An analysis of training and generalization errors in shallow and deep networks
Name
1802.06266.pdf
Description
Accepted version
Size
2.52 MB
Format
Adobe PDF
Checksum (MD5)
b15cdeb7a3554463049db5b971f52c33
Author(s)
Mhaskar, HN
Poggio, Tomaso A
Date Issued
2020
Journal
Neural Networks
Publisher
Elsevier BV
Citation
Mhaskar, HN and Poggio, T. 2020. "An analysis of training and generalization errors in shallow and deep networks." Neural Networks, 121.
Version
Author's final manuscript
Abstract
© 2019 Elsevier Ltd This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze this phenomenon in the case of regression problems when each unit evaluates a periodic activation function. We argue that the minimal expected value of the square loss is inappropriate to measure the generalization error in approximation of compositional functions in order to take full advantage of the compositional structure. Instead, we measure the generalization error in the sense of maximum loss, and sometimes, as a pointwise error. We give estimates on exactly how many parameters ensure both zero training error as well as a good generalization error. We prove that a solution of a regularization problem is guaranteed to yield a good training error as well as a good generalization error and estimate how much error to expect at which test data.
MIT Department
Center for Brains, Minds, and Machines
McGovern Institute for Brain Research at MIT
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.NEUNET.2019.08.028
