Understanding the difficulty of training deep feedforward neural networks

Xavier Glorot, Yoshua Bengio
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:249-256, 2010.

Abstract

Whereas before 2006 it appears that deep multi-layer neural networks were not successfully trained, since then several algorithms have been shown to successfully train them, with experimental results showing the superiority of deeper vs less deep architectures. All these experimental results were obtained with new initialization or training mechanisms. Our objective here is to understand better why standard gradient descent from random initialization is doing so poorly with deep neural networks, to better understand these recent relative successes and help design better algorithms in the future. We first observe the influence of the non-linear activations functions. We find that the logistic sigmoid activation is unsuited for deep networks with random initialization because of its mean value, which can drive especially the top hidden layer into saturation. Surprisingly, we find that saturated units can move out of saturation by themselves, albeit slowly, and explaining the plateaus sometimes seen when training neural networks. We find that a new non-linearity that saturates less can often be beneficial. Finally, we study how activations and gradients vary across layers and during training, with the idea that training may be more difficult when the singular values of the Jacobian associated with each layer are far from 1. Based on these considerations, we propose a new initialization scheme that brings substantially faster convergence.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-glorot10a, title = {Understanding the difficulty of training deep feedforward neural networks}, author = {Glorot, Xavier and Bengio, Yoshua}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {249--256}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf}, url = {https://proceedings.mlr.press/v9/glorot10a.html}, abstract = {Whereas before 2006 it appears that deep multi-layer neural networks were not successfully trained, since then several algorithms have been shown to successfully train them, with experimental results showing the superiority of deeper vs less deep architectures. All these experimental results were obtained with new initialization or training mechanisms. Our objective here is to understand better why standard gradient descent from random initialization is doing so poorly with deep neural networks, to better understand these recent relative successes and help design better algorithms in the future. We first observe the influence of the non-linear activations functions. We find that the logistic sigmoid activation is unsuited for deep networks with random initialization because of its mean value, which can drive especially the top hidden layer into saturation. Surprisingly, we find that saturated units can move out of saturation by themselves, albeit slowly, and explaining the plateaus sometimes seen when training neural networks. We find that a new non-linearity that saturates less can often be beneficial. Finally, we study how activations and gradients vary across layers and during training, with the idea that training may be more difficult when the singular values of the Jacobian associated with each layer are far from 1. Based on these considerations, we propose a new initialization scheme that brings substantially faster convergence.} }
Endnote
%0 Conference Paper %T Understanding the difficulty of training deep feedforward neural networks %A Xavier Glorot %A Yoshua Bengio %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-glorot10a %I PMLR %P 249--256 %U https://proceedings.mlr.press/v9/glorot10a.html %V 9 %X Whereas before 2006 it appears that deep multi-layer neural networks were not successfully trained, since then several algorithms have been shown to successfully train them, with experimental results showing the superiority of deeper vs less deep architectures. All these experimental results were obtained with new initialization or training mechanisms. Our objective here is to understand better why standard gradient descent from random initialization is doing so poorly with deep neural networks, to better understand these recent relative successes and help design better algorithms in the future. We first observe the influence of the non-linear activations functions. We find that the logistic sigmoid activation is unsuited for deep networks with random initialization because of its mean value, which can drive especially the top hidden layer into saturation. Surprisingly, we find that saturated units can move out of saturation by themselves, albeit slowly, and explaining the plateaus sometimes seen when training neural networks. We find that a new non-linearity that saturates less can often be beneficial. Finally, we study how activations and gradients vary across layers and during training, with the idea that training may be more difficult when the singular values of the Jacobian associated with each layer are far from 1. Based on these considerations, we propose a new initialization scheme that brings substantially faster convergence.
RIS
TY - CPAPER TI - Understanding the difficulty of training deep feedforward neural networks AU - Xavier Glorot AU - Yoshua Bengio BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-glorot10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 249 EP - 256 L1 - http://proceedings.mlr.press/v9/glorot10a/glorot10a.pdf UR - https://proceedings.mlr.press/v9/glorot10a.html AB - Whereas before 2006 it appears that deep multi-layer neural networks were not successfully trained, since then several algorithms have been shown to successfully train them, with experimental results showing the superiority of deeper vs less deep architectures. All these experimental results were obtained with new initialization or training mechanisms. Our objective here is to understand better why standard gradient descent from random initialization is doing so poorly with deep neural networks, to better understand these recent relative successes and help design better algorithms in the future. We first observe the influence of the non-linear activations functions. We find that the logistic sigmoid activation is unsuited for deep networks with random initialization because of its mean value, which can drive especially the top hidden layer into saturation. Surprisingly, we find that saturated units can move out of saturation by themselves, albeit slowly, and explaining the plateaus sometimes seen when training neural networks. We find that a new non-linearity that saturates less can often be beneficial. Finally, we study how activations and gradients vary across layers and during training, with the idea that training may be more difficult when the singular values of the Jacobian associated with each layer are far from 1. Based on these considerations, we propose a new initialization scheme that brings substantially faster convergence. ER -
APA
Glorot, X. & Bengio, Y.. (2010). Understanding the difficulty of training deep feedforward neural networks. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:249-256 Available from https://proceedings.mlr.press/v9/glorot10a.html.

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