Convergence for adaptive resampling of random Fourier features
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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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 8 of its 24 references that are in the map. First posted on arXiv 3 Sep 2025.
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8 of 24 references.
References · 8
- 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 422
- 2021Deep learning: a statistical viewpointcited by 239
- 2020Loss landscapes and optimization in over-parameterized non-linear systems and neural networkscited by 231
- 2021Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolationcited by 130
- 2020Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don'tcited by 94
- 2018A Priori Estimates of the Population Risk for Two-layer Neural Networkscited by 76
- 2020Mathematical Perspective of Machine Learningcited by 5
- 2024Adaptive Random Fourier Features Training Stabilized By Resampling With Applications in Image Regressioncited by 2
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Citing papers per year: 2025: 1.
1 paper.