PiPE combines positional encodings with persistent homology features in a message-passing framework and is claimed to be provably more expressive than either approach alone, with empirical gains on molecular benchmarks.
Persistent Homology and Graphs Representation Learning
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abstract
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we consider the case when these embeddings are real-valued. By viewing these embeddings as scalar functions on a domain of interest, we can utilize the tools available in persistent homology to study the topological information encoded in these representations. Our construction effectively defines a unique persistence-based graph descriptor, on both the graph and node levels, for every node representation algorithm. To demonstrate the effectiveness of the proposed method, we study the topological descriptors induced by DeepWalk, Node2Vec and Diff2Vec.
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cs.LG 1years
2025 1verdicts
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Positional Encoding meets Persistent Homology on Graphs
PiPE combines positional encodings with persistent homology features in a message-passing framework and is claimed to be provably more expressive than either approach alone, with empirical gains on molecular benchmarks.