Concept Bottleneck Models

Concept Bottleneck Models (CBMs) in medical imaging aim to improve model interpretability by predicting intermediate clinical concepts before final diagnoses. However, most existing CBMs treat concepts as discriminative predictors of pathology labels, without explicitly modelling the underlying clinical generative process where diseases produce observable radiographic findings. We propose XpertCausal, a radiologist-guided causal CBM for chest X-ray interpretation which models pathology-to-concept relationships using a probabilistic noisy-OR framework. This generative model is then inverted via Bayesian inference to estimate pathology probabilities from predicted concepts. Radiologist-curated concept-pathology associations are used to constrain model structure to radiologist-defined clinically plausible reasoning pathways. We evaluate XpertCausal on MIMIC-CXR across pathology classification performance, calibration, explanation quality, and alignment with radiologist-defined reasoning pathways. Compared with both a non-causal CBM baseline and a causal ablation with unconstrained learned associations, XpertCausal achieves improved AUROC, calibration, and clinically relevant explanation quality, while learning concept-pathology relationships that more closely align with expert knowledge. These results demonstrate that incorporating clinically motivated causal structure and expert domain knowledge into CBMs can lead to more accurate, interpretable, and clinically aligned models for CXR interpretation.

Concept Bottleneck Models (CBMs) have become a popular approach to enable interpretability in neural networks by constraining classifier inputs to a set of human-understandable concepts. While effective, current models embed concepts in flat Euclidean space, treating them as independent, orthogonal dimensions. Concepts, however, are highly structured and organized in semantic hierarchies. To resolve this mismatch, we propose Hyperbolic Concept Bottleneck Models (HypCBM), a post-hoc framework that grounds the bottleneck in this structure by reformulating concept activation as asymmetric geometric containment in hyperbolic space. Rather than treating entailment cones as a pre-training penalty, we show they encode a natural test-time activation signal: the margin of inclusion within a concept's entailment cone yields sparse, hierarchy-aware activations without any additional supervision or learned modules. We further introduce an adaptive scaling law for hierarchically faithful interventions, propagating user corrections coherently through the concept tree. Empirically, HypCBM rivals post-hoc Euclidean models trained on 20$\times$ more data in sparse regimes required for human interpretability, with stronger hierarchical consistency and improved robustness to input corruptions.

Concept Bottleneck Models (CBMs) predict through human-interpretable concepts, but they typically output point concept probabilities that conflate epistemic uncertainty (reducible model underspecification) with aleatoric uncertainty (irreducible input ambiguity). This makes concept-level uncertainty hard to interpret and, more importantly, hard to act upon. We introduce CREDENCE (Credal Ensemble Concept Estimation), a CBM framework that decomposes concept uncertainty by construction. CREDENCE represents each concept as a credal prediction (a probability interval), derives epistemic uncertainty from disagreement across diverse concept heads, and estimates aleatoric uncertainty via a dedicated ambiguity output trained to match annotator disagreement when available. The resulting signals support prescriptive decisions: automate low-uncertainty cases, prioritize data collection for high-epistemic cases, route high-aleatoric cases to human review, and abstain when both are high. Across several tasks, we show that epistemic uncertainty is positively associated with prediction errors, whereas aleatoric uncertainty closely tracks annotator disagreement, providing guidance beyond error correlation. Our implementation is available at the following link: https://github.com/Tankiit/Credal_Sets/tree/ensemble-credal-cbm

