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"by the biases. several regularization methods have been developed that are targeted specifically at residual architectures. resdrop (yamada et al., 2016), stochastic depth (huang et al., 2016), and randomdrop (yamada et al., 2019) all regularize residual networks by randomly dropping residualblocksduringthetrainingprocess. inthelattercase,thepropensityfordroppingablock isdeterminedbyabernoullivariable,whoseparameterislinearlydecreasedduringtraining. at testtime,theresidualblocksareaddedbackinwiththeirexpectedprobability. thesemethods are effectively versions of dropout, in which all the hidden units in a block are simultaneously this work is subject to a creative commons cc-by-nc-nd license. (c) mit press.notes 203 droppedinconcert. inthemultiplepathsviewofresidualnetworks(figure11.4b),theysimply removesomeofthepathsateachtrainingstep. wuetal.(2018b)developedblockdrop,which analyzesanexistingnetworkanddecideswhichresidualblockstouseatruntimewiththegoal of improving the efficiency of inference. other regularization methods have been developed for networks with multiple paths inside the residual block. shake-shake (gastaldi, 2017a,b) randomly re-weights the paths during the forward and backward passes. in the forward pass, this can be viewed as synthesizing random data, and in the backward pass, as injecting another form of noise into the training method. shakedrop (yamada et al., 2019) draws a bernoulli variable that decides whether each block will be subject to shake-shake or behave like a standard residual unit on this training step. batchnormalization: batchnormalizationwasintroducedbyioffe&szegedy(2015)outside of the context of residual networks. they showed empirically that it allowed higher learning rates,increasedconvergencespeed,andmadesigmoidactivationfunctionsmorepractical(since the distribution of outputs is controlled, so examples are less likely to fall in the saturated extremes of the sigmoid). balduzzi et al. (2017) investigated the activation of hidden units in laterlayersofdeepnetworkswithrelufunctionsatinitialization. theyshowedthatmanysuch hiddenunitswerealwaysactiveoralwaysinactiveregardlessoftheinputbutthatbatchnorm reduced this tendency. although batch normalization helps stabilize the forward propagation of signals through a network,yangetal.(2019)showedthatitcausesgradientexplosioninrelunetpworkswithout skip connections, with each layer increasing the magnitude of the gradients by π/(π−1) ≈ 1.21. this argument is summarized by luther (2020). since a residual network can be seen as a combination of paths of different lengths (figure 11.4), this effect must also be present in residualnetworks. presumably,however,thebenefitofremovingthe2k increasesinmagnitude in the forward pass of a network with k layers outweighs the harm done by increasing the gradients by 1.21k in the backward pass, so overall batchnorm makes training more stable. variations of batch normalization: several variants of batchnorm have been proposed (figure 11.14). batchnorm normalizes each channel separately based on statistics gathered across the batch. ghost batch normalization or ghostnorm (hoffer et al., 2017) uses only part of the batch to compute the normalization statistics, which makes them noisier and increases the amount of regularization when the batch size is very large (figure 11.14b). whenthebatchsizeisverysmallorthefluctuationswithinabatchareverylarge(asisoftenthe caseinnaturallanguageprocessing),thestatisticsinbatchnormmaybecomeunreliable. ioffe (2017) proposed batch renormalization, which keeps a running average of the batch statistics and modifies the normalization of any batch to ensure that it is more representative. another problemisthatbatchnormalizationisunsuitableforuseinrecurrentneuralnetworks(networks forprocessing sequences, in whichthe previous outputis fedbackas anadditional input aswe movethroughthesequence(seefigure12.19). here,thestatisticsmustbestoredateachstepin thesequence,andit’sunclearwhattodoifatestsequenceislongerthanthetrainingsequences. a third problem is that" |
