# End-to-End Kernel Learning with Supervised Convolutional Kernel Networks

arXiv: https://arxiv.org/abs/1605.06265 · HTML: https://mlsanity.com/paper/1605.06265/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2016.

## Built on by (most cited first, 28 of 28)

- [KerGNNs: Interpretable Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/2201.00491/) (2022)
- [Approximation and Learning with Deep Convolutional Models: a Kernel Perspective](https://mlsanity.com/paper/2102.10032/) (2021)
- [Locality defeats the curse of dimensionality in convolutional teacher-student scenarios](https://mlsanity.com/paper/2106.08619/) (2021)
- [Learning with convolution and pooling operations in kernel methods](https://mlsanity.com/paper/2111.08308/) (2021)
- [A Rainbow in Deep Network Black Boxes](https://mlsanity.com/paper/2305.18512/) (2023)
- [On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernels](https://mlsanity.com/paper/2203.09255/) (2022)
- [Regularization of polynomial networks for image recognition](https://mlsanity.com/paper/2303.13896/) (2023)
- [The Unreasonable Effectiveness of Patches in Deep Convolutional Kernels Methods](https://mlsanity.com/paper/2101.07528/) (2021)
- [On the Benefits of Large Learning Rates for Kernel Methods](https://mlsanity.com/paper/2202.13733/) (2022)
- [Deformation Robust Roto-Scale-Translation Equivariant CNNs](https://mlsanity.com/paper/2111.10978/) (2021)
- [Learning in RKHM: a C^*-Algebraic Twist for Kernel Machines](https://mlsanity.com/paper/2210.11855/) (2022)
- [Descriptive Kernel Convolution Network with Improved Random Walk Kernel](https://mlsanity.com/paper/2402.06087/) (2024)
- [Pseudo-keypoint RKHS Learning for Self-supervised 6DoF Pose Estimation](https://mlsanity.com/paper/2311.09500/) (2023)
- [Convolutional Deep Kernel Machines](https://mlsanity.com/paper/2309.09814/) (2023)
- [MoSE: Unveiling Structural Patterns in Graphs via Mixture of Subgraph Experts](https://mlsanity.com/paper/2509.09337/) (2025)
- [Structured Convolutional Kernel Networks for Airline Crew Scheduling](https://mlsanity.com/paper/2105.11646/) (2021)
- [Convolutional Motif Kernel Networks](https://mlsanity.com/paper/2111.02272/) (2021)
- [Generalized Reference Kernel for One-class Classification](https://mlsanity.com/paper/2205.00534/) (2022)
- [Frequency Dropout: Feature-Level Regularization via Randomized Filtering](https://mlsanity.com/paper/2209.09844/) (2022)
- [Higher Order Gauge Equivariant CNNs on Riemannian Manifolds and Applications](https://mlsanity.com/paper/2305.16657/) (2023)
- [OTFPF: Optimal Transport-Based Feature Pyramid Fusion Network for Brain Age Estimation with 3D Overlapped ConvNeXt](https://mlsanity.com/paper/2205.04684/) (2022)
- [COmic: Convolutional Kernel Networks for Interpretable End-to-End Learning on (Multi-)Omics Data](https://mlsanity.com/paper/2212.02504/) (2022)
- [Tunneling the Loss Landscape: Bypassing Memorization with Monte Carlo Parameter Swapping](https://mlsanity.com/paper/2608.01833/) (2026)
- [Neural Generalization of Multiple Kernel Learning](https://mlsanity.com/paper/2102.13337/) (2021)
- [On Inductive Biases for Machine Learning in Data Constrained Settings](https://mlsanity.com/paper/2302.10692/) (2023)
- [Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered CKNs](https://mlsanity.com/paper/2408.04277/) (2024)
- [Stochastic Kernel Regularisation Improves Generalisation in Deep Kernel Machines](https://mlsanity.com/paper/2410.06171/) (2024)
- [L2GNet: Optimal Local-to-Global Representation of Anatomical Structures for Generalized Medical Image Segmentation](https://mlsanity.com/paper/2502.05229/) (2025)

## Abstract (arXiv)

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolutional kernel networks (CKNs) in the context of unsupervised learning; then, we derive backpropagation rules to take advantage of labeled training data. The resulting model is a new type of convolutional neural network, where optimizing the filters at each layer is equivalent to learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We show that our method achieves reasonably competitive performance for image classification on some standard "deep learning" datasets such as CIFAR-10 and SVHN, and also for image super-resolution, demonstrating the applicability of our approach to a large variety of image-related tasks.