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QPM: Discrete Optimization for Globally Interpretable Image Classification
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Introduces QPM, which uses a binary quadratic program to select a small set of shared features and assign exactly 5 per class, then fine-tunes the backbone for globally interpretable, accurate image classifiers.
Problem
Global interpretability of image classifiers: existing compactness-based interpretable models use real-valued, biased, or variable-size class representations, making global class explanations hard to compare or contrast.
Approach
Select 50 features out of 2048 and assign each class exactly 5 of them via a globally optimal binary quadratic program (maximizing class-feature correlation, penalizing redundant feature selection, and biasing toward localized features); then fix the binary assignment and fine-tune so each feature becomes a shared general concept among its assigned classes.
Key results
- On CUB-2011 with ResNet50, QPM reaches 85.1% accuracy with 50 total features and 5 per class, above Q-SENN (84.7%) and SLDD-Model (84.5%).
- On ImageNet, QPM reaches 74.2% accuracy versus Q-SENN's 74.3%, and is marginally behind Q-SENN there.
- QPM achieves 47.9 structural grounding on CUB, versus 34.0 for the baseline ResNet and 29.2 for SLDD-Model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use QPM instead of Q-SENN | ResNet image classifier · CUB | accuracy: 84.7 -> 85.1 | Helped |
| Use QPM instead of Q-SENN | ResNet image classifier · CARS | accuracy: 91.5 -> 91.8 | Helped |
| Use QPM instead of Q-SENN | ResNet image classifier · ImageNet-1K | accuracy: 74.3 -> 74.2 | Hurt |
| Add exactly 5 assigned features per class instead of enforcing only 5 on average (ablation) | QPM · CUB | accuracy: 84.3±0.2 -> 85.1±0.3 | Helped |
| Add exactly 5 assigned features per class instead of enforcing only 5 on average (ablation) | QPM · CARS | accuracy: 91.6±0.3 -> 91.8±0.1 | No clear effect |
| Add the feature-selection bias for local feature maps (ablation) | QPM · CUB | Scale-Invariant-Diversity@5 | Helped |
| Add feature-feature similarity reduction to the QP objective (ablation) | QPM · CUB | accuracy | Helped |
Surprising findings
- Q-SENN's Scale-Invariant-Diversity and interpretability metrics are high on ImageNet, yet QPM is only marginally behind Q-SENN in accuracy there despite using a cheaper procedure.
Limitations
- Global optimization of the QP is expensive; optimization time grows strongly with the number of selected features.
- Compactness and accuracy gains are reported only for ResNet-style backbones on fine-grained datasets with 5 seeds; ImageNet results use only 3 seeds.
- Polysemantic features remain possible; interpretability is not measured for grounding directly.
Experimental setup
Datasets: CUB-2011 Stanford Cars ImageNet-1K TravelingBirds Places365
Benchmarks: CUB-2011 Stanford Cars ImageNet-1K
Metrics: accuracy total features features per class Scale-Invariant-Diversity@5 generality contrastiveness structural grounding
Baselines: Baseline ResNet50 glm-saga PIP-Net ProtoPool SLDD-Model Q-SENN
Builds on: Q-SENN PIP-Net ProtoPool glm-saga feature diversity loss
Closest papers by meaning
- CHiQPM: Calibrated Hierarchical Interpretable Image Classification (NeurIPS 2025 · similarity 0.86)
- Q-SENN: Quantized Self-Explaining Neural Networks (AAAI 2024 · similarity 0.86)
- A Simple Interpretable Transformer for Fine-Grained Image Classification and Analysis (ICLR 2024 · similarity 0.84)
- NeSyFOLD: A Framework for Interpretable Image Classification (AAAI 2024 · similarity 0.84)
- Enhancing Pre-trained Representation Classifiability can Boost its Interpretability (ICLR 2025 · similarity 0.84)
- PICNN: A Pathway towards Interpretable Convolutional Neural Networks (AAAI 2024 · similarity 0.84)
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