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

[gk408829]

Track

Track 2 — Topological Neural Networks

Team Name

E(n)igma

Model

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

Status

Draft / work in progress

Summary

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

The goal is to integrate ETNN as a Track 2 model in TopoBench, initially targeting the combinatorial-complex setting. The implementation will focus on correctness, maintainability, equivariance-aware testing, and memory-efficient sparse message passing.

Planned implementation

• Add ETNN backbone under the appropriate TopoBench domain.
• Add Hydra model configuration.
• Implement sparse relation-index message passing.
• Avoid dense pairwise coordinate tensor construction.
• Use native PyTorch reductions where appropriate.
• Add unit tests for constructor/config behavior.
• Add forward-pass shape tests.
• Add translation equivariance/invariance tests.
• Add rotation/reflection equivariance/invariance tests where applicable.
• Add pipeline smoke test.
• Run the official GraphUniverse evaluation notebook.
• Add generated results.json.

Feasibility and contingencies

This draft PR initially targets a faithful TopoBench-native implementation of ETNN in the combinatorial-complex setting. During the first implementation phase, I will verify that the required ETNN inputs can be mapped cleanly to the TopoBench/GraphUniverse pipeline, in particular:

• availability of geometric coordinates or position features;
• availability of rank-wise cell features;
• availability of incidence or relation indices between cells;
• compatibility with the expected TopoBench backbone and readout interfaces.

If a faithful ETNN implementation requires a specialized feature encoder, geometric preprocessing step, or readout mechanism, I will integrate the minimal required component into the TopoBench pipeline, following the challenge guidelines and existing TopoBench design patterns.

If the full combinatorial-complex ETNN formulation is not directly compatible with the challenge pipeline, I will document the incompatibility and adjust the implementation scope in one of the following ways:

• implement the closest faithful ETNN variant supported by the available TopoBench data structures;
• restrict the implementation to the supported ranks/relations while preserving the E(n)-equivariant message-passing mechanism;
• consult the maintainers before making any substantial deviation from the reference architecture.

The goal is to keep the implementation faithful to the ETNN paper while ensuring that it remains maintainable, testable, and compatible with the official evaluation workflow.

Reference

C. Battiloro, E. Karaismailoğlu, M. Tec, G. Dasoulas, M. Audirac, and F. Dominici, “E(n) Equivariant Topological Neural Networks,” in International Conference on Learning Representations (ICLR), 2025.

Paper: https://arxiv.org/abs/2405.15429

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

Notes

This PR is opened early as a draft to signal the intended Track 2 model choice and to make development progress visible.