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In Goodfellow's Deep Learning book (http://www.deeplearningbook.org/contents/regularization.html 7.12) they state:

Because we usually use an inclusion probability of 1/2, the weight scaling rule usually amounts to dividing the weights by 2 at the end of training, and then using the model as usual. Another way to achieve the same result is to multiply the states of the units by 2 during training.

Could someone explain the purpose of rescaling when using dropout? I am having trouble grasping what exactly this is correcting for.

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Consider the case you have dropout with p probability where p is (0,1] ,

the expected value of an output feature is p*E(WT+x),as only p units are used, say if feature>=4 then class A else B, now for the same input if in test time you do not have any dropout the Expected value of the activation is: E(WT+x) as all units are used, thus to prevent the decision boundary from shifting you reweigh the weights by 1/p to keep the expected activation same at the final layer.

In short you are doing weighted average(and not the addition) of the exponential set of networks learnt with dropout.

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  • $\begingroup$ It seems to me that if dropout is used only in the last layer (as it is usually the case for convnets with a fully-connected layer at the end), then the scaling is not needed, because it will not affect choosing the largest output of the model (for classification task). $\endgroup$ – MichaelSB May 5 at 0:37

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