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NeSyFOLD: A Framework for Interpretable Image Classification
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Proposes NeSyFOLD, which replaces the CNN layers after the last convolutional layer with a stratified answer set program learned by FOLD-SE-M from binarized kernel outputs, plus an automatic semantic labeling algorithm and an EBP-sparse variant for smaller rule-sets.
Problem
CNN image classifiers are black boxes; their predictions are hard to explain or audit for bias. Existing global rule-extraction (ERIC) yields large rule-sets and lacks automatic semantic meaning for rule predicates.
Approach
Binarize last-conv-layer kernel activations, learn a default-logic rule-set (ASP) with FOLD-SE-M to replace the post-conv layers, use Elite BackProp to get sparse kernels for smaller rule-sets, and automatically label kernel predicates with concepts via IoU against ADE20k segmentation masks.
Key results
- NeSyFOLD-EBP yields smaller rule-sets than ERIC on P2 (12 vs 52 antecedents) with accuracy 0.92 vs 0.89.
- On GT43, NF-E reaches 0.85 fidelity and accuracy versus ERIC's 0.73, with rule size 99 vs 626.
- Semantic label adherence increases with margin and is higher for EBP-trained CNN kernels.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace the CNN layers after the last convolutional layer with the NeSyFOLD rule-set | VGG16 classifier · P2, P3.1, P3.2, P3.3, P5, P10, GT43, MS | accuracy: ERIC 0.89 ± 0.01 -> NF 0.92 ± 0.01 (P2); ERIC 0.81 ± 0.01 -> NF 0.84 ± 0.03 (P3.1); ERIC 0.90 -> NF 0.92 ± 0.0 (P3.2); E | Helped |
| train the CNN with Elite BackProp (EBP) (ablation) | NeSyFOLD · P2, P3.1, P3.2, P3.3, P5, P10, GT43, MS | rule-set size: 28 ± 5 -> 12 ± 5 (P2); 49 ± 9 -> 16 ± 5 (P3.1); 26 ± 7 -> 7 ± 1 (P3.2); 60 ± 11 -> 23 ± 4 (P3.3); 131 ± 10 -> 30 ± 8 (P5 | Helped |
| train the CNN with Elite BackProp (EBP) (ablation) | NeSyFOLD · P2, P3.1, P3.2, P3.3, P5, P10, GT43, MS | accuracy: 0.92 ± 0.01 -> 0.92 ± 0.01 (P2); 0.84 ± 0.03 -> 0.86 ± 0.02 (P3.1); 0.92 ± 0.0 -> 0.91 ± 0.01 (P3.2); 0.79 ± 0.01 -> 0.7 | Mixed |
| use Elite BackProp (EBP) to train the CNN (ablation) | NeSyFOLD · P3.1, P3.2, P3.3 | kernel-label adherence | Helped |
| increase the semantic-label margin (ablation) | NeSyFOLD predicate labeling · P3.1, P3.2, P3.3 | kernel-label adherence | Helped |
| increase the semantic-label margin (ablation) | NeSyFOLD predicate labeling · P3.1, P3.2, P3.3 | number of concepts per predicate label | Helped |
Surprising findings
- On P10, all models perform poorly (ERIC 0.36 accuracy, NF-E 0.44), attributed to few distinct edges in the images.
Limitations
- ERIC code is proprietary so comparison is limited to the datasets reported in ERIC papers
- Accuracy and fidelity drop as the number of classes grows
- Semantic labeling depends on ADE20k-style segmentation masks and adherence was judged manually
Experimental setup
Datasets: Places GTSRB ADE20k ImageNet
Benchmarks: Places subsets P2, P3.1, P3.2, P3.3, P5, P10 GTSRB (GT43)
Metrics: accuracy fidelity rule-set size predicate count percentage adherence
Baselines: ERIC NeSyFOLD (vanilla CNN)
Builds on: FOLD-SE-M Elite BackProp ERIC
Closest papers by meaning
- PICNN: A Pathway towards Interpretable Convolutional Neural Networks (AAAI 2024 · similarity 0.86)
- Interpretable Image Classification via Non-parametric Part Prototype Learning (CVPR 2025 · similarity 0.86)
- Explainable Neural Networks with Guarantee: A Sparse Estimation Approach (AAAI 2025 · similarity 0.85)
- Improving Prototypical Visual Explanations with Reward Reweighing, Reselection, and Retraining (ICML 2024 · similarity 0.84)
- Enhancing Performance of Explainable AI Models with Constrained Concept Refinement (ICML 2025 · similarity 0.84)
- Explaining Domain Shifts in Language: Concept Erasing for Interpretable Image Classification (CVPR 2025 · similarity 0.84)
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