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Interpretable Image Classification with Differentiable Prototypes Assignment
Dawid Rymarczyk, Łukasz Struski, Michał Górszczak, Koryna Lewandowska, Jacek Tabor, Bartosz Zieliński
TL;DR
Prototype-based image classifiers need interpretable explanations but can require many class-specific prototypes and costly pruning. ProtoPool shares prototypes across classes, learns their assignments differentiably, and uses focal similarity to emphasize salient features. It reports strong accuracy with fewer prototypes and more distinctive prototypes in user studies, while retaining limitations around prototype meaning, hyperparameter selection, adversarial attacks, and deployment risks.
Problem
Prototype-based explanations are useful for interpreting deep-learning predictions, but class-specific prototype sets scale poorly when visual features are shared across classes.
Method
ProtoPool uses a shared prototype pool with differentiable Gumbel-Softmax assignments and focal similarity that emphasizes salient features.
Results
ProtoPool achieves the highest user-study scores, with 3.66 ± 2.00 versus 2.85 ± 2.63 without focal similarity and 2.87 ± 2.68 for ProtoTree.
Takeaways & Limitations
The method reduces prototype count while maintaining high accuracy and provides positive, class-related explanations without pruning operations.
Takeaways & Limitations
Prototype meaning can remain uncertain, Gumbel-Softmax temperature requires careful tuning, and prototype-based systems are vulnerable to adversarial attacks and misleading deployment contexts.
Abstract
from arXiv · showhide
We introduce ProtoPool, an interpretable image classification model with a pool of prototypes shared by the classes. The training is more straightforward than in the existing methods because it does not require the pruning stage. It is obtained by introducing a fully differentiable assignment of prototypes to particular classes. Moreover, we introduce a novel focal similarity function to focus the model on the rare foreground features. We show that ProtoPool obtains state-of-the-art accuracy on the CUB-200-2011 and the Stanford Cars datasets, substantially reducing the number of prototypes. We provide a theoretical analysis of the method and a user study to show that our prototypes are more distinctive than those obtained with competitive methods.
1 Introduction
ProtoPool addresses the scalability and interpretability limits of prototype-based classifiers by sharing prototypes across classes, assigning them differentiably, and focusing similarity on salient features. The method removes pruning from training while reducing prototypes and supporting positive, interpretable explanations.
- Motivation: ProtoPNet’s class-specific prototype sets scale poorly because shared visual features require many prototypes and can introduce background prototypes.The limitation also makes the model harder for users to interpret.
- Evidence: ProtoPool combines fewer prototypes with higher accuracy among reduced-prototype models and evaluates interpretability through theoretical analysis, experiments, and a user study.The paper reports that its prototypes are more distinctive than those from competing methods.
- ProtoPool: ProtoPool shares prototypes between classes without a predefined concept dictionary, reducing their number while modeling similarities between classes.The paper illustrates shared prototypes for features common to Prothonotary and Wilson Warblers.
- ProtoPool: Soft prototype-to-class assignments are learned with a differentiable distribution and Gumbel-Softmax, enabling end-to-end training without a pruning stage.This addresses the pruning requirement in earlier prototype-sharing approaches.
- ProtoPool: Focal similarity emphasizes salient image features by focusing activation on a narrow visual region rather than distributing it across the image.The resulting explanations use positive reasoning on salient features.
2 Related works
Related work includes post hoc explainers and self-explainable models, with prototypical methods explaining predictions through image-part matching and prototype-based reasoning.
- Post hoc explainers reveal hidden model reasoning using saliency maps, Concept Activation Vectors, counterfactual examples, or perturbation analysis.
- Self-explainable prototypical models compare image parts with reference patterns to explain predictions and provide class-level explanations.
- ProtoPShare reduces prototype counts through data-dependent merge-pruning, whereas ProtoTree uses a soft neural decision tree that may rely on negative reasoning.
3 ProtoPool
ProtoPool uses a shared prototype pool with differentiable slot assignments, focal similarity, and orthogonality constraints to support interpretable classification with fewer prototypes.
