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GIST: Gauge-Invariant Spectral Transformers for Scalable Graph Neural Operators

NeurIPS 2026 · Graph learning › GNN architectures · approach: Spectral GNN design · 0 citations (OpenAlex)

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Proposes GIST, an O(N) graph neural operator whose attention uses only inner products of random-projection spectral embeddings (FastRP), which are unbiased estimates of a gauge-invariant graph kernel, and reports SOTA on several mesh-regression benchmarks plus competitive node classification.

Problem

Spectral positional encodings for graph transformers and neural operators on irregular meshes require O(N^3) eigendecomposition and break gauge invariance, hurting discretization and inductive transfer.

Approach

Restrict attention to pairwise inner products of efficient random spectral embeddings f(P)R, which are unbiased estimators of the gauge-invariant kernel f(P)f(P)^T; combine with ReLU linear attention and a multi-scale three-branch block to get end-to-end linear complexity and a discretization-mismatch bound.

Key results

• On DrivAerNet++ GIST reaches 18.60% relative L2 error vs 20.05% for the prior best (TripNet), and 20.10% vs 20.35% on DrivAerNet.
• On AirfRANS GIST achieves 0.0028 MSE vs 0.0142 for Transolver; on ShapeNet-Car 4.68 vs 4.99.
• Node classification: 95.61% accuracy on Amazon Photo (SOTA vs SpecFormer 95.48%) and 99.50% micro-F1 on PPI, while Cora (84.00) and ogbn-arxiv (72.12) are within 1.5 and 0.5 points of the best.

Surprising findings

• On a controlled 50%-decimation test, a non-gauge-invariant variant drops from 0.991 to 0.526 test R^2 while GIST keeps 0.840, isolating gauge invariance as the factor for cross-resolution transfer.
• GraphGPS runs out of memory on ogbn-arxiv, so scalable attention baselines are rarely evaluated at that scale.

Limitations

• Discretization-mismatch bound assumes i.i.d. uniform sampling on bounded-curvature manifolds, which real quasi-uniform meshes only approximately satisfy.
• Spectral embeddings are precomputed under a static input graph; dynamic graphs are not handled.
• Gains on ogbn-arxiv are limited since a single fixed Laplacian is used; heterophilic graphs are not evaluated.

Experimental setup

Datasets: Cora PubMed Amazon Photo ogbn-arxiv PPI AirfRANS ShapeNet-Car DrivAerNet DrivAerNet++

Benchmarks: Cora PubMed Amazon Photo ogbn-arxiv PPI AirfRANS ShapeNet-Car DrivAerNet DrivAerNet++

Metrics: accuracy micro-F1 MSE relative L2 error R^2

Baselines: GCN GraphSAGE GAT GATv2 GCNII GraphGPS SGFormer SpecFormer PolyFormer Exphormer Transolver RegDGCNN

Builds on: FastRP EfficientViT linear transformer SignNet Transolver

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