Track: Track2; Team name: r2; Model: AirTNN

[aniervs]

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Description

This PR contributes AirTNN (Topological Neural Networks over the Air, Fiorellino, Battiloro & Di Lorenzo — arXiv:2502.10070) as a Track 2 (TNN) submission for the TDL Challenge 2026, operating on the cell domain.

Files added

• topobench/nn/backbones/cell/airtnn.py: the AirTNN backbone and AirTNNLayer.
• configs/model/cell/airtnn.yaml: full TBModel composition.
• test/nn/backbones/cell/test_airtnn.py: unit tests.
• test/pipeline/test_pipeline.py: set to MODELS = ["cell/airtnn"].
• 2026_tdl_challenge/outputs/airtnn_full/results.json: results of training and evaluation in GraphUniverse

Adaptation to TopoBench.
The reference implementation filters dense [batch, num_cells, F] tensors against a single shared Laplacian via a custom batch_mm. TopoBench batches complexes as a disjoint union, so the signal is a flat [N, F] tensor and the Laplacians are block-diagonal sparse operators. Each shift therefore becomes a single torch.sparse.mm(L, x); block-diagonal multiplication keeps per-complex message passing isolated, so this is exact (not an approximation) and additionally supports the inductive, variable-size setting GraphUniverse requires. Channel fading is sampled per nonzero of the sparse operator (independent channel per complex); noise is added per cell.

Complexity (per layer).
Sparse shifts cost O(k · nnz(L) · F) and the linear maps O(k · N · F²);
memory O(nnz(L) + N · F).

Additional context

• Paper: Fiorellino, Battiloro, Di Lorenzo, Topological Neural Networks over the Air, arXiv:2502.10070.
• Channel model on GraphUniverse. GraphUniverse has no wireless channel, so the primary runs use snr_db = 100 (the ideal filter). An SNR sweep (100 / 20 / 10) is planned as a robustness ablation rather than the main result.