Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks

conference paper Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks published yes Aleksandr Shevchenko author F2B06EC2-C99E-11E9-89F0-752EE6697425 Marco Mondelli author 27EB676C-8706-11E9-9510-7717E66974250000-0002-3242-7020 MaMo department DaAl department Prix Lopez-Loretta 2019 - Marco Mondelli project 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.ista.ac.at/download/9198/9217/2020_PMLR_Shevchenko.pdf application/pdfno ML Research Press2020 eng Proceedings of the 37th International Conference on Machine Learning 1912.10095 1198773-8784 https://research-explorer.ista.ac.at/record/17465 A. Shevchenko, M. Mondelli, in:, Proceedings of the 37th International Conference on Machine Learning, ML Research Press, 2020, pp. 8773–8784. A. Shevchenko and M. Mondelli, “Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks,” in Proceedings of the 37th International Conference on Machine Learning, 2020, vol. 119, pp. 8773–8784. 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, A., & Mondelli, M. (2020). Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks. In Proceedings of the 37th International Conference on Machine Learning (Vol. 119, pp. 8773–8784). ML Research Press. Shevchenko A, Mondelli M. Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks. In: Proceedings of the 37th International Conference on Machine Learning. Vol 119. ML Research Press; 2020:8773-8784. Shevchenko, Aleksandr, and Marco Mondelli. “Landscape Connectivity and Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” Proceedings of the 37th International Conference on Machine Learning, vol. 119, ML Research Press, 2020, pp. 8773–84. Shevchenko, Aleksandr, and Marco Mondelli. “Landscape Connectivity and Dropout Stability of SGD Solutions for Over-Parameterized Neural Networks.” In Proceedings of the 37th International Conference on Machine Learning, 119:8773–84. ML Research Press, 2020. 91982021-02-25T09:36:22Z2026-10-10T22:31:20Z