Permutation Equivariant Layers for Higher Order Interactions

Horace Pan, Risi Kondor
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:5987-6001, 2022.

Abstract

Recent work on permutation equivariant neural networks has mostly focused on the first order case (sets) and second order case (graphs). We describe the machinery for generalizing permutation equivariance to arbitrary $k$-ary interactions between entities for any value of $k$. We demonstrate the effectiveness of higher order permutation equivariant models on several real world applications and find that our results compare favorably to existing permutation invariant/equivariant baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-pan22a, title = { Permutation Equivariant Layers for Higher Order Interactions }, author = {Pan, Horace and Kondor, Risi}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {5987--6001}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/pan22a/pan22a.pdf}, url = {https://proceedings.mlr.press/v151/pan22a.html}, abstract = { Recent work on permutation equivariant neural networks has mostly focused on the first order case (sets) and second order case (graphs). We describe the machinery for generalizing permutation equivariance to arbitrary $k$-ary interactions between entities for any value of $k$. We demonstrate the effectiveness of higher order permutation equivariant models on several real world applications and find that our results compare favorably to existing permutation invariant/equivariant baselines. } }
Endnote
%0 Conference Paper %T Permutation Equivariant Layers for Higher Order Interactions %A Horace Pan %A Risi Kondor %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-pan22a %I PMLR %P 5987--6001 %U https://proceedings.mlr.press/v151/pan22a.html %V 151 %X Recent work on permutation equivariant neural networks has mostly focused on the first order case (sets) and second order case (graphs). We describe the machinery for generalizing permutation equivariance to arbitrary $k$-ary interactions between entities for any value of $k$. We demonstrate the effectiveness of higher order permutation equivariant models on several real world applications and find that our results compare favorably to existing permutation invariant/equivariant baselines.
APA
Pan, H. & Kondor, R.. (2022). Permutation Equivariant Layers for Higher Order Interactions . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:5987-6001 Available from https://proceedings.mlr.press/v151/pan22a.html.

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