CHiQPM: Calibrated Hierarchical Interpretable Image Classification

Conference: NeurIPS 2025 arXiv: 2511.20779 Code: None Area: Explainable AI / Image Classification Keywords: Interpretable Machine Learning, Hierarchical Explanation, Conformal Prediction, Image Classification, Human-AI Complementarity

TL;DR

CHiQPM proposes a calibrated hierarchical interpretable image classification method that selects and assigns features to classes via quadratic programming, constructs hierarchical explanation paths, and incorporates interpretable Conformal Prediction set prediction, retaining 99% of black-box model accuracy while providing both global and local interpretability.

Background & Motivation

Background: Deep learning is increasingly adopted in safety-critical domains such as medical diagnosis and autonomous driving. Interpretable-by-design models represent an important direction toward trustworthy AI. The QPM family of methods provides global interpretability through compact binary class representations (each class described by a small number of features), enabling contrastive explanations of inter-class differences.

Limitations of Prior Work: - Although QPM generates contrastive class representations, such contrasts are sparse (e.g., on CUB-2011, only an average of 0.13% of class pairs are contrastive). - Existing interpretable models lack principled uncertainty quantification for local explanations—saliency maps convey no confidence information. - Prototype networks (e.g., ProtoTree) appear interpretable, yet their similarity spaces are learned freely, making their behavior unpredictable to humans. - Conformal Prediction (CP) provides set-prediction guarantees, but the resulting prediction sets typically contain semantically unrelated classes.

Key Challenge: The trade-off between interpretability and accuracy—more compact representations are easier to interpret but limit accuracy; CP-generated sets lack semantic coherence.

Goal: - How to increase the proportion of contrastive class pairs while maintaining high accuracy? - How to provide hierarchical local explanations that mirror human reasoning? - How to produce semantically coherent class sets via CP set prediction?

Key Insight: Combining feature detection with a hierarchical class structure. The binary feature assignments from QPM naturally induce a class hierarchy tree; traversing this tree yields semantically coherent set predictions.

Core Idea: Introduce hierarchical constraints and a Feature Grounding Loss into the QPM framework so that feature assignments naturally form a traversable class hierarchy, and integrate CP into this structure to realize interpretable, calibrated set prediction.

Method

Overall Architecture

The CHiQPM pipeline consists of five stages: 1. Train a dense model: Train a black-box backbone with a Feature Diversity Loss \(\mathcal{L}_{div}\) to ensure that initial feature map activations are distributed across different spatial locations. 2. Compute QP constants: Compute the class–feature similarity matrix \(\mathbf{A}\), the feature–feature similarity matrix \(\mathbf{R}\), the linear bias term \(\mathbf{b}\), and the set of similar class pairs \(\mathbb{K}\). 3. Solve the QP with hierarchical constraints: Extend QPM's objective with hierarchical constraints, jointly optimizing feature selection \(\mathbf{s} \in \{0,1\}^{n_f}\) and class–feature assignment \(\mathbf{W} \in \{0,1\}^{n_c \times n_f}\). 4. Fine-tune features: Fine-tune the compressed model using the Feature Grounding Loss \(\mathcal{L}_{feat}\) with ReLU activations. 5. Calibrate: Calibrate the hierarchical set predictor using CP.

Key Designs

Quadratic Programming with Hierarchical Constraints: The original QPM objective maximizes the correlation between selected features and classes while enforcing feature distinctiveness and locality. CHiQPM augments this with hierarchical constraints that require the feature assignment \(\mathbf{W}^*\) to induce a meaningful hierarchy over classes. Specifically, QP constraints ensure that each class is assigned exactly \(k\) features (compactness) and that their combination uniquely identifies the class. The hierarchical constraints further encourage similar classes to share more features, forming semantically meaningful groupings in the class tree.

Feature Grounding Loss \(\mathcal{L}_{feat}\): This is one of the paper's key contributions. Conventional features may be polysemantic—a single feature simultaneously detects multiple human concepts. \(\mathcal{L}_{feat}\), combined with ReLU activations, encourages learned features to be more grounded and sparse, meaning each feature is more likely to correspond to a single human-interpretable concept (e.g., a "red eye" feature distinguishing two species of black birds in Figure 1). The ReLU activation ensures non-negative feature responses, giving "feature not detected" a clear semantic meaning.

Hierarchical Local Explanations: Given an input image, CHiQPM constructs an instance-specific explanation hierarchy. Each level \(n\) corresponds to classification using the top-\(n\) most salient features: - Level 1: Only the strongest feature is used, potentially matching multiple classes that share it. - Level 2: The second feature is added, further narrowing the candidate set. - Level \(k\): The class is uniquely identified.

This hierarchy answers multiple questions: which meaningful features are detected in the image? How does each successive feature narrow the candidate class set? Which set should be predicted to guarantee a target coverage rate?