- Overall architecture: ProtoPool combines convolutional layers, a prototype pool layer, and a fully connected classification layer.The pool contains trainable prototypes, while class slots aggregate prototype similarities before producing normalized prediction logits.
- Overall architecture: Each class slot represents a distribution over shared prototypes, allowing prototypes to be assigned to multiple classes.The architecture example uses three slots per class, with some prototypes shared across Prothonotary Warbler and Wilson Warbler.
- Focal similarity: Focal similarity widens the gap between maximal and average activation so prototypes focus on salient, localized image features.The method addresses background concentration and the limitation that standard max activation passes gradients only through the most active image part.
- Assigning one prototype per slot: ProtoPool uses Gumbel-Softmax to make prototype assignment differentiable while approaching one-hot assignments at low temperatures.The distribution interpolates between continuous categorical densities and discrete one-hot distributions, with τ ∈[0.1, 0.5] approaching the latter.
- Slots orthogonality: The orthogonality loss discourages assigning the same prototype to multiple slots within one class.Its result is that successive slots of a class are assigned to different prototypes.
- Prototypes projection: Prototype projection replaces each learned prototype with the nearest training-patch representation from its assigned classes.This makes abstract prototypes visualizable while accounting for the set of classes assigned to each prototype.
- Comparison with other prototypical models: ProtoPool achieves the highest accuracy on CUB-200-2011 even against models using ten times more prototypes, while remaining competitive on Stanford Cars with fewer prototypes.An ensemble of three ProtoPools also surpasses an ensemble of five TesNets using 17 times more prototypes.
4 Experiments
ProtoPool is evaluated on CUB-200-2011 and Stanford Cars using multiple pretrained backbones and comparisons with prototypical-part models. It achieves strong accuracy with substantially fewer prototypes while providing class-specific prediction explanations.
- Experimental setup: ProtoPool is evaluated on CUB-200-2011 and Stanford Cars using ResNet and DenseNet backbones pretrained on ImageNet.ResNet-50 with CUB-200-2011 is instead pretrained on iNaturalist2017 for comparison with ProtoTree.
- Local explanations: ProtoPool explanations combine prototypical parts, activation maps, similarity values, and final-layer weights to produce a class score.The predicted class is the one with the largest sum of similarity values multiplied by their weights.
- Global explanations: ProtoPool assigns visually meaningful parts, including red feathers, black eyes, and tail features, to Scarlet Tanager.These examples illustrate class-level visual characteristics represented by the model’s prototypes.
- Comparison with other prototypical models: ProtoPool achieves the highest accuracy on CUB-200-2011, surpassing models with many more prototypical parts.On Stanford Cars, it outperforms similarly compact models but is slightly below TesNet, which uses ten times more prototypes.
- Comparison with other prototypical models: ProtoPool uses 10% of ProtoPNet’s prototypes while sharing them between classes through end-to-end, fully differentiable training.The comparison considers prototype count, reasoning type, and sharing between classes.
- Prototype sharing: A convex tailgate prototype is shared by nine car classes, including mostly luxury cars and the Fiat 500.This illustrates how one visual feature can support multiple classes.
5 Interpretability
ProtoPool supports local and global explanations by sharing positive visual prototypes across classes. Its shared-prototype assignments are stable across runs, and focal similarity produces more salient prototypes in a user study.
- Local and global interpretations: ProtoPool provides local explanations and global class descriptions using prototypical parts shared between data classes.The shared parts describe class relations through positive reasoning rather than prototype absence.
- Differences between prototypical methods: ProtoPool and ProtoTree use around 10% of the prototypical parts used by ProtoPNet and TesNet.ProtoPool obtains class similarity directly from slots, while ProtoTree requires traversing a decision tree.
- Differences between prototypical methods: ProtoPool relies only on positive reasoning, unlike ProtoTree’s use of negative reasoning, and directly represents inter-class similarity through shared slots.ProtoPNet and TesNet do not provide a mechanism for detecting inter-class similarities.
