# Convergence for adaptive resampling of random Fourier features

arXiv: https://arxiv.org/abs/2509.03151 · HTML: https://mlsanity.com/paper/2509.03151/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 3 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't](https://mlsanity.com/paper/2009.10713/) (2020)
- [A Priori Estimates of the Population Risk for Two-layer Neural Networks](https://mlsanity.com/paper/1810.06397/) (2018)
- [Mathematical Perspective of Machine Learning](https://mlsanity.com/paper/2007.01503/) (2020)
- [Adaptive Random Fourier Features Training Stabilized By Resampling With Applications in Image Regression](https://mlsanity.com/paper/2410.06399/) (2024)

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

- [Cluster-Based Generalized Additive Models Informed by Random Fourier Features](https://mlsanity.com/paper/2512.19373/) (2025)

## Abstract (arXiv)

The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier frequencies. The challenge is to sample the Fourier frequencies well. This work proves convergence of a data adaptive method based on resampling the frequencies asymptotically optimally, as the number of nodes and amount of data tend to infinity. Numerical results based on resampling and adaptive random walk steps together with approximations of the least squares problem by conjugate gradient iterations confirm the analysis for regression and classification problems.