# Changing the Kernel During Training Leads to Double Descent in Kernel Regression

arXiv: https://arxiv.org/abs/2311.01762 · HTML: https://mlsanity.com/paper/2311.01762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 70 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Builds on (most cited first, 30 of 38)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [High-dimensional dynamics of generalization error in neural networks](https://mlsanity.com/paper/1710.03667/) (2017)
- [SGD on Neural Networks Learns Functions of Increasing Complexity](https://mlsanity.com/paper/1905.11604/) (2019)
- [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)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes](https://mlsanity.com/paper/1910.12478/) (2019)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [On the linearity of large non-linear models: when and why the tangent kernel is constant](https://mlsanity.com/paper/2010.01092/) (2020)
- [The Neural Tangent Kernel in High Dimensions: Triple Descent and a Multi-Scale Theory of Generalization](https://mlsanity.com/paper/2008.06786/) (2020)
- [Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate](https://mlsanity.com/paper/1806.05161/) (2018)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [Improving DNN Robustness to Adversarial Attacks using Jacobian Regularization](https://mlsanity.com/paper/1803.08680/) (2018)
- [Scaling description of generalization with number of parameters in deep learning](https://mlsanity.com/paper/1901.01608/) (2019)
- [A Model of Double Descent for High-dimensional Binary Linear Classification](https://mlsanity.com/paper/1911.05822/) (2019)
- [On the Similarity between the Laplace and Neural Tangent Kernels](https://mlsanity.com/paper/2007.01580/) (2020)
- [The Recurrent Neural Tangent Kernel](https://mlsanity.com/paper/2006.10246/) (2020)
- [Kernel regression in high dimensions: Refined analysis beyond double descent](https://mlsanity.com/paper/2010.02681/) (2020)
- [A U-turn on Double Descent: Rethinking Parameter Counting in Statistical Learning](https://mlsanity.com/paper/2310.18988/) (2023)
- [Diving into the shallows: a computational perspective on large-scale shallow learning](https://mlsanity.com/paper/1703.10622/) (2017)

## Built on by (most cited first, 1 of 1)

- [A Rigorous, Tractable Measure of Model Complexity](https://mlsanity.com/paper/2605.21167/) (2026)

## Abstract (arXiv)

We investigate changing the bandwidth of a translational-invariant kernel during training when solving kernel regression with gradient descent. We present a theoretical bound on the out-of-sample generalization error that advocates for decreasing the bandwidth (and thus increasing the model complexity) during training. We further use the bound to show that kernel regression exhibits a double descent behavior when the model complexity is expressed as the minimum allowed bandwidth during training. Decreasing the bandwidth all the way to zero results in benign overfitting, and also circumvents the need for model selection. We demonstrate the double descent behavior on real and synthetic data and also demonstrate that kernel regression with a decreasing bandwidth outperforms that of a constant bandwidth, selected by cross-validation or marginal likelihood maximization. We finally apply our findings to neural networks, demonstrating that by modifying the neural tangent kernel (NTK) during training, making the NTK behave as if its bandwidth were decreasing to zero, we can make the network overfit more benignly, and converge in fewer iterations.