Deep Layer-wise Networks Have Closed-Form Weights
Chieh Tzu Wu, Aria Masoomi, Arthur Gretton, Jennifer Dy
Abstract
There is currently a debate within the neuroscience community over the likelihood of the brain performing backpropagation (BP). To better mimic the brain, training a network one layer at a time with only a "single forward pass" has been proposed as an alternative to bypass BP; we refer to these networks as "layer-wise" networks. We continue the work on layer-wise networks by answering two outstanding questions. First, do they have a closed-form solution? Second, how do we know when to stop adding more layers? This work proves that the "Kernel Mean Embedding" is the closed-form solution that achieves the network global optimum while driving these networks to converge towards a highly desirable kernel for classification; we call it the Neural Indicator Kernel.
BibTeX
@InProceedings{pmlr-v151-tzu-wu22a,
title = { Deep Layer-wise Networks Have Closed-Form Weights },
author = {Tzu Wu, Chieh and Masoomi, Aria and Gretton, Arthur and Dy, Jennifer},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {188--225},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/tzu-wu22a/tzu-wu22a.pdf},
url = {https://proceedings.mlr.press/v151/tzu-wu22a.html},
abstract = { There is currently a debate within the neuroscience community over the likelihood of the brain performing backpropagation (BP). To better mimic the brain, training a network one layer at a time with only a "single forward pass" has been proposed as an alternative to bypass BP; we refer to these networks as "layer-wise" networks. We continue the work on layer-wise networks by answering two outstanding questions. First, do they have a closed-form solution? Second, how do we know when to stop adding more layers? This work proves that the "Kernel Mean Embedding" is the closed-form solution that achieves the network global optimum while driving these networks to converge towards a highly desirable kernel for classification; we call it the Neural Indicator Kernel. }
}