Neural Tangent Kernel

Also known as NTK

Follow this topic Ask about this topic

Momentum

4 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28

Latest papers 32

All topics

Certified Approximation for Interpretable Representer Landmarks
Sep 30, 2026Jayanta Mukherjee, Shourya Verma, Mengbo Wang +2Neural Network Interpretability Kernel Methods
Department of Computer Science Purdue University West Lafayette, IN 47907, USA
First Learn, Then Memorize: The Spectral Bias of Diffusion Models
Sep 28, 2026Raphaël Urfin, Tony Bonnaire, Giulio Biroli +1Neural Network Generalization Memorization in Generative Models
Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005 Paris, France · Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405 Orsay, France · Department of Computing Sciences, Bocconi University, Milano, Italy
A Spectral Theory of Grokking: Weight Decay induces Feature Learning
Sep 22, 2026Lenz Pracher, Pascal de Jong, Oskar Lieshaus +2Neural Network Generalization Weight Decay
Arnold-Sommerfeld-Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Munich, Germany · Department of Applied Physics, Standford University, Standford, CA, USA · Department of Mathematics, University of Cambridge, Cambridge, UK
Latent-MoE: Domain-Aware Mixture-of-Experts for PDEs with Multi-Regime Physics
Sep 7, 2026Hanwen Wang, Paris PerdikarisNeural PDE Solvers Physics-Informed ML
Graduate Group of Applied Mathematics and Computational Science University of Pennsylvania Philadelphia, PA 19104 · Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia, PA 19104
Kernel Reboot: Breaking the Boundaries of Neural Tangent Kernels for Neural Fields
Sep 2, 2026Amir Mallak, Alaa Maalouf, Lior Wolf +2Implicit Neural Representations Meta-Learning
Department of Computer Science, University of Haifa · Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology · School of Computer Science and AI, Tel Aviv University
AdaptNTK: Adaptive Uncertainty Quantification and Active Learning for Neural Network Potentials
Aug 31, 2026Prajwal Ananth, Shuwen YueUncertainty Quantification Machine Learning Interatomic Potentials
Center for Applied Mathematics, Cornell University, Ithaca, NY, USA · R. F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY, USA
Correlation flow governs learning at criticality
Aug 8, 2026Andrea Combette, Nelly Pustelnik, Antoine VenailleNeural Network Initialization Neural Network Training Dynamics
CNRS, ENS de Lyon, Laboratoire de Physique UMR5672, Lyon, France
Tight Worst-Case Bounds for the Smallest Eigenvalue of ReLU NTK Gram Matrices
Aug 4, 2026Zhao SongReLU Neural Networks Spectral Methods
The Differential Neural Tangent Kernel and Its Positivity
Jul 11, 2026Bangti Jin, Longjun WuNeural PDE Solvers Physics-Informed ML
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China
A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel
Jul 7, 2026Arkaprabha Ganguli, Emil ConstantinescuNeural Network Generalization Kernel Regression
Mathematics & Computer Science Division, Argonne National Laboratory, Lemont, IL, USA
Scalable Uncertainty Quantification for Extreme Weather Forecasting via Empirical Neural Tangent Kernels
Jun 1, 2026Jose Marie Antonio Miñoza, Rex Gregor Laylo, Sebastian C. IbañezUncertainty Quantification Independent Component Analysis
Center for AI Research · Department of Education · Makati, Philippines
Spectral Reach: Understanding Neural Scaling as Progress into the Spectral Tail
May 29, 2026Konstantin Nikolaou, Jonas Scheunemann, Sven Krippendorf +2Representation Learning Neural Network Training Dynamics
Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany · Department of Applied Mathematics and Theoretical Physics and Department of Physics, University of Cambridge, Cambridge, UK
Label-NTK Alignments and A Tighter Convergence Bound in the NTK Regime
May 24, 2026Ruchirinkil Marreddy, Chaoyue LiuNeural Network Generalization Neural Tangent Kernel
Elmore Family School of Electrical and Computer Engineering Purdue University
Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization
May 22, 2026Youngjae Park, Jaemin Kim, Junghwa HongGauss-Newton Optimization Neural Network Optimization
Dept. of Control and Instrumentation Engineering, Korea University, Sejong, South Korea · BK21 FOUR Smart Mobility Education and Research Team, Korea University, Sejong, South Korea
Training Infinitely Deep and Wide Transformers
May 17, 2026Raphaël Barboni, Maarten V. de Hoop, Takashi Furuya +1Transformer Wasserstein Gradient Flows
Bocconi University · Rice University · Doshisha University, RIKEN AIP +1
The Neural Tangent Kernel for Classification
May 17, 2026Jonathan Plenk, Sergio Calvo-Ordonez, Alvaro Cartea +3Classification Neural Network Training Dynamics
Mathematical Institute, University of Oxford · Oxford-Man Institute of Quantitative Finance, University of Oxford · OATML, University of Oxford +2
Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel
May 14, 2026Ruihua Chen, Yisi Luo, Bangyu Wu +2Neural Tangent Kernel Inverse Problems
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China · School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, China · School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610000, China
Force-Aware Neural Tangent Kernels for Scalable and Robust Active Learning of MLIPs
May 13, 2026Eszter Varga-Umbrich, Zachary Weller-Davies, Paul Duckworth +3Machine Learning Interatomic Potentials Distribution Shift
InstaDeep, UK · Department of Engineering, University of Cambridge, Cambridge, UK
State-Space NTK Collapse Near Bifurcations
May 12, 2026James Hazelden, Eric Shea-BrownRecurrent Neural Networks Neural Network Training Dynamics
University of Washington
The Global Empirical NTK: Self-Referential Bias and Dimensionality of Gradient Descent Learning
May 9, 2026James Hazelden, Laura Driscoll, Eli Shlizerman +1Representation Learning Neural Tangent Kernel
Applied Mathematics, University of Washington; Allen Institute · Allen Institute · Neurobiology & Biophysics, University of Washington +2
Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit
May 8, 2026Konstantin Riedl, Konstantinos Spiliopoulos, Justin SirignanoNeural Network Optimization Spectral Bias
Mathematical Institute University of Oxford · Department of Mathematics & Statistics Boston University
Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer
May 8, 2026Clarissa Lauditi, Cengiz Pehlevan, Blake BordelonDeep Linear Networks Neural Network Training Dynamics
John A. Paulson School of Engineering and Applied Sciences, Harvard University · Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University · Center for Mathematical Sciences and Applications, Harvard University +1
Pretrained Model Representations as Acquisition Signals for Active Learning of MLIPs
May 5, 2026Eszter Varga-Umbrich, Shikha Surana, Paul Duckworth +3Machine Learning Interatomic Potentials Active Learning
1InstaDeep · University of Cambridge
Rethinking the Rank Threshold for LoRA Fine-Tuning
May 5, 2026Juneyoung ParkLow-Rank Adaptation Binary Classification
OptAI Inc.
Learning Dynamics of Zeroth-Order Optimization: A Kernel Perspective
May 5, 2026Zhe Li, Bicheng Ying, Zidong Liu +1Zeroth-Order Optimization LLM Fine-Tuning
Department of Computing and Information Sciences Ph.D., Rochester Institute of Technology, Rochester, NY, USA · Google Inc., Los Angeles, CA, USA · ComboCurve Inc., Houston, TX, USA
A Theory of Generalization in Deep Learning
May 2, 2026Elon Litman, Gabe GuoNeural Network Generalization Benign Overfitting
Stanford University
Topological Neural Tangent Kernel
May 1, 2026Sanjukta KrishnagopalSpectral Bias Neural Tangent Kernel
Department of Computer Science, University of California Santa Barbara
Adversarial Robustness of NTK Neural Networks
Apr 28, 2026Yuxuan HouNeural Network Robustness Adversarial Robustness
1Qiuzhen College, Tsinghua University
Collective Kernel EFT for Pre-activation ResNets
Apr 17, 2026Hidetoshi Kawase, Toshihiro OtaNeural Tangent Kernel
CyberAgent, Inc., Shibuya, Tokyo 150–6121 Japan
Gradient Flow Through Diagram Expansions: Learning Regimes and Explicit Solutions
Feb 4, 2026Dmitry Yarotsky, Eugene Golikov, Yaroslav GusevTensor Decomposition Mean-Field Theory
Applied AI Institute, Moscow, Russia · Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia.

