Deep Layer-wise Networks Have Closed-Form Weights

Chieh Tzu Wu, Aria Masoomi, Arthur Gretton, Jennifer Dy
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:188-225, 2022.

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.

Cite this Paper

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. } }
Endnote
%0 Conference Paper %T Deep Layer-wise Networks Have Closed-Form Weights %A Chieh Tzu Wu %A Aria Masoomi %A Arthur Gretton %A Jennifer Dy %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-tzu-wu22a %I PMLR %P 188--225 %U https://proceedings.mlr.press/v151/tzu-wu22a.html %V 151 %X 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.
APA
Tzu Wu, C., Masoomi, A., Gretton, A. & Dy, J.. (2022). Deep Layer-wise Networks Have Closed-Form Weights . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:188-225 Available from https://proceedings.mlr.press/v151/tzu-wu22a.html.

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