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In Deep Residual Learning for Image Recognition, I am trying to understand better the "dotted shortcuts" from Figure 3, where the first convolutional layer in those shortcuts is applied with stride of 2. I understand the linear transformation via 1x1 convolution to handle the increase in dimension, i.e., Eqn.(2). It's the stride of 2 that confuses me a little conceptually.

The authors state "... when the shortcuts go across feature maps of two sizes, they are performed with a stride of 2." Implementing that (downsampling by factor of 2) I understand, but throwing away 75% of the spatial data doesn't feel like it preserves the concept of an "identity mapping."

Am I misunderstanding something or just being unnecessarily rigorous when thinking of "identity mapping?"

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I came across the same question as you and I also think it is an identity, and you don't need to be rigorous. Sometimes the shape has changed, and in order to add them together, you have to change the shape of original tensor (or blob in caffe) by adjusting the stride.

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