# On the Pinsker bound of inner product kernel regression in large dimensions

arXiv: https://arxiv.org/abs/2409.00915 · HTML: https://mlsanity.com/paper/2409.00915/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 79 references that are in the map.
- First posted on arXiv 2 Sep 2024.

## Builds on (most cited first, 30 of 43)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)
- [On the Inductive Bias of Neural Tangent Kernels](https://mlsanity.com/paper/1905.12173/) (2019)
- [Linearized two-layers neural networks in high dimension](https://mlsanity.com/paper/1904.12191/) (2019)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration](https://mlsanity.com/paper/2101.10588/) (2021)
- [Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime](https://mlsanity.com/paper/2105.15004/) (2021)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [Learning with invariances in random features and kernel models](https://mlsanity.com/paper/2102.13219/) (2021)
- [The Interpolation Phase Transition in Neural Networks: Memorization and Generalization under Lazy Training](https://mlsanity.com/paper/2007.12826/) (2020)
- [Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces](https://mlsanity.com/paper/1801.06720/) (2018)
- [Dimension free ridge regression](https://mlsanity.com/paper/2210.08571/) (2022)
- [Spectrum of inner-product kernel matrices in the polynomial regime and multiple descent phenomenon in kernel ridge regression](https://mlsanity.com/paper/2204.10425/) (2022)
- [Consistency of Interpolation with Laplace Kernels is a High-Dimensional Phenomenon](https://mlsanity.com/paper/1812.11167/) (2018)
- [How rotational invariance of common kernels prevents generalization in high dimensions](https://mlsanity.com/paper/2104.04244/) (2021)
- [On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domains](https://mlsanity.com/paper/2305.02657/) (2023)
- [Generalization Ability of Wide Neural Networks on ℝ](https://mlsanity.com/paper/2302.05933/) (2023)
- [On the Optimality of Misspecified Spectral Algorithms](https://mlsanity.com/paper/2303.14942/) (2023)
- [A non-asymptotic theory of Kernel Ridge Regression: deterministic equivalents, test error, and GCV estimator](https://mlsanity.com/paper/2403.08938/) (2024)
- [Generalization in Kernel Regression Under Realistic Assumptions](https://mlsanity.com/paper/2312.15995/) (2023)
- [The Three Stages of Learning Dynamics in High-Dimensional Kernel Methods](https://mlsanity.com/paper/2111.07167/) (2021)
- [Precise Learning Curves and Higher-Order Scaling Limits for Dot Product Kernel Regression](https://mlsanity.com/paper/2205.14846/) (2022)
- [Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networks](https://mlsanity.com/paper/2109.09304/) (2021)
- [Learning with convolution and pooling operations in kernel methods](https://mlsanity.com/paper/2111.08308/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning Curves of Stochastic Gradient Descent in Kernel Regression](https://mlsanity.com/paper/2505.22048/) (2025)
- [Learning Curves and Benign Overfitting of Spectral Algorithms in Large Dimensions](https://mlsanity.com/paper/2604.23212/) (2026)

## Abstract (arXiv)

Building on recent studies of large-dimensional kernel regression, particularly those involving inner product kernels on the sphere mathbbSd, we investigate the Pinsker bound for inner product kernel regression in such settings. Specifically, we address the scenario where the sample size n is given by α dγ(1+od(1)) for some α, γ>0. We have determined the exact minimax risk for kernel regression in this setting, not only identifying the minimax rate but also the exact constant, known as the Pinsker constant, associated with the excess risk.