Track: Track2; Team name: TJPaik; Model: Directed Simplicial Neural Networks (Dir-SNN)

[TJPaik]

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 a TopoBench implementation of Directed Simplicial Neural Networks (Dir-SNN), based on Lecha et al., Higher-Order Topological Directionality and Directed Simplicial Neural Networks (ICASSP 2025 / arXiv:2409.08389).

Paper: https://arxiv.org/pdf/2409.08389
Reference implementation: https://github.com/ManuelLecha/DirSNN

Main changes:

• Adds the simplicial/dirsnn backbone, implementing the edge-level Dir-SNN layer with polynomial directed-adjacency propagation.
• Adds DirSNNWrapper, which forwards directed lower/upper edge adjacencies to the backbone and projects learned edge embeddings back to nodes through incidence_1 for downstream TopoBench readout.
• Adds DirectedSimplicialLifting, a TopoBench lifting that materializes the four directed lower edge adjacencies from Eq. (3) and six directed upper edge adjacencies from Eq. (4) of the paper.
• Adds Hydra configs for the default all-10-adjacency challenge model and a dirsnn_official_lower variant matching the official lower-adjacency experimental setup.
• Adds unit tests for the backbone, wrapper, and directed lifting.
• Adds the GraphUniverse challenge results.json generated by the official 2026 evaluation harness.

Challenge requirements covered:

• Track: Track2
• Team name: TJPaik
• Model: Directed Simplicial Neural Networks (Dir-SNN)
• Backbone: topobench/nn/backbones/simplicial/dirsnn.py
• Hydra config: configs/model/simplicial/dirsnn.yaml
• Results file: 2026_tdl_challenge/outputs/dirsnn/results.json
• Requested label: track-2-tnn
• Registration form: pending

Issue

This is a submission to the 2026 Topological Deep Learning Challenge. There is no linked issue to close.

Additional context

The default simplicial/dirsnn config uses all ten directed edge adjacencies: four lower and six upper. The additional simplicial/dirsnn_official_lower config forwards only the four lower adjacencies, matching the narrower setup used in the reference experiments.

TopoBench graph inputs are undirected/symmetric, so DirectedSimplicialLifting uses a deterministic canonical orientation u -> v when u < v. The directed_input=True path is intentionally guarded for now because raw directed edge ordering would otherwise be misaligned with SimplicialComplex's canonical 1-simplex ordering.

Validation:

• GitHub CI passes: Linting / ruff, Testing / build (3.11), Docs / build (3.11).
• Local full test suite: uv run --extra test python -m pytest test/ -> 668 passed.
• Local focused tests: Dir-SNN backbone, wrapper, and directed lifting tests pass.
• Local lint check on changed Python files passes.