# Neural Kernels Without Tangents

arXiv: https://arxiv.org/abs/2003.02237 · HTML: https://mlsanity.com/paper/2003.02237/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 30 of 56)

- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [Dataset Distillation with Infinitely Wide Convolutional Networks](https://mlsanity.com/paper/2107.13034/) (2021)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Efficient Dataset Distillation Using Random Feature Approximation](https://mlsanity.com/paper/2210.12067/) (2022)
- [Discover and Cure: Concept-aware Mitigation of Spurious Correlation](https://mlsanity.com/paper/2305.00650/) (2023)
- [Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeed](https://mlsanity.com/paper/2102.11742/) (2021)
- [Separation of Scales and a Thermodynamic Description of Feature Learning in Some CNNs](https://mlsanity.com/paper/2112.15383/) (2021)
- [Limitations of the NTK for Understanding Generalization in Deep Learning](https://mlsanity.com/paper/2206.10012/) (2022)
- [A self consistent theory of Gaussian Processes captures feature learning effects in finite CNNs](https://mlsanity.com/paper/2106.04110/) (2021)
- [How rotational invariance of common kernels prevents generalization in high dimensions](https://mlsanity.com/paper/2104.04244/) (2021)
- [Contrastive Learning Can Find An Optimal Basis For Approximately View-Invariant Functions](https://mlsanity.com/paper/2210.01883/) (2022)
- [Approximation and Learning with Deep Convolutional Models: a Kernel Perspective](https://mlsanity.com/paper/2102.10032/) (2021)
- [Implicit Regularization or Implicit Conditioning? Exact Risk Trajectories of SGD in High Dimensions](https://mlsanity.com/paper/2206.07252/) (2022)
- [Neural Tangent Kernel: A Survey](https://mlsanity.com/paper/2208.13614/) (2022)
- [Interpolating Classifiers Make Few Mistakes](https://mlsanity.com/paper/2101.11815/) (2021)
- [Universal Sharpness Dynamics in Neural Network Training: Fixed Point Analysis, Edge of Stability, and Route to Chaos](https://mlsanity.com/paper/2311.02076/) (2023)
- [The Limitations of Large Width in Neural Networks: A Deep Gaussian Process Perspective](https://mlsanity.com/paper/2106.06529/) (2021)
- [Learning with convolution and pooling operations in kernel methods](https://mlsanity.com/paper/2111.08308/) (2021)
- [What Can the Neural Tangent Kernel Tell Us About Adversarial Robustness?](https://mlsanity.com/paper/2210.05577/) (2022)
- [Six Lectures on Linearized Neural Networks](https://mlsanity.com/paper/2308.13431/) (2023)
- [Phase diagram of early training dynamics in deep neural networks: effect of the learning rate, depth, and width](https://mlsanity.com/paper/2302.12250/) (2023)
- [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)
- [More is Better in Modern Machine Learning: when Infinite Overparameterization is Optimal and Overfitting is Obligatory](https://mlsanity.com/paper/2311.14646/) (2023)
- [Eigenspace Restructuring: a Principle of Space and Frequency in Neural Networks](https://mlsanity.com/paper/2112.05611/) (2021)
- [Mechanism of feature learning in convolutional neural networks](https://mlsanity.com/paper/2309.00570/) (2023)
- [Can we achieve robustness from data alone?](https://mlsanity.com/paper/2207.11727/) (2022)
- [On the Parameterization of Second-Order Optimization Effective Towards the Infinite Width](https://mlsanity.com/paper/2312.12226/) (2023)
- [Generalization Guarantees for Neural Architecture Search with Train-Validation Split](https://mlsanity.com/paper/2104.14132/) (2021)
- [Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks](https://mlsanity.com/paper/2201.04753/) (2022)

## Abstract (arXiv)

We investigate the connections between neural networks and simple building blocks in kernel space. In particular, using well established feature space tools such as direct sum, averaging, and moment lifting, we present an algebra for creating "compositional" kernels from bags of features. We show that these operations correspond to many of the building blocks of "neural tangent kernels (NTK)". Experimentally, we show that there is a correlation in test error between neural network architectures and the associated kernels. We construct a simple neural network architecture using only 3x3 convolutions, 2x2 average pooling, ReLU, and optimized with SGD and MSE loss that achieves 96% accuracy on CIFAR10, and whose corresponding compositional kernel achieves 90% accuracy. We also use our constructions to investigate the relative performance of neural networks, NTKs, and compositional kernels in the small dataset regime. In particular, we find that compositional kernels outperform NTKs and neural networks outperform both kernel methods.