mlsanityData to 7 Oct 2026

Equivariant Machine Learning on Graphs with Nonlinear Spectral Filters

arXiv 2406.01249 ↗First posted 3 Jun 2024cs.LG stat.MLcited by 2

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Abstract (arXiv)

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of shift equivariance, which is the basis of convolution networks on images, to general graphs. Unlike images, graphs do not have a natural notion of domain translation. Therefore, we consider the graph functional shifts as the symmetry group: the unitary operators that commute with the graph shift operator. Notably, such symmetries operate in the signal space rather than directly in the spatial space. We remark that each linear filter layer of a standard spectral graph neural network (GNN) commutes with graph functional shifts, but the activation function breaks this symmetry. Instead, we propose nonlinear spectral filters (NLSFs) that are fully equivariant to graph functional shifts and show that they have universal approximation properties. The proposed NLSFs are based on a new form of spectral domain that is transferable between graphs. We demonstrate the superior performance of NLSFs over existing spectral GNNs in node and graph classification benchmarks.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 65 of its 102 references that are in the map. First posted on arXiv 3 Jun 2024.

Builds on

65 of 102 references.

References · 65

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38 more
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Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  2. 2026Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNscited by 0