Built-in Interpretable Conformal Prediction: CHiQPM uniquely integrates CP into its hierarchical explanation. The prediction set at level \(n\) is defined as all classes that share the top-\(n\) salient features with the most probable class in the hierarchy tree. Through CP calibration, the system dynamically selects an appropriate level for each instance: easy instances may require only level \(k\) (a single class), while difficult instances may fall back to level 2 or 1, predicting a semantically coherent group (e.g., all black birds).

Loss & Training

The overall training procedure: 1. Stage 1: Train the dense model with \(\mathcal{L}_{CE} + \lambda_{div} \mathcal{L}_{div}\). 2. Stage 2: Solve the QP to obtain optimal feature selection and assignment. 3. Stage 3: Fine-tune the compressed model with \(\mathcal{L}_{CE} + \lambda_{feat} \mathcal{L}_{feat}\) and ReLU activations to improve feature grounding.

Key Experimental Results

Main Results

CHiQPM is evaluated across multiple datasets and architectures. Core results:

Dataset	Architecture	Black-box Acc.	CHiQPM Acc.	Retention Ratio	Contrastive Pair Ratio
CUB-2011	ResNet-50	~82%	~81%	99%+	Significant gain vs. QPM
ImageNet-1K	ResNet-50	~76%	~75%	~99%	Gap halved
CUB-2011	Multiple archs	Varies	Close to black-box	99%+	Most classes gain contrastive explanations

Key finding: CHiQPM achieves state-of-the-art accuracy as a point predictor, retaining over 99% of non-interpretable model accuracy. On ImageNet-1K, the accuracy gap relative to the black-box baseline is reduced by more than half.

Ablation Study

Component	Contrastive Pair Ratio	Accuracy	Coverage Efficiency
Base QPM	Baseline	Baseline	—
+ Hierarchical constraints	↑ Significant	Maintained	Usable
+ Feature Grounding Loss	↑	Maintained or ↑	Improved
+ ReLU activation	↑	Maintained	Improved
Full CHiQPM	Best	Best	Best

CP set prediction efficiency: On CUB-2011 (5/50 features per class), CHiQPM's built-in CP method achieves coverage–set-size curves competitive with standard CP baselines (THR, APS), while producing semantically coherent prediction sets.

Key Findings

1. Interpretability without sacrificing accuracy: CHiQPM retains over 99% of black-box model accuracy while providing comprehensive global and local interpretability.
2. Substantial gain in contrastive coverage: Compared to QPM, CHiQPM significantly increases the proportion of class pairs with contrastive explanations, enabling more classes to be distinguished by feature differences.
3. Cognitive plausibility of hierarchical explanations: The hierarchical explanation structure more closely mirrors human reasoning—first identifying a broad category (black bird), then narrowing to a specific species.
4. Semantically coherent set predictions: Classes within a CP prediction set are adjacent in the hierarchy and are semantically similar.

Highlights & Insights

• Natural integration of CP with interpretable models: Rather than post-hoc application of CP, the model architecture itself supports hierarchical set prediction—an elegant design choice.
• Feature Grounding Loss addresses polysemanticity: The approach directly tackles the fundamental problem of feature polysemanticity in interpretable ML.
• Scalable to ImageNet: The method operates on ImageNet with 1,000 classes, demonstrating scalability.
• Human-AI complementarity perspective: Unlike AI systems designed to replace human judgment, CHiQPM is designed to assist human expert decision-making.

Limitations & Future Work

• The computational cost of QP solving grows with the number of classes, which may limit applicability to extremely large-scale classification tasks.
• The semantic grounding quality of features still depends on the representational quality of the backbone model.
• The hierarchy depth is directly tied to the number of features \(k\); with very few features, the resulting hierarchy may be too shallow.
• The paper validates the method primarily on visual classification tasks; applicability to other modalities (text, multimodal) remains to be explored.

Related Work & Insights

• QPM / Q-SENN family: The direct predecessors of CHiQPM; this work extends them with hierarchical structure and calibration capabilities.
• Conformal Prediction: A distribution-free set-prediction framework; CHiQPM is the first to intrinsically integrate CP with an interpretable model.
• Prototype networks (ProtoPNet, ProtoTree): Another class of interpretable models, but the unpredictability of their learned similarity spaces is an inherent limitation.
• Concept Bottleneck Models (CBM): Use human concepts as a bottleneck, but require concept-level annotations.

Rating

• Novelty: ⭐⭐⭐⭐ — The integration of hierarchical CP with interpretable models is a genuine contribution.
• Technical Depth: ⭐⭐⭐⭐ — QP optimization and CP theory are tightly coupled.
• Experimental Thoroughness: ⭐⭐⭐⭐ — Multi-dataset, multi-architecture validation with thorough ablation.
• Writing Quality: ⭐⭐⭐⭐ — Clear structure and intuitive illustrations.
• Value: ⭐⭐⭐⭐ — Interpretability without accuracy sacrifice has practical value in safety-critical domains.

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