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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AMUSE is a new optimizer integrating Muon orthogonalization with Schedule-Free averaging via adaptive interpolation for schedule-free anytime training that improves Pareto frontiers on vision and LLM tasks.
Adam's adaptive preconditioning and first-moment averaging improve high-probability tracking error in noise-dominated nonstationary regimes but can increase it under strong drift, where SGD achieves a smaller floor, with explicit beta-dependent bounds.
citing papers explorer
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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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AMUSE: Anytime Muon with Stable Gradient Evaluation
AMUSE is a new optimizer integrating Muon orthogonalization with Schedule-Free averaging via adaptive interpolation for schedule-free anytime training that improves Pareto frontiers on vision and LLM tasks.
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Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization
Adam's adaptive preconditioning and first-moment averaging improve high-probability tracking error in noise-dominated nonstationary regimes but can increase it under strong drift, where SGD achieves a smaller floor, with explicit beta-dependent bounds.