
TL;DR
The paper introduces TopoNTK, a novel infinite-width kernel for simplicial message passing that captures higher-order topological interactions, enhancing expressivity and interpretability in relational learning.
Contribution
It presents the TopoNTK, combining Hodge interactions to incorporate higher-order topology into graph neural tangent kernels, enabling more expressive and interpretable relational models.
Findings
TopoNTK captures higher-order topological features.
The spectrum of TopoNTK influences learning speed of different components.
Validated on synthetic and real-world higher-order link prediction tasks.
Abstract
Graph neural tangent kernels give a principled infinite-width theory for graph neural networks, but inherit a basic limitation of graph models: they see only pairwise structure. Many relational systems contain higher-order interactions that are more naturally represented by simplicial complexes. We introduce the Topological Neural Tangent Kernel (TopoNTK), an infinite-width kernel for simplicial message passing on edge features. TopoNTK combines lower Hodge interactions, capturing graph-like coupling through shared vertices, with upper Hodge interactions, capturing coupling through filled simplices. This makes the kernel sensitive to topology invisible to graph kernels, allowing complexes with the same graph but different filled simplices to induce different kernels. Beyond expressivity, the Hodge structure gives the kernel an interpretable learning geometry. Edge signals decompose into…
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