# Convolutional Kernel Networks

arXiv: https://arxiv.org/abs/1406.3332 · HTML: https://mlsanity.com/paper/1406.3332/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2014.

## Built on by (most cited first, 30 of 47)

- [Deep Learning for Instance Retrieval: A Survey](https://mlsanity.com/paper/2101.11282/) (2021)
- [On Aliased Resizing and Surprising Subtleties in GAN Evaluation](https://mlsanity.com/paper/2104.11222/) (2021)
- [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)
- [Learning with convolution and pooling operations in kernel methods](https://mlsanity.com/paper/2111.08308/) (2021)
- [Fast Neural Kernel Embeddings for General Activations](https://mlsanity.com/paper/2209.04121/) (2022)
- [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)
- [On the Sample Complexity of Learning under Invariance and Geometric Stability](https://mlsanity.com/paper/2106.07148/) (2021)
- [Regularization of polynomial networks for image recognition](https://mlsanity.com/paper/2303.13896/) (2023)
- [Graph-adaptive Rectified Linear Unit for Graph Neural Networks](https://mlsanity.com/paper/2202.06281/) (2022)
- [A Kernel-Expanded Stochastic Neural Network](https://mlsanity.com/paper/2201.05319/) (2022)
- [The Unreasonable Effectiveness of Patches in Deep Convolutional Kernels Methods](https://mlsanity.com/paper/2101.07528/) (2021)
- [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)
- [Deep Learning with Kernels through RKHM and the Perron-Frobenius Operator](https://mlsanity.com/paper/2305.13588/) (2023)
- [Neural Hilbert Ladders: Multi-Layer Neural Networks in Function Space](https://mlsanity.com/paper/2307.01177/) (2023)
- [Descriptive Kernel Convolution Network with Improved Random Walk Kernel](https://mlsanity.com/paper/2402.06087/) (2024)
- [Shifting the Paradigm: A Diffeomorphism Between Time Series Data Manifolds for Achieving Shift-Invariancy in Deep Learning](https://mlsanity.com/paper/2502.19921/) (2025)
- [Pseudo-keypoint RKHS Learning for Self-supervised 6DoF Pose Estimation](https://mlsanity.com/paper/2311.09500/) (2023)
- [Correlated Weights in Infinite Limits of Deep Convolutional Neural Networks](https://mlsanity.com/paper/2101.04097/) (2021)
- [Convolutional Deep Kernel Machines](https://mlsanity.com/paper/2309.09814/) (2023)
- [Feature Hallucination for Self-supervised Action Recognition](https://mlsanity.com/paper/2506.20342/) (2025)
- [Faster Convergence in Deep-Predictive-Coding Networks to Learn Deeper Representations](https://mlsanity.com/paper/2101.06848/) (2021)
- [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)
- [Deep Layer-wise Networks Have Closed-Form Weights](https://mlsanity.com/paper/2202.01210/) (2022)
- [Infinite-Dimensional Feature Interaction](https://mlsanity.com/paper/2405.13972/) (2024)
- [Learning from Few Samples: Transformation-Invariant SVMs with Composition and Locality at Multiple Scales](https://mlsanity.com/paper/2109.12784/) (2021)
- [Dual Convexified Convolutional Neural Networks](https://mlsanity.com/paper/2205.14056/) (2022)

## Abstract (arXiv)

An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is encoded by a reproducing kernel. Unlike traditional approaches where neural networks are learned either to represent data or for solving a classification task, our network learns to approximate the kernel feature map on training data. Such an approach enjoys several benefits over classical ones. First, by teaching CNNs to be invariant, we obtain simple network architectures that achieve a similar accuracy to more complex ones, while being easy to train and robust to overfitting. Second, we bridge a gap between the neural network literature and kernels, which are natural tools to model invariance. We evaluate our methodology on visual recognition tasks where CNNs have proven to perform well, e.g., digit recognition with the MNIST dataset, and the more challenging CIFAR-10 and STL-10 datasets, where our accuracy is competitive with the state of the art.