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
4 Pith papers cite this work. Polarity classification is still indexing.
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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.
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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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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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.