Go to LOG 2025 Conference homepageLow-Shot Graph Learning with Topological and Spectral Embeddings
Keywords: Graph representation learning, few-shot learning, graph classification, persistent homology, spectral embeddings, density of states, graph neural networks, graph transformers, topological data analysisf
TL;DR: Direct topological and spectral embeddings, combined with a compact Graph Transformer, enable state-of-the-art low-shot graph classification under scarce supervision.
Abstract: Deep graph learning has achieved remarkable success, but its reliance on abundant labeled data limits use in many scientific domains, where each label may require costly experiments or simulations. We revisit graph classification in the low-shot regime and ask whether explicit, theory-grounded descriptors can provide a reliable foundation and how they can be combined with modern architectures. We study two families of label-free embeddings: *topological vectors* from persistent homology that capture multiscale connectivity, and *spectral vectors* from the Laplacian density of states that summarize diffusion geometry. To harness their complementary strengths, we introduce *prototype embeddings*, which project graphs onto class-level prototypes in the joint topological–spectral space, and *STAMP*, a lightweight controller that conditions GNN and GT backbones on these descriptors through layer-wise modulation.
Across ten TU benchmarks and label budgets $K \in$ {1,5,10,25,50}, prototype embeddings with simple classifiers consistently outperform strong baselines in the extreme low-label setting, while *STAMP* achieves the best overall rank and smallest accuracy gap once $K \ge 10$. Our results demonstrate that explicit structural priors offer a powerful and complementary route to label-efficient graph learning, closing much of the gap to larger deep models without pretraining.
Submission Type: Full paper proceedings track submission (max 9 main pages).
Software: https://github.com/1999-karthik/STAMP
Submission Number: 18
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