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Deep Residual Learning for Image Recognition

Deep Residual Learning for Image RecognitionKaiming HeXiangyu ZhangShaoqing RenJian SunMicrosoft Research{kahe, v-xiangz, v-shren, neural networks are more difficult to train. Wepresent a Residual Learning framework to ease the trainingof networks that are substantially deeper than those usedpreviously. We explicitly reformulate the layers as learn-ing Residual functions with reference to the layer inputs, in-stead of Learning unreferenced functions. We provide com-prehensive empirical evidence showing that these residualnetworks are easier to optimize, and can gain accuracy fromconsiderably increased depth. On the ImageNet dataset weevaluate Residual nets with a depth of up to 152 layers 8 deeper than VGG nets [41] but still having lower complex-ity. An ensemble of these Residual nets achieves erroron the ImageNettestset.}

underlying mapping as H(x), we let the stacked nonlinear layers fit another mapping of F(x) := H(x) x. The orig-inal mapping is recast into F(x)+x. We hypothesize that it is easier to optimize the residual mapping than to optimize the original, unreferenced mapping. To the extreme, if an identity mapping were optimal, it would be easier to push

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