Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.
Phase transitions for feature learning in neural networks
6 Pith papers cite this work. Polarity classification is still indexing.
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Grokking reflects escape from a metastable low-dimensional regime where transverse curvature accumulates before generalization, with subspace motion necessary but curvature boost insufficient.
On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
Multi-task grokking in Transformers produces staggered generalization, low-dimensional manifolds, weight-decay phase structure, holographic solutions, and transverse redundancy.
For multi-index polynomials, the top r eigenspace of the AGOP matrix from KRR recovers the central subspace at sample complexity n ~ d^{p+δ} where p is the degree of the informative component.
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.
citing papers explorer
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Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning
Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.
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Low-Dimensional and Transversely Curved Optimization Dynamics in Grokking
Grokking reflects escape from a metastable low-dimensional regime where transverse curvature accumulates before generalization, with subspace motion necessary but curvature boost insufficient.
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Phases of Muon: When Muon Eclipses SignSGD
On power-law covariance least squares problems, SignSVD (Muon) and SignSGD (Adam proxy) show three phases of relative performance depending on data exponent α and target exponent β.
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The Geometry of Multi-Task Grokking: Transverse Instability, Superposition, and Weight Decay Phase Structure
Multi-task grokking in Transformers produces staggered generalization, low-dimensional manifolds, weight-decay phase structure, holographic solutions, and transverse redundancy.
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Average Gradient Outer Product in kernel regression provably recovers the central subspace for multi-index models
For multi-index polynomials, the top r eigenspace of the AGOP matrix from KRR recovers the central subspace at sample complexity n ~ d^{p+δ} where p is the degree of the informative component.
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There Will Be a Scientific Theory of Deep Learning
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.