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+",thiscanonlybesustainedforafewlayersbecausethenumberofchannels (and hence the number of parameters required to process them) becomes increasingly large. this problem can be alleviated by applying a 1×1 convolution to reduce the number of channels before the next 3×3 convolution is applied. in a convolutional network,theinputisperiodicallydownsampled. concatenationacrossthedownsampling makes no sense since the representations have different sizes. consequently, the chain of concatenation is broken at this point, and a smaller representation starts a new chain. inaddition, anotherbottleneck1×1convolutioncanbeappliedwhenthedownsampling occurs to control the representation size further. thisnetworkperformscompetitivelywithresnetmodelsonimageclassification(see figure 10.21); indeed, it can perform better for a comparable parameter count. this is presumably because it can reuse processing from earlier layers more flexibly. 11.5.3 u-nets and hourglass networks section10.5.3describedasemanticsegmentationnetworkthathadanencoder-decoderor hourglass structure. the encoder repeatedly downsamples the image until the receptive fields are large and information is integrated from across the image. then the decoder draft: please send errata to [email protected] 11 residual networks figure11.10u-netforsegmentinghelacells. theu-nethasanencoder-decoder structure, in which the representation is downsampled (orange blocks) and then re-upsampled (blue blocks). the encoder uses regular convolutions, and the de- coder uses transposed convolutions. residual connections append the last repre- sentationateachscaleintheencodertothefirstrepresentationatthesamescale inthedecoder(orangearrows). theoriginalu-netused“valid”convolutions,so the size decreased slightly with each layer, even without downsampling. hence, the representations from the encoder were cropped (dashed squares) before ap- pending to the decoder. adapted from ronneberger et al. (2015). upsamples it back to the size of the original image. the final output is a probability over possible object classes at each pixel. one drawback of this architecture is that the low-resolution representation in the middle of the network must “remember” the high-resolution details to make the final result accurate. this is unnecessary if residual connectionstransfertherepresentationsfromtheencodertotheirpartnerinthedecoder. the u-net (figure 11.10) is an encoder-decoder architecture where the earlier repre- sentations are concatenated to the later ones. the original implementation used “valid” convolutions, so the spatial size decreases by two pixels each time a 3×3 convolutional layer is applied. this means that the upsampled version is smaller than its counterpart in the encoder, which must be cropped before concatenation. subsequent implementa- tions have used zero padding, where this cropping is unnecessary. note that the u-net is completely convolutional, so after training, it can be run on an image of any size. problem11.9 the u-net was intended for segmenting medical images (figure 11.11) but has found many other uses in computer graphics and vision. hourglass networks are similar but applyfurtherconvolutionallayersintheskipconnectionsandaddtheresultbacktothe decoder rather than concatenating it. a series of these models form a stacked hourglass network that alternates between considering the image at local and global levels. such networksareusedforposeestimation(figure11.12). thesystemistrainedtopredictone “heatmap” for each joint, and the estimated position is the maximum of each heatmap. this work is subject to a creative commons cc-by-nc-nd license. (c) mit press.11.6 why do nets with residual connections perform so well? 199 figure 11.11 segmentation using u-net in 3d. a) three slices through a 3d volume of mouse cortex taken by scanning electron microscope. b) a single u- net is used to classify voxels as being inside or outside neurites. connected regions are identified with different colors. c) for a better result, an ensemble of five u-nets is trained, and a voxel is only classified as"