The element-wise addition in a residual block requires that the dimensions of the input $\mathbf{x}$ and the residual output $\mathcal{F}$ match. When changing channel dimensions or downsampling feature map sizes across stages (performed with a stride of 2), a dimension-matching operation must be applied to the shortcut.

To match dimensions, a linear projection $W_s$ is applied along the shortcut connection: $\mathbf{y} = \mathcal{F}(\mathbf{x}, \{W_i\}) + W_s\mathbf{x}$ Three shortcut strategies are evaluated for handling dimension changes:

• Option A: Zero-padding shortcuts are used to increase dimensions, keeping all shortcuts parameter-free.
• Option B: Projection shortcuts (implemented via $1 \times 1$ convolutions) are used only when increasing dimensions, while all other shortcuts remain parameter-free identity mappings.
• Option C: All shortcuts in the network are linear projections.

While all three options substantially outperform plain baselines, Option B achieves slightly better accuracy than Option A because zero-padded entries do not participate in residual learning. Option C yields only a marginal improvement over Option B at the expense of adding many extra parameters. Because projection shortcuts are not essential for solving the degradation problem, identity shortcuts are preferred to minimize model size and computational complexity.