A descent-free method recovers the singularity order k of dead directions in neural networks from the directional-Fisher rate, classifies them, and assembles global learning coefficients matching closed forms.
Sumio Watanabe.Mathematical Theory of Bayesian Statistics
5 Pith papers cite this work. Polarity classification is still indexing.
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Dead-Direction Signatures provide closed-form spectral readings of dead directions in network activations and gradients that track rank deficits at singular minima, offering a cheap directional alternative to SGLD-based LLC.
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.
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.
Volume asymptotics of sublevel sets determine and recover the visible intrinsic divisorial spectrum of singularities via finite reconstruction.
citing papers explorer
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Measuring Dead Directions: Decomposing and Classifying Singular Structure off Canonical Alignment
A descent-free method recovers the singularity order k of dead directions in neural networks from the directional-Fisher rate, classifies them, and assembles global learning coefficients matching closed forms.
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Dead-Direction Signatures: A Cheap Spectral Reading of Singular Complexity
Dead-Direction Signatures provide closed-form spectral readings of dead directions in network activations and gradients that track rank deficits at singular minima, offering a cheap directional alternative to SGLD-based LLC.
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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.
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On the Divisorial Geometry of Volume Asymptotics of Sublevel Sets
Volume asymptotics of sublevel sets determine and recover the visible intrinsic divisorial spectrum of singularities via finite reconstruction.