. Accuracy improves by up to 5.8% with Graph-UTS augmentation, by up to 1.9% with UTS-Reg, and achieves comparable performance to TOGL with UTS-Pool.