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?"