mlsanityData to 7 Oct 2026

A representer theorem for deep kernel learning

arXiv 1709.10441 ↗First posted 29 Sep 2017cs.LG cs.NA math.NAcited by 26

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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.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Sep 2017.

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Citing papers per year: 2021: 5; 2022: 4; 2023: 5; 2024: 7; 2025: 2; 2026: 3.

26 papers.

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  1. 2021What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theorycited by 60
  2. 2023Deep networks for system identification: a Surveycited by 35
  3. 2022A Kernel-Expanded Stochastic Neural Networkcited by 9
  4. 2023Deep Learning with Kernels through RKHM and the Perron-Frobenius Operatorcited by 7
  5. 2022Multiresolution kernel matrix algebracited by 6
  6. 2023Deep Kernel Principal Component Analysis for Multi-level Feature Learningcited by 6
  7. 2024Hypothesis Spaces for Deep Learningcited by 4
  8. 2021Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing datacited by 3
  9. 2023Convolutional Deep Kernel Machinescited by 3
  10. 2024Spectral complexity of deep neural networkscited by 3
  11. 2024Towards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanicscited by 3
  12. 2024Multiscale scattered data analysis in samplet coordinatescited by 3
14 more
  1. 2021Analysis of Structured Deep Kernel Networkscited by 2
  2. 2021Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flowscited by 1
  3. 2021Exploring Adversarial Examples for Efficient Active Learning in Machine Learning Classifierscited by 1
  4. 2023Representer Point Selection for Explaining Regularized High-dimensional Modelscited by 1
  5. 2024C^*-Algebraic Machine Learning: Moving in a New Directioncited by 1
  6. 2025Operator-Based Generalization Bound for Deep Learning: Insights on Multi-Task Learningcited by 1
  7. 2026Efficient Analysis of the Distilled Neural Tangent Kernelcited by 1
  8. 2026A Universal Reproducing Kernel Hilbert Space from Polynomial Alignment and IMQ Distancecited by 1
  9. 2022LEFM-Nets: Learnable Explicit Feature Map Deep Networks for Segmentation of Histopathological Images of Frozen Sectionscited by 0
  10. 2022Counterfactual Learning with Multioutput Deep Kernelscited by 0
  11. 2024Global-to-Local Support Spectrums for Language Model Explainabilitycited by 0
  12. 2024A resource-efficient model for deep kernel learningcited by 0
  13. 2025Feature Understanding and Sparsity Enhancement via 2-Layered kernel machines (2L-FUSE)cited by 0
  14. 2026Featured Reproducing Kernel Banach Spaces for Learning and Neural Networkscited by 0