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.

Design assumptions

The official GraphUniverse evaluation pipeline should not be assumed to provide physical node coordinates such as data.pos. Following organizer guidance, this implementation will therefore use a model-specific geometric encoder to construct ETNN-compatible coordinates from the available graph/topological structure.

The initial implementation will use graph-derived structural coordinates, such as Laplacian positional encodings, as rank-0 coordinates. Higher-rank cell coordinates will be computed inside the ETNN encoder/backbone from incident rank-0 cells, for example using barycentric averaging.

These coordinates are not interpreted as physical Euclidean coordinates. They are structural coordinates used to make the ETNN architecture compatible with the GraphUniverse setting while preserving the E(n)-equivariant message-passing mechanism of the model.

The design choice and any limitations will be documented clearly in the final submission.

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.