Using graphon limits for dense graphs, the authors decompose cross-domain output shifts for Lipschitz backbones into graph-specific finite-sample terms and a relabeling-invariant domain discrepancy, with stability results for spectral positional encodings.
Sign and basis invariant networks for spectral graph representation learning.arXiv preprint arXiv:2202.13013
7 Pith papers cite this work, alongside 25 external citations. Polarity classification is still indexing.
7
Pith papers citing it
25
external citations · Pith
abstract
We introduce SignNet and BasisNet -- new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if $v$ is an eigenvector then so is $-v$; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choices of basis eigenvectors. We prove that under certain conditions our networks are universal, i.e., they can approximate any continuous function of eigenvectors with the desired invariances. When used with Laplacian eigenvectors, our networks are provably more expressive than existing spectral methods on graphs; for instance, they subsume all spectral graph convolutions, certain spectral graph invariants, and previously proposed graph positional encodings as special cases. Experiments show that our networks significantly outperform existing baselines on molecular graph regression, learning expressive graph representations, and learning neural fields on triangle meshes. Our code is available at https://github.com/cptq/SignNet-BasisNet .
representative citing papers
Under a denoising objective, linear attention is suboptimal; Graph Convolutional Attention matches idealized spectral attention on SBMs and improves graph denoising and diffusion in proportion to spectral diversity.
Frozen embeddings from a pretrained heterogeneous graph transformer over a 6.9M-node metabolic-engineering knowledge graph predict fermentation titers at R²=0.41, outperforming tabular baselines (R²=0.24).
MidSurfNet combines a neural face pairing module with an interference implicit field to generate generalized mid-surfaces, reporting 87.32% pairing accuracy and improved handling of multi-wall and self-matching cases on a 1500-model dataset.
GTLM injects graph-aware attention biases into LLMs using only 0.015% extra parameters, enabling native graph processing that matches 7B models with a 1B model on text-attributed graph benchmarks.
Adaptive canonicalization selects input canonical forms by maximizing network predictive confidence to yield continuous symmetry-preserving models with universal approximation for equivariant geometric networks.
Local d-hop uniqueness in GNN node features matches global UID expressiveness for ILP solving while providing stronger generalization.
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