Establishes asymptotic consistency of factor estimates and √T-normality in factor-augmented regressions for fixed R ≥ r using anisotropic local laws from random matrix theory.
Advances in neural information processing systems , volume=
6 Pith papers cite this work. Polarity classification is still indexing.
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A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
Extends high-dimensional KRR to product kernels, proving convergence rates that recover minimax optimality for source condition s ≤ 1, saturation for s > 1, and multiple-descent phenomena with respect to sample size n.
Wahkon unifies Kolmogorov superposition with RKHS regularization to produce a deep network whose penalized estimator is exactly the MAP under a hierarchical GP prior and achieves minimax-optimal rates.
AdamO modifies Adam with an orthogonality correction to ensure the spectral radius of the TD update operator stays below one, providing a theoretical stability guarantee for offline RL.
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.
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Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.