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We expand the expected loss over the class-conditional distribution: Eh|c[L(h, c)] =E h|c (POc h)⊤(POc h) (9) =E h|c h⊤P ⊤ Oc POc h (10) =E h|c h⊤POc h (Idempotence:P ⊤P=P) (11) =E h|c Tr(h⊤POc h) (Scalar trace identity) (12) =E h|c Tr(POc · 2016

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cs.LG 1

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2026 1

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UNVERDICTED 1

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CCAR: Intrinsic Robustness as an Emergent Geometric Property

cs.LG · 2026-04-18 · unverdicted · novelty 6.0

CCAR adds a regularization term that forces class activations into orthogonal subspaces, linking this structure to higher Fisher Discriminant Ratio and improved robustness on noisy and corrupted data.

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  • CCAR: Intrinsic Robustness as an Emergent Geometric Property cs.LG · 2026-04-18 · unverdicted · none · ref 1

    CCAR adds a regularization term that forces class activations into orthogonal subspaces, linking this structure to higher Fisher Discriminant Ratio and improved robustness on noisy and corrupted data.