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On dimensionality of feature vectors in MPNNs
We revisit the classical result of Morris et al.~(AAAI'19) that message-passing graphs neural networks (MPNNs) are equal in their distinguishing power to the Weisfeiler--Leman (WL) isomorphism test.
Three iterations of $(d-1)$-WL test distinguish non isometric clouds of $d$-dimensional points
Our main result states that the $(d-1)$-dimensional WL test is complete for point clouds in $d$-dimensional Euclidean space, for any $d\ge 2$, and that only three iterations of the test suffice.
No Agreement Without Loss: Learning and Social Choice in Peer Review
It may be assumed that each reviewer has her own mapping from the set of features to a recommendation, and that different reviewers have different mappings in mind.
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