Depth induces an implicit low-rank bias in deep unconstrained feature models trained with unregularized multiclass cross-entropy, promoting softmax codes over neural collapse via more efficient norm propagation.
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Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
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The Implicit Bias of Depth: From Neural Collapse to Softmax Codes
Depth induces an implicit low-rank bias in deep unconstrained feature models trained with unregularized multiclass cross-entropy, promoting softmax codes over neural collapse via more efficient norm propagation.
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Pointwise Generalization in Deep Neural Networks
Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.