Intrinsic dimensionality and generalization properties of the R-norm inductive bias

Navid Ardeshir, Daniel J. Hsu, Clayton H. Sanford
Proceedings of Thirty Sixth Conference on Learning Theory, PMLR 195:3264-3303, 2023.

Abstract

We study the structural and statistical properties of R-norm minimizing interpolants of datasets labeled by specific target functions. The R-norm is the basis of an inductive bias for two-layer neural networks, recently introduced to capture the functional effect of controlling the size of network weights, independently of the network width. We find that these interpolants are intrinsically multivariate functions, even when there are ridge functions that fit the data, and also that the R-norm inductive bias is not sufficient for achieving statistically optimal generalization for certain learning problems. Altogether, these results shed new light on an inductive bias that is connected to practical neural network training.

Cite this Paper

BibTeX
@InProceedings{pmlr-v195-ardeshir23a, title = {Intrinsic dimensionality and generalization properties of the R-norm inductive bias}, author = {Ardeshir, Navid and Hsu, Daniel J. and Sanford, Clayton H.}, booktitle = {Proceedings of Thirty Sixth Conference on Learning Theory}, pages = {3264--3303}, year = {2023}, editor = {Neu, Gergely and Rosasco, Lorenzo}, volume = {195}, series = {Proceedings of Machine Learning Research}, month = {12--15 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v195/ardeshir23a/ardeshir23a.pdf}, url = {https://proceedings.mlr.press/v195/ardeshir23a.html}, abstract = {We study the structural and statistical properties of R-norm minimizing interpolants of datasets labeled by specific target functions. The R-norm is the basis of an inductive bias for two-layer neural networks, recently introduced to capture the functional effect of controlling the size of network weights, independently of the network width. We find that these interpolants are intrinsically multivariate functions, even when there are ridge functions that fit the data, and also that the R-norm inductive bias is not sufficient for achieving statistically optimal generalization for certain learning problems. Altogether, these results shed new light on an inductive bias that is connected to practical neural network training.} }
Endnote
%0 Conference Paper %T Intrinsic dimensionality and generalization properties of the R-norm inductive bias %A Navid Ardeshir %A Daniel J. Hsu %A Clayton H. Sanford %B Proceedings of Thirty Sixth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2023 %E Gergely Neu %E Lorenzo Rosasco %F pmlr-v195-ardeshir23a %I PMLR %P 3264--3303 %U https://proceedings.mlr.press/v195/ardeshir23a.html %V 195 %X We study the structural and statistical properties of R-norm minimizing interpolants of datasets labeled by specific target functions. The R-norm is the basis of an inductive bias for two-layer neural networks, recently introduced to capture the functional effect of controlling the size of network weights, independently of the network width. We find that these interpolants are intrinsically multivariate functions, even when there are ridge functions that fit the data, and also that the R-norm inductive bias is not sufficient for achieving statistically optimal generalization for certain learning problems. Altogether, these results shed new light on an inductive bias that is connected to practical neural network training.
APA
Ardeshir, N., Hsu, D.J. & Sanford, C.H.. (2023). Intrinsic dimensionality and generalization properties of the R-norm inductive bias. Proceedings of Thirty Sixth Conference on Learning Theory, in Proceedings of Machine Learning Research 195:3264-3303 Available from https://proceedings.mlr.press/v195/ardeshir23a.html.

Related Material