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On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization

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arxiv 1802.06509 v2 pith:HVVEY2SH submitted 2018-02-19 cs.LG

classification cs.LG
keywords depthoptimizationaccelerationdeepeffectexpressivenessincreasinglinear
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abstract

Conventional wisdom in deep learning states that increasing depth improves expressiveness but complicates optimization. This paper suggests that, sometimes, increasing depth can speed up optimization. The effect of depth on optimization is decoupled from expressiveness by focusing on settings where additional layers amount to overparameterization - linear neural networks, a well-studied model. Theoretical analysis, as well as experiments, show that here depth acts as a preconditioner which may accelerate convergence. Even on simple convex problems such as linear regression with $\ell_p$ loss, $p>2$, gradient descent can benefit from transitioning to a non-convex overparameterized objective, more than it would from some common acceleration schemes. We also prove that it is mathematically impossible to obtain the acceleration effect of overparametrization via gradients of any regularizer.

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Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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