Track: Track1; Team name: MISN_AY; Model: JacobiConv

[yusufm423]

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 adds JacobiConv as a Track 1 GNN submission for the TDL Challenge 2026 using:

model=graph/jacobiconv

JacobiConv was introduced in:

How Powerful are Spectral Graph Neural Networks?
Xiyuan Wang and Muhan Zhang
https://arxiv.org/abs/2205.11172v1

Reference implementation:
https://github.com/GraphPKU/JacobiConv

Motivation

JacobiConv is a lightweight spectral GNN that represents graph filters using a Jacobi polynomial basis.

Instead of repeatedly applying nonlinear message-passing layers, it builds higher-order graph signals through a polynomial recurrence and learns how to combine them. This avoids explicit eigendecomposition while still allowing flexible spectral filtering.

What is contributed

• Added the JacobiConv backbone:
  • topobench/nn/backbones/graph/jacobiconv.py
• Added the Hydra configuration:
  • configs/model/graph/jacobiconv.yaml
• Added unit tests:
  • test/nn/backbones/graph/test_jacobiconv.py
• Added pipeline coverage:
  • test/pipeline/test_pipeline.py
• Updated the official evaluation notebook for:
  • graph/jacobiconv
• Added the generated challenge results:
  • 2026_tdl_challenge/outputs/jacobiconv/results.json

TopoBench integration

JacobiConv follows the standard TopoBench graph-backbone interface:

forward(x, edge_index, batch=None, edge_weight=None, edge_attr=None, **kwargs)

It returns node embeddings with shape:

[num_nodes, out_channels]

The implementation reuses the existing:

• AllCellFeatureEncoder
• GNNWrapper
• MLPReadout

Testing

The unit tests cover:

• model initialization;
• output shape;
• invalid arguments;
• multiple polynomial orders;
• edge weights and edge attributes;
• edgeless graphs;
• batched inputs;
• gradient flow; and
• wrapper compatibility.

The pipeline test also runs graph/jacobiconv end to end on graph/MUTAG.

Evaluation

The official challenge notebook was run across:

• 2 tasks;
• 12 GraphUniverse settings;
• 3 seeds: 42, 43, and 44.

Summary:

Task	Metric	Best result
Community detection	Accuracy, higher is better	~0.727
Triangle counting	MSE per triangle, lower is better	~0.0114

The complete per-setting, per-seed, and OOD results are stored in:

2026_tdl_challenge/outputs/jacobiconv/results.json

Reproduction

pytest test/nn/backbones/graph/test_jacobiconv.py -v
pytest test/pipeline/test_pipeline.py -v
python -m topobench model=graph/jacobiconv dataset=graph/MUTAG

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[yusufm423]

Could a maintainer please add the track-1-gnn label for the 2026 TDL Challenge?