Track: Track1; Team name: r2; Model: OptBasisGNN

[aniervs]

Checklist

• My pull request has a clear and explanatory title.
• My pull request passes the Linting test.
• I added appropriate unit tests and I made sure the code passes all unit tests. (refer to comment below)
• My PR follows PEP8 guidelines. (refer to comment below)
• My code is properly documented, using numpy docs conventions, and I made sure the documentation renders properly.
• I linked to issues and PRs that are relevant to this PR.

Description

This PR contributes OptBasisGNN (Graph Neural Networks with Learnable and Optimal Polynomial Bases, Guo & Wei, ICML 2023 — arXiv:2302.12432) as a Track 1 (GNN) submission for the TDL Challenge 2026, operating on the graph domain.

OptBasisGNN is a spectral polynomial-filter GNN. It computes the optimal orthonormal polynomial basis that minimizes the filter's optimisation condition number, via an implicit three-term recurrence that never requires eigendecomposition. The only learnable parameters in the backbone are the per-channel combination coefficients α; feature transformation and readout are the standard TopoBench encoder/readout.

Draft: opening early to register the architecture.

Files (planned)

• topobench/nn/backbones/graph/optbasis.py: the OptBasisGNN backbone.
• configs/model/graph/optbasis.yaml
• test/nn/backbones/graph/test_optbasis.py: unit tests.
• test/pipeline/test_pipeline.py: set to MODELS = ["graph/optbasis"].

Integration No new wrapper, encoder, or readout is needed: the backbone follows the standard graph contract forward(x, edge_index, batch=None, edge_weight=None). It is a single decoupled filtering block of polynomial order K (depth = K propagation hops), not a stack of L message-passing layers.

Complexity. O(K·|E| + K·|V|) time (K sparse shifts + two-vector orthogonalisation per hop), O(|E| + |V|·hidden) memory.

Issue

This is a TDL Challenge 2026, Track 1 model submission. OptBasisGNN adds the learnable/optimal spectral-filter family to TopoBench (currently absent from the graph backbones), and is directly relevant to the challenge's structural-sensitivity questions: spectral filters adapt their low/high-pass response across the homophily/heterophily axis that GraphUniverse sweeps.

Additional context

• Paper: Guo & Wei, Graph Neural Networks with Learnable and Optimal Polynomial Bases, ICML 2023, arXiv:2302.12432. Reference code: github.com/yuziGuo/FarOptBasis.