2024-04-18-cabannes24a.md

title	software	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
The Galerkin method beats Graph-Based Approaches for Spectral Algorithms	https://github.com/VivienCabannes/laplacian	Historically, the machine learning community has derived spectral decompositions from graph-based approaches. We break with this approach and prove the statistical and computational superiority of the Galerkin method, which consists in restricting the study to a small set of test functions. In particular, we introduce implementation tricks to deal with differential operators in large dimensions with structured kernels. Finally, we extend on the core principles beyond our approach to apply them to non-linear spaces of functions, such as the ones parameterized by deep neural networks, through loss-based optimization procedures.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	cabannes24a	0	The {G}alerkin method beats Graph-Based Approaches for Spectral Algorithms	451	459	451-459	451	false	Cabannes, Vivien A. and Bach, Francis	given family Vivien A. Cabannes given family Francis Bach	2024-04-18		Proceedings of The 27th International Conference on Artificial Intelligence and Statistics	238	inproceedings	date-parts 2024 4 18	https://proceedings.mlr.press/v238/cabannes24a/cabannes24a.pdf