Pith. sign in

REVIEW 3 cited by

Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1810.02244 v5 pith:VMTKM7CY submitted 2018-10-04 cs.LG cs.AIcs.CVcs.NEstat.ML

Christopher Morris , Martin Ritzert , Matthias Fey , William L. Hamilton , Jan Eric Lenssen , Gaurav Rattan , Martin Grohe This is my paper · ORCID
classification cs.LGcs.AIcs.CVcs.NEstat.ML
keywords gnnsgraphhigher-orderneuralgraphsnetworksconfirmsdimensional
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically -- showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the $1$-dimensional Weisfeiler-Leman graph isomorphism heuristic ($1$-WL). We show that GNNs have the same expressiveness as the $1$-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called $k$-dimensional GNNs ($k$-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Structured Spectral Graph Learning for Anomaly Classification in 3D Chest CT Scans

    cs.CV 2025-08 conditional novelty 5.0 of 10

    A graph neural network with spectral convolution over axial slice triplet nodes improves multi-label chest CT anomaly classification on two public datasets.

  2. Structured Spectral Graph Representation Learning for Multi-label Abnormality Analysis from 3D CT Scans

    cs.CV 2025-10 conditional novelty 4.0 of 10

    A graph-of-slice-triplets encoder with spectral convolution outperforms 3D CNN/Transformer baselines on multi-label chest CT abnormality classification and transfers to report generation and abdominal CT.

  3. An AI Approach for Learning the Spectrum of the Laplace-Beltrami Operator

    cs.CV 2025-07 conditional novelty 4.0 of 10

    A graph neural network predicts eigenvalues 2-50 of the Laplace-Beltrami operator on mechanical CAD meshes about 5 times faster than FEM and is claimed accurate on 99.3% of held-out parts.

Pith tools