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# KAFT: Topology-Factorized Jacobian-Aligned Feedback for Deep GNNs
> Internal class names (`GraphGrAPETrainer`, file paths starting with
> `graft_*` / dataset keys `'GRAFT'`) are the original code identifier.
> The method is referred to as **KAFT** in the paper.
Code release accompanying the NeurIPS 2026 submission.
## Overview
We replace the BP backward pass in deep message-passing GNNs with a backward-only
rule whose feedback operator factors into a fixed graph polynomial
`P_l(Â) = Â^min(L-1-l, K)` and a learned feature-side matrix `R_l ∈ R^{C×d}`
fitted via multi-probe Jacobian alignment. The forward pass is unchanged.
```
δ_l = σ'(Z_l) ⊙ [ P_l(Â) · Ē · R_l ]
```
with `Ē` an optionally graph-spread output error. Hidden-layer feedback is
computed in O(1) parallel depth on GPUs.
## Layout
```
src/ core method
trainers.py BPTrainer, GraphGrAPETrainer (= KAFT), DFA/DFA-GNN, alignment
data.py PyG dataset loaders, normalized  / row-Â, sparse-mm helpers
experiments/ one runner per reported result block (see `## Reproducing`)
figures/ figure generators + the four rendered PDFs in the paper
paper/ neurips_v4_main.tex + experiments_master.tex (cross-reference)
```
## Reproducing the paper
End-to-end runtime for every figure / table is approximately 12 GPU-hours on
a single NVIDIA A6000 (48 GB).
```bash
# §2.3 / Fig 1: BP backward bottleneck diagnostic
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_diag_section23_v2.py
python figures/gen_fig1_diagnostic.py
# Tables 1 & 2: backward-rule leaderboard + main accuracy sweep
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_combo_20seeds.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_hero_extras.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_pepita_baseline.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_ff_baseline.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_cafo_baseline.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_ablation_20seeds.py
# Fig 2: Planetoid depth sweep (11 / 13 points)
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_shallow_depth.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_bp_graft_depth.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_dfagnn_depth.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_depth_extras.py
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_dblp_depth_scaling.py
python figures/gen_depth_sweep_fig.py
# Fig 3 / Table real-world hero: 4 large graphs at L=20
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_realworld_hero_L20.py 0 20
python figures/gen_realworld_depth_fig.py
# Fig 4 (depth + perturbation panels)
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_cora_perturb.py
python figures/gen_fig4_combined.py
# WikiCS regime-boundary check (negative result)
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_wikics_paper_setup.py
# Wall-clock + alignment-quality diagnostics
CUDA_VISIBLE_DEVICES=0 python -u experiments/run_grad_reach_20seeds.py
```
Run scripts from the repo root so `from src.trainers import ...` resolves.
## Hyperparameters
Defaults match the paper:
- Adam, lr 0.01, weight decay 5e-4
- 200 epochs (Fig 1 diagnostic uses 100)
- hidden dim 64
- ReLU, no LR schedule, no dropout / batch-norm / residual unless noted as a
stackability variant
- KAFT: `num_probes=64`, `align_mode='chain_norm'`, `lr_feedback=0.5`,
`max_topo_power=K=3`, `diffusion_alpha=0.5`, `diffusion_iters=10`.
- Seeds 0..19.
## Datasets
Auto-downloaded by `torch_geometric` on first use:
- Planetoid: Cora, CiteSeer, PubMed
- CitationFull: Cora, Cora_ML, CiteSeer, DBLP, PubMed
- Coauthor: CS, Physics
- WikiCS
## Dependencies
```
torch >= 2.0
torch_geometric >= 2.4
torch_sparse, torch_scatter (matching torch version)
numpy, scipy, scikit-learn, matplotlib
```
`requirements.txt` lists the same.
## License
This code is released under the MIT License (see `LICENSE`). It is the
sole authorship of the corresponding author of the paper.
## Third-party libraries
Used as runtime dependencies, not bundled. All permissively licensed (BSD-3 /
MIT / PSF). The author has full permission to use them.
| Library | License |
|--------------------|--------------|
| PyTorch | BSD-3 |
| PyTorch Geometric | MIT |
| scikit-learn | BSD-3 |
| NumPy | BSD |
| SciPy | BSD |
| matplotlib | PSF-equivalent |
|
