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Poster
Implicit Bias of Gradient Descent on Reparametrized Models: On Equivalence to Mirror Descent
Zhiyuan Li · Tianhao Wang · Jason Lee · Sanjeev Arora

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #814
in Poster Session 4 »

As part of the effort to understand implicit bias of gradient descent in overparametrized models, several results have shown how the training trajectory on the overparametrized model can be understood as mirror descent on a different objective. The main result here is a complete characterization of this phenomenon under a notion termed commuting parametrization, which encompasses all the previous results in this setting. It is shown that gradient flow with any commuting parametrization is equivalent to continuous mirror descent with a related mirror map. Conversely, continuous mirror descent with any mirror map can be viewed as gradient flow with a related commuting parametrization. The latter result relies upon Nash's embedding theorem.

Keywords: Gradient Descent · implicit bias · mirror descent

Author Information

Zhiyuan Li (Stanford University)
Tianhao Wang (Yale University)
Jason Lee (University of Southern California)
Sanjeev Arora (Princeton University)

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