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"batch normalization needs access to the whole batch. however, this may not be easily available when training is distributed across several machines. layernormalizationorlayernorm(baetal.,2016)avoidsusingbatchstatisticsbynormalizing eachdataexampleseparately,usingstatisticsgatheredacrossthechannelsandspatialposition (figure 11.14c). however, there is still a separate learned scale γ and offset δ per channel. group normalization or groupnorm (wu & he, 2018) is similar to layernorm but divides the channels into groups and computes the statistics for each group separately across the within- groupchannelsandthespatialpositions(figure11.14d). again,therearestillseparatescaleand offset parameters per channel. instance normalization or instancenorm (ulyanov et al., 2016) takes this to the extreme where the number of groups is the same as the number of channels, soeachchannelisnormalizedseparately(figure11.14e),usingstatisticsgatheredacrossspatial draft: please send errata to [email protected] 11 residual networks figure 11.14 normalization schemes. batchnorm modifies each channel sepa- rately but adjusts each batch member in the same way based on statistics gath- ered across the batch and spatial position. ghost batchnorm computes these statistics from only part of the batch to make them more variable. layernorm computes statistics for each batch member separately, based on statistics gath- eredacrossthechannelsandspatialposition. itretainsaseparatelearnedscaling factor for each channel. groupnorm normalizes within each group of channels and also retains a separate scale and offset parameter for each channel. instan- cenormnormalizeswithineachchannelseparately,computingthestatisticsonly across spatial position. adapted from wu & he (2018). positionalone. salimans&kingma(2016)investigatednormalizingthenetworkweightsrather thantheactivations,butthishasbeenlessempiricallysuccessful. teyeetal.(2018)introduced montecarlobatchnormalization,whichcanprovidemeaningfulestimatesofuncertaintyinthe predictionsofneuralnetworks. arecentcomparisonofthepropertiesofdifferentnormalization schemes can be found in lubana et al. (2021). why batchnorm helps: batchnormhelpscontroltheinitialgradientsinaresidualnetwork (figure 11.6c). however, the mechanism by which batchnorm improves performance is not well understood. the stated goal of ioffe & szegedy (2015) was to reduce problems caused by internal covariate shift, which is the change in the distribution of inputs to a layer caused by updating preceding layers during the backpropagation update. however, santurkar et al. (2018) provided evidence against this view by artificially inducing covariate shift and showing that networks with and without batchnorm performed equally well. motivated by this, they searched for another explanation for why batchnorm should improve performance. they showed empirically for the vgg network that adding batch normalization decreases the variation in both the loss and its gradient as we move in the gradient direction. inotherwords,thelosssurfaceisbothsmootherandchangesmoreslowly,whichiswhylarger learning rates are possible. they also provide theoretical proofs for both these phenomena and show that for any parameter initialization, the distance to the nearest optimum is less for networks with batch normalization. bjorck et al. (2018) also argue that batchnorm improves the properties of the loss landscape and allows larger learning rates. otherexplanationsofwhybatchnormimprovesperformanceincludedecreasingtheimportance of tuning the learning rate (ioffe & szegedy, 2015; arora et al., 2018). indeed li & arora (2019)showthatusinganexponentiallyincreasinglearningratescheduleispossiblewithbatch normalization. ultimately, this is because batch normalization makes the network invariant to the scales of the weight matrices (see huszár, 2019, for an intuitive visualization). hoffer et al. (2017) identified that batchnorm has a regularizing effect due to statistical fluc- this work is subject to a creative commons cc-by-nc-nd license. (c) mit press.notes 205 tuations from the random composition of the batch. they proposed using a ghost batch size, in which the mean and standard" |
