2023-02-07-sangalli23a.md

title	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Moving frame net: SE(3)-equivariant network for volumes	Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The method of moving frames is classical for deriving operators invariant to the action of a Lie group in a manifold.Recently, a rotation and translation equivariant neural network for image data was proposed based on the moving frames approach. In this paper we significantly improve that approach by reducing the computation of moving frames to only one, at the input stage, instead of repeated computations at each layer. The equivariance of the resulting architecture is proved theoretically and we build a rotation and translation equivariant neural network to process volumes, i.e. signals on the 3D space. Our trained model overperforms the benchmarks in the medical volume classification of most of the tested datasets from MedMNIST3D.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	sangalli23a	0	Moving frame net: SE(3)-equivariant network for volumes	81	97	81-97	81	false	Sangalli, Mateus and Blusseau, Samy and Velasco-Forero, Santiago and Angulo, Jes\'{u}s	given family Mateus Sangalli given family Samy Blusseau given family Santiago Velasco-Forero given family Jesús Angulo	2023-02-07		Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations	197	inproceedings	date-parts 2023 2 7	https://proceedings.mlr.press/v197/sangalli23a/sangalli23a.pdf