[16] Taco S Cohen, Mario Geiger, and Maurice Weiler. A general theory of equivariant CNNs on homogeneous spaces. In H. Wallach, H. Larochelle, A. Beygelzimer, F. dAlché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.
[17] Michel Deza and Tayuan Huang. Metrics on permutations, a survey. Journal of Combinatorics, Information & System Sciences, 23(1-4):173-185, 1998.
[18] Stephan Eismann, Raphael J. L. Townshend, Nathaniel Thomas, Milind Jagota, Bowen Jing, and Ron O. Dror. Hierarchical, rotation-equivariant neural networks to select structural models of protein complexes. Proteins: Structure, 89:493 - 501, 2020.
[19] Bryn Elesedy. Provably strict generalisation benefit for invariance in kernel methods. Advances in Neural Information Processing Systems, 34:17273-17283, 2021.
[20] Bryn Elesedy. Group symmetry in PAC learning. In ICLR 2022 Workshop on Geometrical and Topological Representation Learning, 2022.
[21] Bryn Elesedy. Symmetry and Generalisation in Machine Learning. PhD thesis, University of Oxford, 2023.
[22] Bryn Elesedy and Sheheryar Zaidi. Provably strict generalisation benefit for equivariant models. In Marina Meila and Tong Zhang, editors, Proceedings of the 38th International Conference on Machine Learning, ICML 2021, 18-24 July 2021, Virtual Event, volume 139 of Proceedings of Machine Learning Research, pages 2959-2969. PMLR, 2021.
[23] Marc Finzi, Gregory Benton, and Andrew G Wilson. Residual pathway priors for soft equivariance constraints. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, and J. Wortman Vaughan, editors, Advances in Neural Information Processing Systems, volume 34, pages 30037-30049. Curran Associates, Inc., 2021.
[24] Marc Finzi, Max Welling, and Andrew Gordon Wilson. A practical method for constructing equivariant multilayer perceptrons for arbitrary matrix groups. *ArXiv*, abs/2104.09459, 2021.
[25] Jonathan Gordon, David Lopez-Paz, Marco Baroni, and Diane Bouchacourt. Permutation equivariant models for compositional generalization in language. In ICLR, 2020.
[26] B. Haasdonk, A. Vossen, and H. Burkhardt. Invariance in kernel methods byhaar-integration kernels. In Heikki Kalviainen, Jussi Parkkinen, and Arto Kaarna, editors, Image Analysis, pages 841-851, Berlin, Heidelberg, 2005. Springer Berlin Heidelberg.
[27] Osman Semih Kayhan and Jan C van Gemert. On translation invariance in cnns: Convolutional layers can exploit absolute spatial location. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14274-14285, 2020.
[28] Johannes Klicpera, Janek Groß, and Stephan Gümnmann. Directional message passing for molecular graphs. ArXiv, abs/2003.03123, 2020.
[29] Risi Kondor and Shubhendu Trivedi. On the generalization of equivariance and convolution in neural networks to the action of compact groups. In ICML, 2018.
[30] Aryeh Kontorovich and Roi Weiss. Maximum margin multiclass nearest neighbors. In International conference on machine learning, pages 892-900. PMLR, 2014.
[31] Robert Krauthgamer and James R Lee. Navigating nets: Simple algorithms for proximity search. In Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, pages 798-807. Citeseer, 2004.
[32] Yann André LeCun, Bernhard E. Boser, John S. Denker, Donnie Henderson, Richard E. Howard, Wayne E. Hubbard, and Lawrence D. Jackel. Backpropagation applied to handwritten zip code recognition. *Neural Computation*, 1:541–551, 1989.