The normalized inverse-scale direction of LayerNorm's affine parameters is an exact algebraic kernel of the post-final-norm centred activation covariance for any input distribution in LayerNorm transformers.
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Dead directions recover Watanabe's RLCT contribution and triple (λ, m, ν) from directional Fisher curvature decay rates in original parameter space for singular models, extended via K-FAC to networks and gauge-equivariant optimizers.
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Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale
The normalized inverse-scale direction of LayerNorm's affine parameters is an exact algebraic kernel of the post-final-norm centred activation covariance for any input distribution in LayerNorm transformers.
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Dead Directions: Geometric Singular Learning
Dead directions recover Watanabe's RLCT contribution and triple (λ, m, ν) from directional Fisher curvature decay rates in original parameter space for singular models, extended via K-FAC to networks and gauge-equivariant optimizers.