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Factor Graph-based Interpretable Neural Networks
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Proposes AGAIN, a factor-graph-based concept bottleneck model that identifies and rectifies logically inconsistent concept explanations at inference time to keep explanations comprehensible under unknown perturbations.
Problem
Concept-level explanations of interpretable neural networks become incomprehensible under malicious input perturbations, and adversarial training defends only against known perturbation types.
Approach
Encode logical rules between concepts and categories as a factor graph, detect explanations violating these rules via a conditional-probability check, and rectify concept activations at inference with an interactive intervention switch, without training on perturbations.
Key results
- Under unknown perturbation at magnitude 32 on CUB, prior interpretable models reach LSM below 48 while AGAIN reaches up to 92.30.
- AGAIN attains near 100% identification rate (IR) across perturbation magnitudes on both real datasets, with SR averaging about 98%.
- Ablation on CUB shows the full factor graph (category-concept plus concept-concept rules) improves LSM by an average of 6.86 over single-rule-type variants.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add factor-graph reasoning and explanation rectification | AGAIN · CUB, unknown perturbation ε=32 | LSM: 85.7(6.7) -> 92.1(2.1) | Helped |
| Add factor-graph reasoning and explanation rectification | AGAIN · MIMIC-III EWS, unknown perturbation ε=32 | LSM: 84.4(5.7) -> 92.3(4.7) | Helped |
| Add factor-graph reasoning and explanation rectification | AGAIN · CUB, unknown perturbation ε=32 | E-ACC: 83.5(5.2) -> 93.9(0.7) | Helped |
| Add factor-graph reasoning and explanation rectification | AGAIN · CUB, unknown perturbation ε=32 | P-ACC: 59.6(1.2) -> 59.6(0.8) | No clear effect |
| Add both category-concept and concept-concept rules (ablation) | AGAIN · CUB, perturbation ε=32 | LSM: 39.4(3.1) -> 92.1(6.1) | Helped |
| Add concept-concept rules to category-concept rules (ablation) | AGAIN · CUB, perturbation ε=32 | LSM: 84.0(2.5) -> 92.1(6.1) | Helped |
| Add category-concept rules to concept-concept rules (ablation) | AGAIN · CUB, perturbation ε=32 | LSM: 80.1(2.3) -> 92.1(6.1) | Helped |
| Use category-concept rules instead of concept-concept rules alone (ablation) | AGAIN · CUB, perturbation ε=32 | LSM: 80.1(2.3) -> 84.0(2.5) | Helped |
Surprising findings
- Overly strict logical constraints can cause the factor graph to lose its ability to recognize perturbations, so low-weight rule violations are tolerated.
Limitations
- Validity depends on the correctness of the predicted category; wrong categories cause wrong rectifications.
- When domain knowledge changes, the factor graph must be reconstructed, limiting generalizability.
Experimental setup
Datasets: CUB MIMIC-III EWS Synthetic-MNIST
Benchmarks: CUB MIMIC-III EWS Synthetic-MNIST
Metrics: P-ACC E-ACC LSM IR SR
Baselines: CBM Hard AR ICBM PCBM ProbCBM Label-free CBM ProtoCBM ECBMs DeepProblog MBM C-HMCNN LEN
Builds on: concept bottleneck models factor graphs Hoeffding's inequality
Closest papers by meaning
- Factorized Explainer for Graph Neural Networks (AAAI 2024 · similarity 0.88)
- Beyond Topological Self-Explainable GNNs: A Formal Explainability Perspective (ICML 2025 · similarity 0.87)
- Stratified GNN Explanations through Sufficient Expansion (AAAI 2024 · similarity 0.87)
- Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanations (ICML 2025 · similarity 0.87)
- GraphTrail: Translating GNN Predictions into Human-Interpretable Logical Rules (NeurIPS 2024 · similarity 0.87)
- COMRECGC: Global Graph Counterfactual Explainer through Common Recourse (ICML 2025 · similarity 0.86)
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