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| "belonging to the cell if all five networks agree. adapted from falk et al. (2019). 11.6 why do nets with residual connections perform so well? residual networks allow much deeper networks to be trained; it’s possible to extend the resnet architecture to 1000 layers and still train effectively. the improvement in image classification performance was initially attributed to the additional network depth, but two pieces of evidence contradict this viewpoint. first,shallower,widerresidualnetworkssometimesoutperformdeeper,narrowerones with a comparable parameter count. in other words, better performance can sometimes beachievedwithanetworkwithfewerlayersbutmorechannelsperlayer. second,there is evidence that the gradients during training do not propagate effectively through very long paths in the unraveled network (figure 11.4b). in effect, a very deep network may act more like a combination of shallower networks. the current view is that residual connections add some value of their own, as well as allowing deeper networks to be trained. this perspective is supported by the fact that the loss surfaces of residual networks around a minimum tend to be smoother and morepredictablethanthoseforthesamenetworkwhentheskipconnectionsareremoved (figure 11.13). this may make it easier to learn a good solution that generalizes well. 11.7 summary increasingnetworkdepthindefinitelycausesbothtrainingandtestperformanceforimage classification to decrease. this may be because the gradient of the loss with respect to draft: please send errata to [email protected] 11 residual networks figure 11.12 stacked hourglass networks for pose estimation. a) the network inputisanimagecontainingaperson,andtheoutputisasetofheatmaps,with oneheatmapforeachjoint. thisisformulatedasaregressionproblemwherethe targets are heatmap images with small, highlighted regions at the ground-truth jointpositions. thepeakoftheestimatedheatmapisusedtoestablisheachfinal joint position. b) the architecture consists of initial convolutional and residual layers followed by a series of hourglass blocks. c) each hourglass block consists ofanencoder-decodernetworksimilartotheu-netexceptthattheconvolutions usezeropadding,somefurtherprocessingisdoneintheresiduallinks,andthese links add this processed representation rather than concatenate it. each blue cuboid is itself a bottleneck residual block (figure 11.7b). adapted from newell et al. (2016). this work is subject to a creative commons cc-by-nc-nd license. (c) mit press.notes 201 figure 11.13 visualizing neural network loss surfaces. each plot shows the loss surfaceintworandomdirectionsinparameterspacearoundtheminimumfound by sgd for an image classification task on the cifar-10 dataset. these direc- tionsarenormalizedtofacilitateside-by-sidecomparison. a)residualnetwith56 layers. b) results from the same network without skip connections. the surface is smoother with the skip connections. this facilitates learning and makes the final network performance more robust to minor errors in the parameters, so it will likely generalize better. adapted from li et al. (2018b). parametersearlyinthenetworkchangesquicklyandunpredictablyrelativetotheupdate stepsize. residualconnectionsaddtheprocessedrepresentationbacktotheirowninput. now each layer contributes directly to the output as well as indirectly, so propagating gradients through many layers is not mandatory, and the loss surface is smoother. residualnetworksdon’tsufferfromvanishinggradientsbutintroduceanexponential increaseinthevarianceoftheactivationsduringforwardpropagationandcorresponding problems with exploding gradients. this is usually handled by adding batch normaliza- tion, which compensates for the empirical mean and variance of the batch and then shifts and rescales using learned parameters. if these parameters are initialized judi- ciously, very deep networks can be trained. there is evidence that both residual links and batch normalization make the loss surface smoother, which permits larger learning rates. moreover, the variability in the batch statistics adds a source of regularization. residual blocks have been incorporated into convolutional networks. they allow deeper networks to be trained with commensurate increases in image classification per- formance. variations of residual networks include the dense" | |