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With an eye toward understanding complexity control in deep learning, we study how infinitesimal regularization or gradient descent optimization lead to margin maximizing solutions in both homogeneous and non homogeneous models, extending previous work that focused on infinitesimal regularization only in homogeneous models. To this end we study the limit of loss minimization with a diverging norm constraint (the constrained path''), relate it to the limit of a
margin path'' and characterize the resulting solution. For non-homogeneous ensemble models, which output is a sum of homogeneous sub-models, we show that this solution discards the shallowest sub-models if they are unnecessary. For homogeneous models, we show convergence to a ``lexicographic max-margin solution'', and provide conditions under which max-margin solutions are also attained as the limit of unconstrained gradient descent.
Author Information
Mor Shpigel Nacson (Technion)
Suriya Gunasekar (Toyota Technological Institute at Chicago)
Jason Lee (University of Southern California)
Nati Srebro (Toyota Technological Institute at Chicago)
Daniel Soudry (Technion)
Related Events (a corresponding poster, oral, or spotlight)
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2019 Oral: Lexicographic and Depth-Sensitive Margins in Homogeneous and Non-Homogeneous Deep Models »
Tue. Jun 11th 09:20 -- 09:25 PM Room Grand Ballroom
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