# A representer theorem for deep kernel learning

arXiv: https://arxiv.org/abs/1709.10441 · HTML: https://mlsanity.com/paper/1709.10441/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2017.

## Built on by (most cited first, 26 of 26)

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- [Efficient Analysis of the Distilled Neural Tangent Kernel](https://mlsanity.com/paper/2602.11320/) (2026)
- [A Universal Reproducing Kernel Hilbert Space from Polynomial Alignment and IMQ Distance](https://mlsanity.com/paper/2605.03262/) (2026)
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- [Global-to-Local Support Spectrums for Language Model Explainability](https://mlsanity.com/paper/2408.05976/) (2024)
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- [Feature Understanding and Sparsity Enhancement via 2-Layered kernel machines (2L-FUSE)](https://mlsanity.com/paper/2509.07806/) (2025)
- [Featured Reproducing Kernel Banach Spaces for Learning and Neural Networks](https://mlsanity.com/paper/2602.07141/) (2026)

## Abstract (arXiv)

In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for the analysis of machine learning algorithms based on compositions of functions. As a direct consequence in the finite-sample case, the corresponding infinite-dimensional minimization problems can be recast into (nonlinear) finite-dimensional minimization problems, which can be tackled with nonlinear optimization algorithms. Moreover, we show how concatenated machine learning problems can be reformulated as neural networks and how our representer theorem applies to a broad class of state-of-the-art deep learning methods.