Track: Track2; Team name: CoPreSheafers; Model: CTNN

[chrisizeh]

Title

Add copresheaf TNN with triangle-clique lifting for GraphUniverse
Co-authored with @bastianlb.

Summary

This PR adds a copresheaf-based model stack for the 2026 TDL Challenge, using an explicit triangle-clique graph-to-combinatorial lifting as the submission path.

The model is based on Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework by Hajij et al. [1]. From that work, we use the core copresheaf message-passing idea: cells carry stalk features, directed neighborhood routes learn transport maps between source and target stalks, transported messages are aggregated per target rank, and rank-specific update maps produce the next hidden representation.

In this implementation, the input graph is lifted into a rank-2 combinatorial complex: nodes are rank 0 cells, graph edges are rank 1 cells, and each graph triangle is represented as an explicit rank 2 cell. The copresheaf backbone then propagates information across the induced combinatorial neighborhoods. For graph-level tasks, the readout pools across all available ranks; for node-level tasks, it uses the propagated rank-0 features.

Main additions:

• add graph and combinatorial copresheaf backbones with learned route maps, message gates, and configurable neighborhood aggregation
• add GraphTriangleCliqueCCLifting for explicit rank-2 triangle cells
• add structural feature encoding for lifted cells
• add AllRankReadout for graph-level pooling across available ranks
• add Hydra configs for triangle-clique copresheaf experiments
• add resumable GraphUniverse experiment/export tooling and local experiment log handling
• add focused unit tests for the new lifting, layers, encoders, readout, wrappers, and pipeline coverage

Testing

• Added tests under test/nn/... for copresheaf layers, backbones, encoders, wrappers, and readout behavior
• Added tests for GraphTriangleCliqueCCLifting
• Added combinatorial/copresheaf_cc to the pipeline smoke coverage

[1] M. Hajij et al., “Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework,” Oct. 26, 2025

[chrisizeh]

As the other PRs already mentioned, I am also not able to label the PR with the correct track 2 label.
Can some of the organizers please help in this regard.
Thank you!