Track: Track2; Team name: MISN_AY; Model: Bi-SCNN

[yusufm423]

Checklist

• My pull request has a clear and explanatory title.
• My pull request passes the Linting test.
• I added appropriate unit tests and made sure the code passes all unit tests.
• My PR follows PEP8 guidelines.
• My code is properly documented using NumPy documentation conventions.
• I linked to papers, issues, and PRs that are relevant to this PR.

Description

This PR adds Bi-SCNN as a Track 2 simplicial neural network submission for the TDL Challenge 2026 using:

model=simplicial/biscnn

Bi-SCNN was introduced in:

Binarized Simplicial Convolutional Neural Networks
Yi Yan and Ercan E. Kuruoglu
https://arxiv.org/abs/2405.04098

Motivation

Bi-SCNN extends simplicial convolutional neural networks with a weighted binary-sign propagation mechanism.

The model operates on simplicial complexes and processes node-, edge-, and face-level signals through lower, upper, and harmonic Hodge components. Its main objective is to reduce the computational and memory cost of simplicial feature propagation while retaining information from higher-order structures.

The implementation follows the paper's layer equations and preserves the distinction between:

• binary-sign feature propagation;
• full-precision trainable weight matrices; and
• magnitude values obtained through row-wise L1 normalization.

The sign operation is approximated using hard tanh, as described in the paper, so that the model can be trained using ordinary gradient-based optimization.

What is contributed

Added the Bi-SCNN backbone:

topobench/nn/backbones/simplicial/biscnn.py

Added the Hydra configuration:

configs/model/simplicial/biscnn.yaml

Added unit tests:

test/nn/backbones/simplicial/test_biscnn.py

Added pipeline coverage:

test/pipeline/test_pipeline.py

Updated the official challenge evaluation notebook for:

simplicial/biscnn

Added the generated challenge results:

2026_tdl_challenge/outputs/biscnn/results.json

TopoBench integration

Bi-SCNN follows the TopoBench simplicial-backbone interface and accepts:

forward(x_all, laplacian_all, incidence_all=None)

where x_all contains node-, edge-, and face-level features and laplacian_all contains the corresponding lower and upper Hodge operators.

It returns a tuple of rank-specific embeddings:

(node_embeddings, edge_embeddings, face_embeddings)

with output shapes:

[num_nodes, hidden_channels_0]
[num_edges, hidden_channels_1]
[num_faces, hidden_channels_2]

The implementation reuses the existing:

• AllCellFeatureEncoder;
• SCCNNWrapper; and
• PropagateSignalDown readout.

Implementation details

For each simplicial rank, the backbone applies separate trainable matrices to the available:

• lower-Hodge component;
• upper-Hodge component; and
• harmonic or identity component.

The implementation follows the weighted binary-sign construction described in the paper:

1. Compute the full-precision simplicial convolution preactivation.
2. Compute a row-wise magnitude using the mean absolute feature value.
3. Approximate the sign path using hard tanh.
4. Propagate the binary-sign output through intermediate layers.
5. Accumulate the magnitude terms outside the binary path.
6. Multiply the accumulated magnitude with the final binary-sign representation.

Trainable matrices remain full precision; only feature propagation follows the binary-sign path.

Testing

The unit tests cover:

• model initialization;
• hard-tanh sign approximation;
• row-wise L1 normalization;
• full-precision trainable weights;
• magnitude and binary output paths;
• node-, edge-, and face-level output shapes;
• dense and sparse Hodge operators;
• two-dimensional and higher-order simplicial complexes;
• invalid architecture arguments;
• malformed Laplacian inputs; and
• gradient flow.

The pipeline test also runs simplicial/biscnn end to end on graph/MUTAG.

Evaluation

The official challenge notebook was run across:

• 2 tasks;
• 12 GraphUniverse settings per task;
• 3 seeds: 42, 43, and 44;
• 72 total runs.

Summary of the best in-distribution results:

Task	Metric	Best result
Community detection	Accuracy, higher is better	~0.6301
Triangle counting	MSE per structural triangle, lower is better	~0.00197

The best community-detection result was obtained for:

h_hi__d_hi__pl_hi, seed=44

The best normalized triangle-counting result was obtained for:

h_lo__d_hi__pl_hi, seed=43

The complete per-setting, per-seed, and OOD results are stored in:

2026_tdl_challenge/outputs/biscnn/results.json

Reproduction

pytest test/nn/backbones/simplicial/test_biscnn.py -v
pytest test/pipeline/test_pipeline.py -v
python -m topobench model=simplicial/biscnn dataset=graph/MUTAG

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