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Graph and Simplicial Complex Prediction Gaussian Process via Hodgelet Representations

NeurIPS 2026 · Graph learning › Graph self-supervised learning · approach: Heterophily and imbalance on graphs

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Extends graph-level Gaussian processes to attributed simplicial complexes by building Hodgelet representations: wavelet coefficients on each Hodge component (exact, co-exact, harmonic) pooled into scalar features fed to RBF GPs.

Problem

Predicting labels or values for graph and simplicial complex structured data in small-data regimes, where existing GP graph methods ignore edge (and higher-simplex) attributes and GNNs overfit.

Approach

Apply simplicial complex wavelet transforms separately to the Hodge subspaces (exact, co-exact, harmonic) of the Hodge Laplacian, pool coefficient energies permutation-invariantly into Hodgelet representations, and use them as inputs to GPs with additive or product kernels whose wavelet and kernel hyperparameters are learned by marginal likelihood / ELBO.

Key results

• On MUTAG, HTGP (hybrid) reaches 0.872 accuracy versus 0.830 for the best GNN baseline (GIN hybrid).
• On ieee24-regression, HTGP (hybrid) achieves MSE 1.29e-4 versus 1.83e-4 for the best GNN baseline (Transformer).
• On ESOL, WTGP (vertex) and HTGP (vertex) achieve MSE 0.50 versus 0.75 for the Transformer baseline.

Surprising findings

• Edge-only GP models perform poorly on FreeSolv and ESOL, but combining edge and vertex attributes in hybrid models compensates for this.

Limitations

• GP training and inference scale cubically with number of SCs without inducing points.
• Eigendecomposition scales cubically with simplex count, limiting large graphs.
• Edge-only models underperform on some regression tasks; results depend on dataset-specific choice of aggregation function.

Experimental setup

Datasets: MUTAG AIDS FreeSolv ESOL PowerGraph ieee24 Div-curl-free (synthetic) Vortices (synthetic)

Benchmarks: MUTAG AIDS FreeSolv ESOL ieee24-binary ieee24-multiclass ieee24-regression Div-curl-free Vortices

Metrics: accuracy mean squared error

Baselines: GCN GAT GIN Graph Transformer WTGP

Builds on: wavelet GP for graphs (WTGP) simplicial complex wavelet transform Hodge Laplacian variational GP

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