Derives geodesic ridge regularization and Riemannian Gibbs Process prior for feature-learning wide neural networks, generalizing kernel-regime results via function-space axiomatization.
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Neural tangent kernel: Convergence and generalization in neural networks.Advances in neural information processing systems, 31
11 Pith papers cite this work. Polarity classification is still indexing.
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In extensive-width networks, features are recovered sequentially through sharp phase transitions, yielding an effective width k_c that unifies Bayes-optimal generalization error scaling as Θ(k_c d / n).
Online kernel regression equals offline regression with shifted targets; correcting the targets lets online learning match offline performance and outperform true targets in continual image classification.
In linear recurrent models, infinite-width signal propagation remains accurate only for depths t much smaller than sqrt(width n), with a critical regime at t ~ c sqrt(n) where finite-width effects emerge and dominate for larger t.
Learning in low-rank RNNs reduces to an exact low-dimensional ODE system in overlap space, where loss-invisible overlaps encode training history without affecting function.
A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
SiLD is a score-matching framework that learns both manifold projection and intrinsic density from a single objective, with proven sample complexity depending only on intrinsic dimension.
Adversarial training improves PINNs by using the discriminator to mitigate spectral bias and stiffness, with a new NTK-based framework providing theoretical grounding and a practical algorithm.
A two-level DMFT tracks bulk and outlier spectral dynamics in wide networks, predicting width-consistent outlier growth and hyperparameter transfer under muP scaling for deep linear nets while noting bulk restructuring for large-output tasks.
Gradient flow in energy-based models for strictly positive binary distributions produces stable data-consistent fixed points and a learning hierarchy that favors lower-order interactions first, mechanistically explaining distributional simplicity bias.
Negative-capable ridge regression uses controlled negative regularization as anti-shrinkage to increase effective complexity along weak eigendirections and mitigate underfitting in small-data regression.
citing papers explorer
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Canonical Regularisation of Wide Feature-Learning Neural Networks
Derives geodesic ridge regularization and Riemannian Gibbs Process prior for feature-learning wide neural networks, generalizing kernel-regime results via function-space axiomatization.
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Sharp feature-learning transitions and Bayes-optimal neural scaling laws in extensive-width networks
In extensive-width networks, features are recovered sequentially through sharp phase transitions, yielding an effective width k_c that unifies Bayes-optimal generalization error scaling as Θ(k_c d / n).
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Characterizing and Correcting Effective Target Shift in Online Learning
Online kernel regression equals offline regression with shifted targets; correcting the targets lets online learning match offline performance and outperform true targets in continual image classification.
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How Long Does Infinite Width Last? Signal Propagation in Long-Range Linear Recurrences
In linear recurrent models, infinite-width signal propagation remains accurate only for depths t much smaller than sqrt(width n), with a critical regime at t ~ c sqrt(n) where finite-width effects emerge and dominate for larger t.
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Learning reveals invisible structure in low-rank RNNs
Learning in low-rank RNNs reduces to an exact low-dimensional ODE system in overlap space, where loss-invisible overlaps encode training history without affecting function.
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Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equations
A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
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Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine
SiLD is a score-matching framework that learns both manifold projection and intrinsic density from a single objective, with proven sample complexity depending only on intrinsic dimension.
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When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective
Adversarial training improves PINNs by using the discriminator to mitigate spectral bias and stiffness, with a new NTK-based framework providing theoretical grounding and a practical algorithm.
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Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer
A two-level DMFT tracks bulk and outlier spectral dynamics in wide networks, predicting width-consistent outlier growth and hyperparameter transfer under muP scaling for deep linear nets while noting bulk restructuring for large-output tasks.
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Distributional simplicity bias and effective convexity in Energy Based Models
Gradient flow in energy-based models for strictly positive binary distributions produces stable data-consistent fixed points and a learning hierarchy that favors lower-order interactions first, mechanistically explaining distributional simplicity bias.
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A Ridge Too Far: Correcting Over-Shrinkage via Negative Regularization
Negative-capable ridge regression uses controlled negative regularization as anti-shrinkage to increase effective complexity along weak eigendirections and mitigate underfitting in small-data regression.