Track: Track 2; Team: E(n)igma; Model: ETNN

[grvkhnl]

Track

Track 2 - Topological Neural Networks

Team Name

E(n)igma

Model

E(n)-Equivariant Topological Neural Networks (ETNN)

Summary

This PR adds a TopoBench-compatible implementation of E(n)-Equivariant
Topological Neural Networks (ETNN) for the 2026 TDL Challenge.

The implementation focuses on the combinatorial-complex feature-update part of
ETNN. GraphUniverse datasets do not provide physical Euclidean coordinates, so
this submission intentionally implements a coordinate-free ETNN baseline over
TopoBench combinatorial neighborhoods. It preserves ETNN's typed cell-relation
message-passing structure while avoiding unsupported claims about physical
E(n)-equivariance on coordinate-free data.

A fuller design note is included in:

2026_tdl_challenge/submissions/etnn_design_notes.md

Reference

Paper:

Claudio Battiloro, Ege Karaismailoglu, Mauricio Tec, George Dasoulas,
Michelle Audirac, Francesca Dominici.
E(n) Equivariant Topological Neural Networks.
arXiv:2405.15429.

Official implementation:

https://github.com/NSAPH-Projects/topological-equivariant-networks

Implementation Notes

• Adds a combinatorial ETNN backbone at
  topobench/nn/backbones/combinatorial/etnn.py.
• Adds Hydra config configs/model/combinatorial/etnn.yaml.
• Uses GraphTriangleInducedCC to lift graph datasets into rank-0, rank-1,
  and rank-2 combinatorial cells.
• Uses AllCellFeatureEncoder, the existing combinatorial TuneWrapper, and
  PropagateSignalDown readout.
• Treats each configured TopoBench neighborhood as a typed ETNN relation.
• Uses separate relation-specific message MLPs and rank-specific update MLPs.
• Converts sparse neighborhoods to sender-receiver edge indices with rows as
  receivers and columns as senders.
• Handles stored-zero sparse entries and empty-rank placeholder axes in lifted
  mini-batches.
• Keeps tensor allocation device-aware for CPU/CUDA compatibility.

Coordinate-Free Adaptation

The original ETNN contains both feature updates and coordinate updates. In this
GraphUniverse setting, physical coordinates are absent. This PR therefore
implements the ETNN feature-update mechanism over combinatorial-complex
neighborhoods, but omits coordinate-dependent geometric invariants and the
coordinate update.

This is documented directly in the backbone docstrings/comments, including the
mapping to the ETNN paper's message/update equations and the omitted coordinate
update.

Evaluation

The official GraphUniverse evaluation notebook completed all 72 runs.

Committed result:

2026_tdl_challenge/outputs/etnn/results.json

Headline in-distribution metrics:

Task	Metric	Mean +/- std
Community detection	Accuracy	0.4534 +/- 0.1308
Triangle counting	MSE / total triangles	0.1213 +/- 0.1121

Homophily slices:

Task	h_lo	h_mid	h_hi
Community accuracy	0.3195 +/- 0.0045	0.4205 +/- 0.0316	0.6203 +/- 0.0584
Triangle MSE / triangles	0.0259 +/- 0.0289	0.1141 +/- 0.0394	0.2239 +/- 0.1251

Tests

This PR includes coverage for:

• rank-wise ETNN output shapes;
• coordinate-free GraphUniverse compatibility;
• compatibility with the existing combinatorial wrapper/readout path;
• sparse neighborhood direction conventions;
• stored-zero sparse entries;
• empty-rank sparse placeholder compaction;
• Hydra composition with graph-to-combinatorial lifting;
• required end-to-end pipeline test on graph/MUTAG.

Local focused checks:

uv run pytest test/nn/backbones/combinatorial/test_etnn.py test/pipeline/test_etnn_pipeline.py -q
uv run pytest test/pipeline/test_pipeline.py -q

GitHub checks are passing as of the latest pushed commit.

Notes

• PR label: track-2-tnn.
• No minimum training performance is required by the challenge; results are
  provided to benchmark the implementation on the shared GraphUniverse tasks.
• Follow-up coordinate-enabled variants are being kept separate, following
  organizer guidance, so this PR remains focused on the stable coordinate-free
  ETNN baseline.

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