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We argue that the optimization plays a crucial role in generalization of deeplearning models through implicit regularization. We do this by demonstratingthat generalization ability is not controlled by network size but rather bysome other implicit control. We then demonstrate how changing the empiricaloptimization procedure can improve generalization, even if actual optimizationquality is not affected. We do so by studying the geometry of the parameterspace of deep networks, and devising an optimization algorithm attuned to thisgeometry.

Geometry of Optimization and Implicit Regularization in Deep Learning