conference paper
Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks
published
yes
Alexander
Shevchenko
author
Marco
Mondelli
author 27EB676C-8706-11E9-9510-7717E66974250000-0002-3242-7020
MaMo
department
The optimization of multilayer neural networks typically leads to a solution
with zero training error, yet the landscape can exhibit spurious local minima
and the minima can be disconnected. In this paper, we shed light on this
phenomenon: we show that the combination of stochastic gradient descent (SGD)
and over-parameterization makes the landscape of multilayer neural networks
approximately connected and thus more favorable to optimization. More
specifically, we prove that SGD solutions are connected via a piecewise linear
path, and the increase in loss along this path vanishes as the number of
neurons grows large. This result is a consequence of the fact that the
parameters found by SGD are increasingly dropout stable as the network becomes
wider. We show that, if we remove part of the neurons (and suitably rescale the
remaining ones), the change in loss is independent of the total number of
neurons, and it depends only on how many neurons are left. Our results exhibit
a mild dependence on the input dimension: they are dimension-free for two-layer
networks and depend linearly on the dimension for multilayer networks. We
validate our theoretical findings with numerical experiments for different
architectures and classification tasks.
https://research-explorer.app.ist.ac.at/download/9198/9217/2020_PMLR_Shevchenko.pdf
application/pdfno
Proceedings of Machine Learning Research2020
eng
Proceedings of the 37th International Conference on Machine Learning
1912.10095
1198773-8784
Shevchenko, A., & Mondelli, M. (2020). Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks. In <i>Proceedings of the 37th International Conference on Machine Learning</i> (Vol. 119, pp. 8773–8784). Proceedings of Machine Learning Research.
Shevchenko A, Mondelli M. 2020. Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks. Proceedings of the 37th International Conference on Machine Learning. vol. 119, 8773–8784.
Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” <i>Proceedings of the 37th International Conference on Machine Learning</i>, vol. 119, Proceedings of Machine Learning Research, 2020, pp. 8773–84.
Shevchenko, Alexander, and Marco Mondelli. “Landscape Connectivity and Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” In <i>Proceedings of the 37th International Conference on Machine Learning</i>, 119:8773–84. Proceedings of Machine Learning Research, 2020.
A. Shevchenko and M. Mondelli, “Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks,” in <i>Proceedings of the 37th International Conference on Machine Learning</i>, 2020, vol. 119, pp. 8773–8784.
A. Shevchenko, M. Mondelli, in:, Proceedings of the 37th International Conference on Machine Learning, Proceedings of Machine Learning Research, 2020, pp. 8773–8784.
Shevchenko A, Mondelli M. Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks. In: <i>Proceedings of the 37th International Conference on Machine Learning</i>. Vol 119. Proceedings of Machine Learning Research; 2020:8773-8784.
91982021-02-25T09:36:22Z2021-03-02T15:38:39Z