Standard CNNs lack rotational and reflection equivariance, resulting in severe diagnostic instability and high prediction flip rates. They must "re-learn" that a tumor is still a tumor when rotated 90 degrees, wasting parameter capacity and requiring massive labeled datasets.

To resolve this, we engineered a custom 5-layer Group-Equivariant CNN for the PatchCamelyon (PCam) metastasis dataset. By mathematically enforcing the D4 dihedral symmetry group directly into the kernel structure, we mapped features into a rotation-invariant latent space. We then implemented Steerable CNNs (ESCNN) using continuous circular harmonics, bringing the diagnostic flip rate to an absolute 0.00% with a 0.93 AUC.

Finally, we benchmarked these priors against Vision Transformers (ViT), leveraging global self-attention to achieve a 0.97 AUC and 90.66% recall. This project formalizes the fundamental clinical trade-off between strict geometric stability and unconstrained predictive capacity.