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Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets
Rohith Kuditipudi · Xiang Wang · Holden Lee · Yi Zhang · Zhiyuan Li · Wei Hu · Rong Ge · Sanjeev Arora

Thu Dec 12 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #165

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.

Author Information

Rohith Kuditipudi (Duke University)
Xiang Wang (Duke University)
Holden Lee (Princeton)
Yi Zhang (Princeton)
Zhiyuan Li (Princeton University)
Wei Hu (Princeton University)
Rong Ge (Duke University)
Sanjeev Arora (Princeton University)

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