- Stability of shared prototypes: Shared-prototype distributions differ negligibly across five training runs, with most prototypes shared by five classes.The observed stability concerns how many classes share each prototype.
- User study on focal similarity: 40 workers answered 2400 randomized user-study questions evaluating prototype-feature saliency on a 1-to-5 scale.The study compared ProtoPool with and without focal similarity against ProtoTree.
- User study on focal similarity: Mean saliency scores were 3.66 for ProtoPool, 2.87 for ProtoTree, and 2.85 for ProtoPool without focal similarity.ProtoPool with focal similarity mostly received scores from 3 to 5 and was judged more salient than the reference models.
6 Ablation study
The ablation study examines projection, architectural choices, and model size. Projection has negligible impact, while the proposed components and sufficient prototype and slot capacity are important for accuracy.
- Influence of architectural choices: The complete combination of ProtoPool’s proposed mechanisms achieves the best accuracy among the architectural variants.Variants remove orthogonalization loss, replace Gumbel-Softmax with softmax, or replace focal similarity with ProtoPNet similarity.
- Before and after prototype projection: Prototype projection causes negligible differences in ProtoPool accuracy on CUB-200-2011 and Stanford Cars.The CUB-200-2011 experiment uses ResNet-50 pretrained on iNaturalist.
- Number of prototypes and slots: Accuracy increases up to around 200 prototypes and then reaches a plateau on both datasets.This indicates that adding more prototypes beyond that level does not improve the measured accuracy.
- Number of prototypes and slots: ProtoPool accuracy increases up to 10 slots and then reaches a plateau.The study evaluates how slot count affects accuracy alongside the number of prototypical parts.
7 Conclusions
ProtoPool is a self-explainable prototype model that shares prototypes between classes without pruning and uses differentiable assignment. Focal similarity emphasizes salient features while the combined design improves interpretability alongside high accuracy.
- Conclusions: ProtoPool shares prototypes between classes without pruning, reducing their number by up to ten times through fully differentiable assignment.Prototype assignment uses the Gumbel-Softmax trick together with orthogonalization loss.
- Conclusions: Focal similarity focuses ProtoPool on salient features, supporting higher interpretability while maintaining high accuracy.The paper supports this conclusion through theoretical analysis, experiments, and a user study.
Supplementary Materials
The supplementary materials describe the datasets, training setup, prototype dimensions, and differentiable assignment mechanism used by ProtoPool.
- Datasets: ProtoPool is evaluated on CUB-200-2011 with 200 bird species and Stanford Cars with 196 car models.Images are augmented offline, and data preparation follows the procedure used in prior work.
- Architecture and training: The model uses convolutional backbones followed by a 1×1 convolution that maps latent features to dataset-specific depths.The latent depth is 128 for Stanford Cars and 256 for CUB-200-2011.
- Architecture and training: Training freezes the convolutional feature extractor for 10 epochs, then trains to convergence with early stopping before prototype projection and last-layer fine-tuning.The model uses a warmup stage followed by convergence training and post-convergence projection.
- Prototype assignment: ProtoPool assigns prototypes to class slots with a soft distribution that is binarized during training using Gumbel-Softmax.The assignment uses a distribution over the prototype pool rather than a fixed hard assignment.
9 Generating names of prototypical parts
ProtoPool names CUB-200-2011 prototypical parts by filtering human-provided attributes and checking nearest prototype patches for consistent bird regions.
- Attribute filtering: CUB-200-2011 prototype names are derived from attributes collected from Amazon Mechanical Turk.Attributes assigned by fewer than 20% of users are filtered out before class-level filtering.
- Attribute filtering: For each class, attributes appearing in fewer than 20% of its testing images are removed.This class-level filter follows the initial user-agreement filter.
- Prototype validation: Five nearest patches for each prototype are inspected to determine whether they consistently identify the same bird part.The consistency check is used to support the naming of the prototypical part.
10 Results for other backbone networks
Additional experiments compare ProtoPool across backbones and prototype-based methods, while examining focal similarity and class-level prototype sharing.
