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DFA-GNN: Forward Learning of Graph Neural Networks by Direct Feedback Alignment
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Proposes DFA-GNN, a non-backpropagation forward learning framework that extends direct feedback alignment to GCNs with graph-topology-aware feedback and a pseudo error generator for unlabeled nodes in semi-supervised node classification.
Problem
Backpropagation limits biological plausibility, parallelism and scalability for GNN training, and directly applying DFA to graph data fails due to non-i.i.d. dependencies between nodes and missing errors for unlabeled nodes.
Approach
Redesigns DFA feedback links for GCNs by propagating output errors through the normalized adjacency (S^T)^k E B, and generates pseudo errors for unlabeled nodes by label-spreading residual errors from training nodes, with a confidence mask filtering poorly predicted nodes.
Key results
- On 10 benchmarks, DFA-GNN achieves best or second-best accuracy across all datasets, e.g., 87.72% on Cora vs 86.04% for BP and 79.51% on Texas vs 54.26% for BP.
- Ablation on Cora: removing both EG and NF gives 83.02%, adding pseudo error generator gives 86.70%, and adding node filter gives 87.72%.
- On large graphs, DFA-GNN reaches 94.49% on Reddit (BP 94.34%) but 67.83% on ogbn-arxiv vs BP 68.78%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace BP training with DFA-GNN | GCN · Cora, CiteSeer, PubMed, Photo, Texas, Cornell, Actor, Squirrel | accuracy: 86.04 -> 87.72; 78.20 -> 80.49; 85.24 -> 86.28; 93.03 -> 93.04; 54.26 -> 79.51; 71.31 -> 75.24; 31.94 -> 34.07; 37.81 -> | Helped |
| replace BP training with DFA-GNN | GCN · Computer | accuracy: 89.48 -> 86.72 | Hurt |
| replace BP training with DFA-GNN | GCN · Chameleon | accuracy: 41.28 -> 41.19 | Hurt |
| add pseudo error generator to DFA-GNN without node filtering (ablation) | DFA-GNN · Cora, CiteSeer, PubMed, Actor, Chameleon, Squirrel | accuracy: 83.02 -> 86.70; 78.17 -> 79.26; 82.92 -> 84.01; 30.72 -> 31.97; 39.09 -> 39.62; 34.61 -> 34.87 | Helped |
| add node filter to DFA-GNN with pseudo error generation (ablation) | DFA-GNN · Cora, CiteSeer, PubMed, Actor, Chameleon, Squirrel | accuracy: 86.70 -> 87.72; 79.26 -> 80.49; 84.01 -> 86.28; 31.97 -> 34.07; 39.62 -> 41.19; 34.87 -> 38.17 | Helped |
| add pseudo error generation | BP · Cora, CiteSeer, PubMed, Photo, Computer, Actor, Chameleon, Squirrel | accuracy: 86.04 -> 87.41; 78.20 -> 80.24; 85.24 -> 84.74; 93.03 -> 91.95; 89.48 -> 87.78; 31.94 -> 31.53; 41.28 -> 38.71; 37.81 -> | Mixed |
Surprising findings
- Applying the pseudo error generator to BP does not improve BP overall (e.g., BP+EG drops on PubMed, Photo, Computer), while it helps DFA.
- The proposed method outperforms BP on most datasets despite BP being the gold standard, including heterophilic graphs such as Texas and Cornell.
Limitations
- Training time per epoch is higher than BP due to pseudo error generation and filtering.
- Convergence analysis is restricted to a two-hidden-layer GCN case and relies on random Gaussian feedback matrices being approximately orthogonal.
- Pseudo error scaling and filtering rely on manually chosen hyperparameters (alpha, iterations, epsilon).
Experimental setup
Datasets: Cora CiteSeer PubMed Photo Computer Chameleon Squirrel Actor Texas Cornell Flickr Reddit
Benchmarks: Cora CiteSeer PubMed Photo Computer Chameleon Squirrel Actor Texas Cornell Flickr Reddit
Metrics: accuracy training time per epoch memory footprint
Baselines: BP PEPITA FF+LA FF+VN CaFo+MSE CaFo+CE ForwardGNN-SF
Builds on: direct feedback alignment feedback alignment forward-forward algorithm label spreading GCN
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