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Incompleteness of graph neural networks for points clouds in three dimensions

Sergey Pozdnyakov1*, Michele Ceriotti1*

1 Institute of Materials, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

* Corresponding authors emails: sergey.pozdnyakov@epfl.ch, michele.ceriotti@gmail.com
DOI10.24435/materialscloud:66-mm [version v1]

Publication date: May 12, 2023

How to cite this record

Sergey Pozdnyakov, Michele Ceriotti, Incompleteness of graph neural networks for points clouds in three dimensions, Materials Cloud Archive 2023.75 (2023), doi: 10.24435/materialscloud:66-mm.


Graph neural networks are a popular deep-learning architecture in applications to materials and molecules, and the most widespread implementations rely on interatomic distances as geometric descriptors. Unfortunately, GNNs based on distances are not complete, i.e. there are geometries, corresponding to molecules and/or periodic structures, that are indistinguishable by the GNN. For these, the corresponding machine-learning models will be unable to learn differences in the properties of the "degenerate" structures. This dataset contains a collection of molecular and solid structures that cannot be discriminated by distance-based graph neural networks, together with example code showing how to parse them and use to demonstrate the shortcomings of this class of machine-learning algorithms.

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File name Size Description
8.3 MiB Archive containing the counterexample structures in extended xyz format, together with python scripts to analyze them and explanations of the usage.


Files and data are licensed under the terms of the following license: Creative Commons Attribution Share Alike 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

Journal reference (Paper describing the construction of this class of counterexamples)


machine learning graph neural networks point clouds MARVEL

Version history:

2023.75 (version v1) [This version] May 12, 2023 DOI10.24435/materialscloud:66-mm