Example architecture of the D₄-equivariant shape measurement model (D₄CNN). The input galaxy image is transformed over the full D₄ orbit (four rotations and their mirrored counterparts), and we forward the CNN 8 times on each of the eight transformed variants to produce a set of features. These features are then mapped back to the original reference frame and combined through a weighted average to construct a D₄-equivariant feature representation. Finally, an unbiased odd MLP preserves the sign of this equivariant feature, ensuring the output shape transforms with the desired equivariance under D₄ symmetry operations.