equivariance testing

**Equivariance Testing** is a **model validation technique that verifies whether the model's output transforms predictably when the input is transformed** — unlike invariance (output unchanged), equivariance means the output changes in a corresponding, predictable way (e.g., rotating input rotates the output mask). **Invariance vs. Equivariance** - **Invariance**: $f(T(x)) = f(x)$ — output is unchanged by the transformation. - **Equivariance**: $f(T(x)) = T'(f(x))$ — output transforms correspondingly with the input transformation. - **Example**: Classification should be rotation-invariant. Segmentation should be rotation-equivariant. - **Testing**: Apply transformation $T$ and verify the output-transform relationship holds. **Why It Matters** - **Segmentation/Detection**: Object detection and segmentation models should be equivariant to geometric transforms. - **Physics**: Physical models should be equivariant to coordinate transformations (rotation, translation). - **Architecture Design**: Equivariance testing validates that architectures (group-equivariant CNNs, E(n)-equivariant networks) achieve the desired symmetries. **Equivariance Testing** is **testing that outputs transform correctly** — verifying that model outputs respond predictably to input transformations.