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Regularization for Deep Learning

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Regularization for Deep LearningLecture slides for Chapter 7 of Deep Learning Ian Goodfellow 2016-09-27(Goodfellow 2016)Definition Regularization is any modification we make to a Learning algorithm that is intended to reduce its generalization error but not its training error. (Goodfellow 2016)Weight Decay as Constrained OptimizationCHAPTER 7. Regularization FOR DEEP LEARNINGw1w2w wFigure : An illustration of the effect ofL2(or weight decay) Regularization on the valueof the optimalw. The solid ellipses represent contours of equal value of the unregularizedobjective. The dotted circles represent contours of equal value of theL2regularizer. Atthe point w, these competing objectives reach an equilibrium. In the first dimension, theeigenvalue of the Hessian ofJis small. The objective function does not increase muchwhen moving horizontally away fromw .Becausetheobjectivefunctiondoesnotexpre ssastrongpreferencealongthisdirection,th eregularizerhasastrongeffect on this regularizer pullsw1close to zero.

Lecture slides for Chapter 7 of Deep Learning www.deeplearningbook.org ... of an abstract, general, quadratic cost function. How do these effects relate to ... 14 1 19 2 23 3 7 7 7 7 5 = 2 6 6 6 6 4 3 1254 1 423 11 3 15 4 23 2 312303 54225 1 3 7 7 7 7 5 2 6 6 6 6 6 6 4 0 2 0 0 3 0 3 7 7 7 7 7 7 5 y 2 Rm B 2 Rm⇥n h 2 Rn (7.47)

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Bibliography Abadi,M.,Agarwal,A.,Barham,P.,Brevdo,E.,Chen,Z.,Citro,C.,Corrado,G.S.,Davis, A.,Dean,J.,Devin,M.,Ghemawat,S.,Goodfellow,I.,Harp,A.,Irving,G.,Isard,M.,

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