# General Graph Random Features

arXiv: https://arxiv.org/abs/2310.04859 · HTML: https://mlsanity.com/paper/2310.04859/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 7 Oct 2023.

## Builds on (most cited first, 8 of 8)

- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [The Unreasonable Effectiveness of Structured Random Orthogonal Embeddings](https://mlsanity.com/paper/1703.00864/) (2017)
- [Heat kernel based community detection](https://mlsanity.com/paper/1403.3148/) (2014)
- [Taming graph kernels with random features](https://mlsanity.com/paper/2305.00156/) (2023)
- [Quasi-Monte Carlo Graph Random Features](https://mlsanity.com/paper/2305.12470/) (2023)
- [Learning Manifold Implicitly via Explicit Heat-Kernel Learning](https://mlsanity.com/paper/2010.01761/) (2020)

## Built on by (most cited first, 10 of 10)

- [Linear Transformer Topological Masking with Graph Random Features](https://mlsanity.com/paper/2410.03462/) (2024)
- [Graph Random Features for Scalable Gaussian Processes](https://mlsanity.com/paper/2509.03691/) (2025)
- [Optimal Time Complexity Algorithms for Computing General Random Walk Graph Kernels on Sparse Graphs](https://mlsanity.com/paper/2410.10368/) (2024)
- [Variance-Reducing Couplings for Random Features](https://mlsanity.com/paper/2405.16541/) (2024)
- [Computationally-efficient Graph Modeling with Refined Graph Random Features](https://mlsanity.com/paper/2510.07716/) (2025)
- [Manifold Random Features](https://mlsanity.com/paper/2602.03797/) (2026)
- [Heating Up Quasi-Monte Carlo Graph Random Features: A Diffusion Kernel Perspective](https://mlsanity.com/paper/2410.08389/) (2024)
- [LGRPool: Hierarchical Graph Pooling Via Local-Global Regularisation](https://mlsanity.com/paper/2504.08530/) (2025)
- [SWING: Unlocking Implicit Graph Representations for Graph Random Features](https://mlsanity.com/paper/2602.12703/) (2026)
- [Random Wavelet Features for Graph Kernel Machines](https://mlsanity.com/paper/2602.15711/) (2026)

## Abstract (arXiv)

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.