Sep 30, 2026, cs.LGJ/K move · Enter open · S save

Certified Approximation for Interpretable Representer Landmarks

Jayanta Mukherjee, Shourya Verma, Mengbo Wang, Jasorsi Ghosh+1

Department of Computer Science Purdue University West Lafayette, IN 47907, USA

Neural Network Interpretability Kernel Methods Neural Tangent Kernel

Open paper AskPDF arXiv

Representer explanations rank the training landmarks that most influence a self-supervised representation. At scale, this ranking rests on up to four stacked approximations of the empirical neural tangent kernel (eNTK). These are random output heads, a parameter sketch, landmark sampling and a coefficient fit. Existing analyses bound each approximation separately, but none certifies the top-

K

set against their combined error. We introduce CAIRN (Certified Approximation for Interpretable Representer laNdmarks), a framework that carries this error through to the ranking. We derive the exact variance of the sketched multi-head eNTK, which matches measurement within

4\%

where Johnson-Lindenstrauss bounds err by up to

2.5\times

. This yields a high-probability top-

K

certificate for a fixed coefficient fit, alongside exact residual-trace certificates for discarded spectral mass. An exact product-variance identity separates kernel error from fit variability and identifies when a larger kernel budget can still sharpen a ranking. Stochastic Lanczos Quadrature (SLQ) estimates the effective dimension within

0.72\%

and guides the landmark budget without dense eigendecomposition. We show that residual mass does not control class coverage, and residual-greedy selection cuts the worst coverage excess of

k

-means++ from

8.5\times

1.55\times

(

4\times

on the sketched eNTK). Cross-view initializers outperform principal-component initialization in five (AUI) to all six (CSI) settings. Against the KREPES Gauss-Newton solver, CAIRN converges

2.5

11.3\times

faster, trails by at most

0.31

points and gains up to

3.14

points on MNIST. Together, these results make the reliability of representer explanations measurable and show where approximation budgets are best spent.

Momentum

Related topics

Latest papers 32