A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation

ORID tRsnpaRO0m · tags icml2026-repro paper-tRsnpaRO0m

#StatusPageArtifactClaim excerpt
1VERIFIED 2/201-graphops-are-introduced-self-adjoint-positivityartifactGraphops are introduced as self-adjoint, positivity-preserving operators over pr…
2VERIFIED 2/202-restricted-subclass-called-bounded-fiber-operatoartifactA restricted subclass called bounded-fiber operators (bofops) is defined via fib…
3VERIFIED 2/203-establishes-message-passing-neural-networksartifactTheorem 4.1 establishes that message passing neural networks (MPNNs) are Lipschi…
4VERIFIED 2/204-space-bofop-didms-degree-indexed-distribution-meartifactCorollary 5.3 shows the space of bofop-DIDMs (degree-indexed distribution measur…
5VERIFIED 2/205-uses-compactness-continuity-universal-approximatartifactSection 6.1 uses this compactness and continuity to prove a universal approximat…
6VERIFIED 2/206-derives-generalization-bounds-showing-generalizaartifactSection 6.2 derives generalization bounds showing generalization error vanishes …

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