# Implicit Kernel Learning

arXiv: https://arxiv.org/abs/1902.10214 · HTML: https://mlsanity.com/paper/1902.10214/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2019.

## Built on by (most cited first, 13 of 13)

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- [On Learning the Transformer Kernel](https://mlsanity.com/paper/2110.08323/) (2021)
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- [Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features](https://mlsanity.com/paper/2407.00584/) (2024)
- [Kernel Biclustering algorithm in Hilbert Spaces](https://mlsanity.com/paper/2208.03675/) (2022)
- [MetaKernel: Learning Variational Random Features with Limited Labels](https://mlsanity.com/paper/2105.03781/) (2021)
- [Learning High-Dimensional Distributions with Latent Neural Fokker-Planck Kernels](https://mlsanity.com/paper/2105.04538/) (2021)
- [Generative Feature Training of Thin 2-Layer Networks](https://mlsanity.com/paper/2411.06848/) (2024)
- [CKGAN: Training Generative Adversarial Networks Using Characteristic Kernel Integral Probability Metrics](https://mlsanity.com/paper/2504.05945/) (2025)
- [Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimization](https://mlsanity.com/paper/2103.01575/) (2021)
- [On the Laplace Approximation as Model Selection Criterion for Gaussian Processes](https://mlsanity.com/paper/2403.09215/) (2024)
- [Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization](https://mlsanity.com/paper/2606.11255/) (2026)

## Abstract (arXiv)

Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While learning the kernel in a data driven way has been investigated, in this paper we explore learning the spectral distribution of kernel via implicit generative models parametrized by deep neural networks. We called our method Implicit Kernel Learning (IKL). The proposed framework is simple to train and inference is performed via sampling random Fourier features. We investigate two applications of the proposed IKL as examples, including generative adversarial networks with MMD (MMD GAN) and standard supervised learning. Empirically, MMD GAN with IKL outperforms vanilla predefined kernels on both image and text generation benchmarks; using IKL with Random Kitchen Sinks also leads to substantial improvement over existing state-of-the-art kernel learning algorithms on popular supervised learning benchmarks. Theory and conditions for using IKL in both applications are also studied as well as connections to previous state-of-the-art methods.