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Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets

Author(s): Kuditipudi, Rohith; Wang, Xiang; Lee, Holden; Zhang, Yi; Li, Zhiyuan; et al

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 Abstract: Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima---at least those discovered by gradient-based optimization---turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths can be chosen to be piece-wise linear, with as few as two segments. We give mathematical explanations for this phenomenon, assuming generic properties (such as dropout stability and noise stability) of well-trained deep nets, which have previously been identified as part of understanding the generalization properties of deep nets. Our explanation holds for realistic multilayer nets, and experiments are presented to verify the theory. Publication Date: 2019 Citation: Kuditipudi, Rohith, Xiang Wang, Holden Lee, Yi Zhang, Zhiyuan Li, Wei Hu, Rong Ge, and Sanjeev Arora. "Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets." Advances in Neural Information Processing Systems 32 (2019). ISSN: 1049-5258 Type of Material: Conference Article Journal/Proceeding Title: Advances in Neural Information Processing Systems Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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