CCAR: Intrinsic Robustness as an Emergent Geometric Property

TL;DR

This paper introduces CCAR, a regularization method that structures feature space geometrically to enhance robustness against noise and adversarial attacks, linking this to Fisher Discriminant Ratio.

Contribution

It proposes a novel regularization technique that enforces a block-diagonal structure in feature space, improving robustness through geometric disentanglement.

Findings

CCAR creates orthogonal subspaces for class representations.

Theoretical analysis links structural constraints to Fisher Discriminant Ratio.

Empirically, CCAR outperforms baselines on noise and corruption benchmarks.

Abstract

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.