Track: Track1; Team name: LangDiff; Model: MTGCN

[Mullerio]

Checklist

• My pull request has a clear and explanatory title.
• My pull request passes the Linting test.
• I added appropriate unit tests and made sure the code passes all unit tests.
• My PR follows PEP 8 guidelines.
• My code is properly documented using numpy documentation conventions, and I made sure the documentation renders properly.

Description

This PR adds MTGCN, based on the Multi-Track Message Passing framework from , Hongbin Pei et al. ICML (2024) https://proceedings.mlr.press/v235/pei24a.html as a graph backbone. It is partially based on the official implemenation
https://github.com/XJTU-Graph-Intelligence-Lab/Multi-Track-Message-Passing.

The original MTGCN code obtains semantic relations through task specific training. Since the TopoBench backbone cannot depend on the task and or labels, this implementation learns track affiliations from the node features. In particular, the implemenation supports:

• configurable propagation depth
• multiple semantic tracks and assignment heads
• feature-based, graph-based, or hybrid track affiliations
• optional affiliation sharpening
• initial-track and output residual connections
• row or symmetric graph normalization
• optional graph symmetrization and self-loops
• scalar edge weights
• sparse propagation over disjoint PyG graph batches (this is similar to our other submission Track: Track1; Team name: LangDiff; Model: AdvDIFFormer #399)

Tests

The unit tests cover:

• TopoBench wrapper and configuration compatibility, expected output shapes etc.
• support for scalar weights supplied through either edge_weight or one-dimensional edge_attr
• equivalent propagation for undirected graphs represented as one-way or bidirectional edge lists
• no cross-graph message passing when processing disjoint PyG batches
• head-specific track probabilities that sum to one for every node
• affiliation inputs from raw features, graph-derived features, or their combination
• use of each head’s own weights before combining attention heads
• unchanged affiliations in direct mode, sharp mode tracks preferences that still sum to 1
• correct addition of the optional projected input residual

The testing was run locally using:
uv run --no-sync ruff check topobench/nn/backbones/graph/mtgcn.py test/nn/backbones/graph/test_mtgcn.py test/pipeline/test_pipeline.py

uv run --no-sync pytest test/nn/backbones/graph/test_mtgcn.py -q

uv run --no-sync pytest test/pipeline/test_pipeline.py -q

Benchmarking

We ran the benchmarking from the challenge notebook, without tuning the hyperparameters, we have