# Adaptive Random Fourier Features Training Stabilized By Resampling With Applications in Image Regression

arXiv: https://arxiv.org/abs/2410.06399 · HTML: https://mlsanity.com/paper/2410.06399/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Power and Limitations of Random Features for Understanding Neural Networks](https://mlsanity.com/paper/1904.00687/) (2019)
- [Wind Field Reconstruction with Adaptive Random Fourier Features](https://mlsanity.com/paper/2102.02365/) (2021)
- [Understanding the Spectral Bias of Coordinate Based MLPs Via Training Dynamics](https://mlsanity.com/paper/2301.05816/) (2023)
- [Comparing Spectral Bias and Robustness For Two-Layer Neural Networks: SGD vs Adaptive Random Fourier Features](https://mlsanity.com/paper/2402.00332/) (2024)

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

- [Convergence for adaptive resampling of random Fourier features](https://mlsanity.com/paper/2509.03151/) (2025)
- [An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations](https://mlsanity.com/paper/2507.15442/) (2025)

## Abstract (arXiv)

This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al., Foundations of Data Science, 2(3):309--332, 2020. This improved method uses a particle filter-type resampling technique to stabilize the training process and reduce the sensitivity to parameter choices. The Metropolis test can also be omitted when resampling is used, reducing the number of hyperparameters by one and reducing the computational cost per iteration compared to the ARFF method. We present comprehensive numerical experiments demonstrating the efficacy of the proposed algorithm in function regression tasks as a stand-alone method and as a pretraining step before gradient-based optimization, using the Adam optimizer. Furthermore, we apply the proposed algorithm to a simple image regression problem, illustrating its utility in sampling frequencies for the random Fourier features (RFF) layer of coordinate-based multilayer perceptrons. In this context, we use the proposed algorithm to sample the parameters of the RFF layer in an automated manner.