Classification

Dimension Matching and Projection Shortcuts

Element-wise addition in a residual block requires the shortcut output and the residual output F(x,{Wi})\mathcal{F}(\mathbf{x},\{W_i\}) to have the same dimensions. When channel dimensions increase or spatial feature maps are downsampled across stages, the shortcut must be adjusted before addition:

y=F(x,{Wi})+Wsx\mathbf{y}=\mathcal{F}(\mathbf{x},\{W_i\})+W_s\mathbf{x}

Three shortcut strategies handle dimension changes:

  • Option A — zero-padding shortcut: Retain a parameter-free identity shortcut and pad additional channel entries with zeros.
  • Option B — projection only for dimension increases: Apply a 1×11\times1 convolutional projection when dimensions change, using stride 22 when spatial downsampling is required; otherwise use an identity shortcut.
  • Option C — projection for all shortcuts: Replace every shortcut with a 1×11\times1 convolutional projection, even when input and output dimensions already match.

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Updated 2026-09-12

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Foundational Deep Learning Architectures: Transformers and Residual Networks @ University of Michigan - Ann Arbor

Ch.3 Deep Residual Network Architecture - Foundational Deep Learning Architectures: Transformers and Residual Networks @ University of Michigan - Ann Arbor

Residual Formulation and Shortcut Connections - Foundational Deep Learning Architectures: Transformers and Residual Networks @ University of Michigan - Ann Arbor

Identity versus Projection Shortcuts - Foundational Deep Learning Architectures: Transformers and Residual Networks @ University of Michigan - Ann Arbor

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Identity versus Projection Shortcuts - Overcoming Neural Network Degradation Through Residual Learning @ University of Michigan - Ann Arbor