# A la Carte - Learning Fast Kernels

arXiv: https://arxiv.org/abs/1412.6493 · HTML: https://mlsanity.com/paper/1412.6493/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2014.

## Built on by (most cited first, 18 of 18)

- [Posterior and Computational Uncertainty in Gaussian Processes](https://mlsanity.com/paper/2205.15449/) (2022)
- [Overcoming the Spectral Bias of Neural Value Approximation](https://mlsanity.com/paper/2206.04672/) (2022)
- [On Learning the Transformer Kernel](https://mlsanity.com/paper/2110.08323/) (2021)
- [Large-Scale Gaussian Processes via Alternating Projection](https://mlsanity.com/paper/2310.17137/) (2023)
- [Low-Precision Arithmetic for Fast Gaussian Processes](https://mlsanity.com/paper/2207.06856/) (2022)
- [Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features](https://mlsanity.com/paper/2407.00584/) (2024)
- [Collapsed Inference for Bayesian Deep Learning](https://mlsanity.com/paper/2306.09686/) (2023)
- [Spectraformer: A Unified Random Feature Framework for Transformer](https://mlsanity.com/paper/2405.15310/) (2024)
- [Bayesian Non-linear Latent Variable Modeling via Random Fourier Features](https://mlsanity.com/paper/2306.08352/) (2023)
- [Spectral methods: crucial for machine learning, natural for quantum computers?](https://mlsanity.com/paper/2603.24654/) (2026)
- [GP-ConvCNP: Better Generalization for Convolutional Conditional Neural Processes on Time Series Data](https://mlsanity.com/paper/2106.04967/) (2021)
- [Gaussian Process Inference Using Mini-batch Stochastic Gradient Descent: Convergence Guarantees and Empirical Benefits](https://mlsanity.com/paper/2111.10461/) (2021)
- [MetaKernel: Learning Variational Random Features with Limited Labels](https://mlsanity.com/paper/2105.03781/) (2021)
- [StreaMRAK a Streaming Multi-Resolution Adaptive Kernel Algorithm](https://mlsanity.com/paper/2108.10411/) (2021)
- [RFFNet: Large-Scale Interpretable Kernel Methods via Random Fourier Features](https://mlsanity.com/paper/2211.06410/) (2022)
- [Scalable Deep Basis Kernel Gaussian Processes](https://mlsanity.com/paper/2505.18526/) (2025)
- [Unbiased Stochastic Optimization for Gaussian Processes on Finite Dimensional RKHS](https://mlsanity.com/paper/2508.20588/) (2025)
- [Long Range Frequency Tuning for QML](https://mlsanity.com/paper/2602.23409/) (2026)

## Abstract (arXiv)

Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a family of fast, flexible, lightly parametrized and general purpose kernel learning methods, derived from Fastfood basis function expansions. We provide mechanisms to learn the properties of groups of spectral frequencies in these expansions, which require only O(mlogd) time and O(m) memory, for m basis functions and d input dimensions. We show that the proposed methods can learn a wide class of kernels, outperforming the alternatives in accuracy, speed, and memory consumption.