Strong inductive biases provably prevent harmless interpolationDownload PDF

Published: 01 Feb 2023, Last Modified: 22 Oct 2023ICLR 2023 posterReaders: Everyone
Keywords: high-dimensional statistics, non-parametric regression, deep learning theory, generalization bounds, benign overfitting
Abstract: Classical wisdom suggests that estimators should avoid fitting noise to achieve good generalization. In contrast, modern overparameterized models can yield small test error despite interpolating noise — a phenomenon often called "benign overfitting" or "harmless interpolation". This paper argues that the degree to which interpolation is harmless hinges upon the strength of an estimator's inductive bias, i.e., how heavily the estimator favors solutions with a certain structure: while strong inductive biases prevent harmless interpolation, weak inductive biases can even require fitting noise to generalize well. Our main theoretical result establishes tight non-asymptotic bounds for high-dimensional kernel regression that reflect this phenomenon for convolutional kernels, where the filter size regulates the strength of the inductive bias. We further provide empirical evidence of the same behavior for deep neural networks with varying filter sizes and rotational invariance.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics
Submission Guidelines: Yes
Please Choose The Closest Area That Your Submission Falls Into: Theory (eg, control theory, learning theory, algorithmic game theory)
TL;DR: We show that the strength of a model’s inductive bias determines whether interpolation of noisy data is harmless or harmful.
Supplementary Material: zip
Community Implementations: [![CatalyzeX](/images/catalyzex_icon.svg) 1 code implementation](https://www.catalyzex.com/paper/arxiv:2301.07605/code)
9 Replies

Loading