# Sparse Gaussian Processes with Spherical Harmonic Features Revisited

arXiv: https://arxiv.org/abs/2303.15948 · HTML: https://mlsanity.com/paper/2303.15948/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 28 Mar 2023.

## Builds on (most cited first, 11 of 11)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [Deep Equals Shallow for ReLU Networks in Kernel Regimes](https://mlsanity.com/paper/2009.14397/) (2020)
- [Sparse Gaussian Processes with Spherical Harmonic Features](https://mlsanity.com/paper/2006.16649/) (2020)
- [Approximation and Learning with Deep Convolutional Models: a Kernel Perspective](https://mlsanity.com/paper/2102.10032/) (2021)
- [Deep Neural Networks as Point Estimates for Deep Gaussian Processes](https://mlsanity.com/paper/2105.04504/) (2021)
- [Spectral Analysis of the Neural Tangent Kernel for Deep Residual Networks](https://mlsanity.com/paper/2104.03093/) (2021)
- [Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition](https://mlsanity.com/paper/2106.05992/) (2021)

## Built on by (most cited first, 2 of 2)

- [Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regression](https://mlsanity.com/paper/2403.13300/) (2024)
- [On Basis Function Selection for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2609.26624/) (2026)

## Abstract (arXiv)

We revisit the Gaussian process model with spherical harmonic features and study connections between the associated RKHS, its eigenstructure and deep models. Based on this, we introduce a new class of kernels which correspond to deep models of continuous depth. In our formulation, depth can be estimated as a kernel hyper-parameter by optimizing the evidence lower bound. Further, we introduce sparseness in the eigenbasis by variational learning of the spherical harmonic phases. This enables scaling to larger input dimensions than previously, while also allowing for learning of high frequency variations. We validate our approach on machine learning benchmark datasets.