CCAR: Intrinsic Robustness as an Emergent Geometric Property
For supervised learning practitioners, CCAR offers a principled way to engineer robust representations without adversarial training, though it is incremental over existing regularization methods.
CCAR imposes a block-diagonal structure on feature space via a soft inductive bias, making robustness an emergent geometric property. It significantly outperforms baselines on label noise and input corruption benchmarks.
Standard supervised learning optimizes for predictive accuracy but remains agnostic to the internal geometry of learned features, often yielding representations that are entangled and brittle. We propose Class-Conditional Activation Regularization (CCAR) to explicitly engineer the feature space, imposing a block-diagonal structure via a soft inductive bias. By shaping the latent representation to confine class energy to orthogonal subspaces, we create an intrinsic geometric scaffold that naturally filters noise and adversarial perturbations. We provide theoretical analysis linking this structural constraint to the maximization of the Fisher Discriminant Ratio, establishing a formal connection between geometric disentanglement and algorithmic stability. Empirically, this approach demonstrates that robustness is an emergent property of a well-engineered feature space, significantly outperforming baselines on label noise and input corruption benchmarks.