--- _id: '9198' abstract: - lang: eng text: "The optimization of multilayer neural networks typically leads to a solution\r\nwith zero training error, yet the landscape can exhibit spurious local minima\r\nand the minima can be disconnected. In this paper, we shed light on this\r\nphenomenon: we show that the combination of stochastic gradient descent (SGD)\r\nand over-parameterization makes the landscape of multilayer neural networks\r\napproximately connected and thus more favorable to optimization. More\r\nspecifically, we prove that SGD solutions are connected via a piecewise linear\r\npath, and the increase in loss along this path vanishes as the number of\r\nneurons grows large. This result is a consequence of the fact that the\r\nparameters found by SGD are increasingly dropout stable as the network becomes\r\nwider. We show that, if we remove part of the neurons (and suitably rescale the\r\nremaining ones), the change in loss is independent of the total number of\r\nneurons, and it depends only on how many neurons are left. Our results exhibit\r\na mild dependence on the input dimension: they are dimension-free for two-layer\r\nnetworks and depend linearly on the dimension for multilayer networks. We\r\nvalidate our theoretical findings with numerical experiments for different\r\narchitectures and classification tasks." acknowledgement: M. Mondelli was partially supported by the 2019 LopezLoreta Prize. The authors thank Phan-Minh Nguyen for helpful discussions and the IST Distributed Algorithms and Systems Lab for providing computational resources. article_processing_charge: No author: - first_name: Alexander full_name: Shevchenko, Alexander last_name: Shevchenko - first_name: Marco full_name: Mondelli, Marco id: 27EB676C-8706-11E9-9510-7717E6697425 last_name: Mondelli orcid: 0000-0002-3242-7020 citation: ama: '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.' apa: 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. chicago: Shevchenko, Alexander, 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. ieee: 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. ista: 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. mla: Shevchenko, Alexander, 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. short: A. Shevchenko, M. Mondelli, in:, Proceedings of the 37th International Conference on Machine Learning, ML Research Press, 2020, pp. 8773–8784. date_created: 2021-02-25T09:36:22Z date_published: 2020-07-13T00:00:00Z date_updated: 2023-10-17T12:43:19Z day: '13' ddc: - '000' department: - _id: MaMo external_id: arxiv: - '1912.10095' file: - access_level: open_access checksum: f042c8d4316bd87c6361aa76f1fbdbbe content_type: application/pdf creator: dernst date_created: 2021-03-02T15:38:14Z date_updated: 2021-03-02T15:38:14Z file_id: '9217' file_name: 2020_PMLR_Shevchenko.pdf file_size: 5336380 relation: main_file success: 1 file_date_updated: 2021-03-02T15:38:14Z has_accepted_license: '1' intvolume: ' 119' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 8773-8784 project: - _id: 059876FA-7A3F-11EA-A408-12923DDC885E name: Prix Lopez-Loretta 2019 - Marco Mondelli publication: Proceedings of the 37th International Conference on Machine Learning publication_status: published publisher: ML Research Press quality_controlled: '1' status: public title: Landscape connectivity and dropout stability of SGD solutions for over-parameterized neural networks type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 119 year: '2020' ...