- Model comparison: ProtoPool is the only compared method with differentiable prototypical-part assignment and simultaneous data processing.The comparison contrasts ProtoPool with methods using hard assignment or sequential processing.
- Backbone comparisons: ProtoPool achieves competitive results even when compared with models using ten times more prototypes on both datasets.The comparison covers CUB-200-2011 and Stanford Cars across convolutional backbones and prototype counts.
- Model comparison: ProtoPool uses 10% of ProtoPNet’s prototypes while retaining positive-reasoning explanations and sharing prototypes across classes.The comparison also identifies class-similarity detection as a shared property with ProtoPShare.
- Similarity functions: Focal similarity makes ProtoPool activation maps focus on foreground car features such as spoilers, reflectors, and Ferrari logos rather than borders or larger regions.The figure compares ProtoPool with focal similarity against models using other similarity functions.
- Class relations: ProtoPool directly provides class-similarity visualizations through shared prototypes.This capability is illustrated through a graph of relations between classes in the Stanford Cars dataset.
12 Details on ablation study
The ablation and user-study materials examine assignment binarization, class-relation stability, prototype salience, and practical limitations of ProtoPool.
- Assignment ablations: Only the full ProtoPool configuration produces a binary prototype-assignment matrix and binarized q distributions.The relevant visualizations show values concentrated at 0 and 1, unlike ablated configurations.
- Stability of shared prototypes: ProtoPool’s class-relation graphs are consistent across runs, identifying similarities between SUVs and sedans but not between Rolls-Royce and BMW.Each graph represents five classes, with edges encoding the mean number of shared prototypes over five repetitions.
- User study: ProtoPool receives the highest number of positive user-study ratings, defined as scores 4 and 5, in both datasets.Users rated prototypical parts from ProtoPool, ProtoTree, and ProtoPool without focal similarity on a 1–5 salience scale.
- Limitations: ProtoPool inherits uncertainty about the meanings of projected prototypes from other prototype-based models.The authors note that prototype semantics may remain non-obvious even after projection from training data.
- Limitations: The Gumbel-Softmax temperature schedule requires careful hyperparameter search, and accuracy eventually saturates as prototypes increase.These are stated as additional limitations of the method.
15 Negative impact
ProtoPool’s design emphasizes positive, foreground-focused reasoning and prototype sharing, but its capacity eventually saturates and its prototypical parts remain vulnerable to adversarial misuse. User studies report higher interpretability scores than the compared variants.
- Negative impact: Prototypical parts are vulnerable to a new type of adversarial attack, and spoiled or decontextualized prototypes can spread disinformation in applications such as medicine.The paper therefore warns practitioners to consider this danger when deploying ProtoPool.
- Focal similarity: Focal similarity propagates gradients through all patches by subtracting the mean from maximum similarity, unlike the classic approach’s maximum-patch-only gradient.Its similarity distribution changes from unimodal to bimodal over 1000 images.
- Saturation of model capacity: Around 200 prototypes, model capacity plateaus, so adding prototypes does not improve accuracy or provide a clear interpretability–accuracy trade-off.The authors hypothesize prototype entanglement may cause this saturation and suggest orthogonality or iterative pool expansion as possible remedies.
- Focal similarity: Focal similarity supports positive reasoning from salient prototype presence rather than negative reasoning from prototype absence.The paper contrasts recognizing a salient goatee with inferring a goat from missing wings.
- Prototype sharing: Sharing prototypes is essential because semantically similar prototypes can be distant in representation space after exclusive-class training, producing unstable predictions.Shared prototypes address the separation of related semantics across classes described for exclusive prototype sets.
- User studies: ProtoPool user-study confidence scores were 3.66 ± 2.00, compared with 2.85 ± 2.63 without focal similarity and 2.87 ± 2.68 for ProtoTree.Mann–Whitney U tests reported p-value=2.78 · 10^-12 and 1.16 · 10^-11 for the two comparisons, respectively.