For deep linear networks satisfying an alignment condition, the authors derive exact critical regularization strengths β_c = η_j at which each singular direction of the data covariance becomes learnable, via Landau-type effective potentials in the layer singular values.
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Cascading Through the Hierarchy: Regularizer-Induced Feature Detection as Phase Transitions in Deep Linear Neural Networks
For deep linear networks satisfying an alignment condition, the authors derive exact critical regularization strengths β_c = η_j at which each singular direction of the data covariance becomes learnable, via Landau-type effective potentials in the layer singular values.