# End-to-end Kernel Learning via Generative Random Fourier Features

arXiv: https://arxiv.org/abs/2009.04614 · HTML: https://mlsanity.com/paper/2009.04614/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2020.

## Built on by (most cited first, 7 of 7)

- [Kernel PCA for Out-of-Distribution Detection](https://mlsanity.com/paper/2402.02949/) (2024)
- [On Learning the Transformer Kernel](https://mlsanity.com/paper/2110.08323/) (2021)
- [FiGURe: Simple and Efficient Unsupervised Node Representations with Filter Augmentations](https://mlsanity.com/paper/2310.01892/) (2023)
- [Kernel PCA for Out-of-Distribution Detection: Non-Linear Kernel Selection and Approximation](https://mlsanity.com/paper/2505.15284/) (2025)
- [Cluster-Based Generalized Additive Models Informed by Random Fourier Features](https://mlsanity.com/paper/2512.19373/) (2025)
- [Contrastive-Collapsed Loss for Flexible and Geometrically Optimal Embeddings and Faster Convergence](https://mlsanity.com/paper/2607.12916/) (2026)
- [Deep kernel hedging](https://mlsanity.com/paper/2609.34474/) (2026)

## Abstract (arXiv)

Random Fourier features (RFFs) provide a promising way for kernel learning in a spectral case. Current RFFs-based kernel learning methods usually work in a two-stage way. In the first-stage process, learning the optimal feature map is often formulated as a target alignment problem, which aims to align the learned kernel with the pre-defined target kernel (usually the ideal kernel). In the second-stage process, a linear learner is conducted with respect to the mapped random features. Nevertheless, the pre-defined kernel in target alignment is not necessarily optimal for the generalization of the linear learner. Instead, in this paper, we consider a one-stage process that incorporates the kernel learning and linear learner into a unifying framework. To be specific, a generative network via RFFs is devised to implicitly learn the kernel, followed by a linear classifier parameterized as a full-connected layer. Then the generative network and the classifier are jointly trained by solving the empirical risk minimization (ERM) problem to reach a one-stage solution. This end-to-end scheme naturally allows deeper features, in correspondence to a multi-layer structure, and shows superior generalization performance over the classical two-stage, RFFs-based methods in real-world classification tasks. Moreover, inspired by the randomized resampling mechanism of the proposed method, its enhanced adversarial robustness is investigated and experimentally verified.