Open-ended grading is central to equitable and personalized education, yet manual grading remains time-consuming and costly, underscoring the need for automated grading systems. Although recent neural and large language model (LLM) based systems have demonstrated superior performance, they are typically black-box models whose scoring processes and rationales are difficult for educators to verify and trust. Concept bottleneck models (CBMs) have emerged as a promising approach by routing predictions through human-interpretable concepts, providing a mechanistic guarantee of transparency. However, standard CBMs are not tailored to open-ended grading: they do not explicitly model fine-grained rubric dimensions, inadequately capture the ordinal semantics of scoring scales, and neglect inherent reliability issues in human concept annotations. To address these limitations, we propose REC-CBM, a rubric-aware error-correction concept bottleneck model for trustworthy open-ended grading. REC-CBM introduces a rubric-aware concept encoder that learns concept-specific representations over responses and an ordinal pairwise calibration objective that preserves ranking structure among rubric dimensions. It further incorporates a latent concept error-correction module that denoises concept predictions before final grade prediction while preserving interpretability. Comprehensive experiments on publicly available datasets show that REC-CBM consistently improves grading performance and produces more faithful concept-level reasoning than both state-of-the-art baselines. Further analyses validate the contribution of each component and demonstrate the applicability in realistic educational settings. Overall, this work provides a practical, interpretable grading solution that enables educators to inspect, intervene in, and trust automated decisions, advancing more transparent and trustworthy education.

Concept Bottleneck Models (CBMs) route predictions exclusively through a clinically grounded concept layer, binding interpretability to concept-label consistency. When a dataset contains concept-level inconsistencies, identical concept profiles mapped to conflicting diagnosis labels create an unresolvable bottleneck that imposes a hard ceiling on achievable accuracy. In this paper, we apply rough set theory to the Derm7pt dermoscopy benchmark and characterize the full extent and clinical structure of this inconsistency. Among 305 unique concept profiles formed by the 7 dermoscopic criteria of the 7-point melanoma checklist, 50 (16.4%) are inconsistent, spanning 306 images (30.3% of the dataset). This yields a theoretical accuracy ceiling of 92.1%, independent of backbone architecture or training strategy for CBMs that exclusively operate with hard concepts. In addition, we characterize the conflict-severity distribution, identify the clinical features most responsible for boundary ambiguity, and evaluate two filtering strategies with quantified effects on dataset composition and CBM interpretability. Symmetric removal of all boundary-region images yields Derm7pt+, a fully consistent benchmark subset of 705 images with perfect quality of classification and no hard accuracy ceiling. Building on this filtered dataset, we present a hard CBM evaluated across 19 backbone architectures from the EfficientNet, DenseNet, ResNet, and Wide ResNet families. Under symmetric filtering, explored for completeness, EfficientNet-B5 achieves the best label F1 score (0.85) and label accuracy (0.90) on the held-out test set, with a concept accuracy of 0.70. Under asymmetric filtering, EfficientNet-B7 leads across all four metrics, reaching a label F1 score of 0.82 and concept accuracy of 0.70. These results establish reproducible baselines for concept-consistent CBM evaluation on dermoscopic data.

Continual learning aims to update models under distribution shift without forgetting, yet many high-stakes deployments, such as healthcare, also require interpretability. In practice, models that adapt well (e.g., deep networks) are often opaque, while models that are interpretable (e.g., decision trees) are brittle under shift, making it difficult to achieve both properties simultaneously. In response, we propose Tree of Concepts, an interpretable continual learning framework that uses a shallow decision tree to define a fixed, rule-based concept interface and trains a concept bottleneck model to predict these concepts from raw features. Continual updates act on the concept extractor and label head while keeping concept semantics stable over time, yielding explanations that do not drift across sequential updates. On multiple tabular healthcare benchmarks under continual learning protocols, our method achieves a stronger stability-plasticity trade-off than existing baselines, including replay-enhanced variants. Our results suggest that structured concept interfaces can support continual adaptation while preserving a consistent audit interface in non-stationary, high-stakes domains.

Concept Bottleneck Models (CBMs) aim to improve interpretability in Deep Learning by structuring predictions through human-understandable concepts, but they provide no way to verify whether learned concepts align with the human's intended meaning, hurting interpretability. We introduce Prototype-Grounded Concept Models (PGCMs), which ground concepts in learned visual prototypes: image parts that serve as explicit evidence for the concepts. This grounding enables direct inspection of concept semantics and supports targeted human intervention at the prototype level to correct misalignments. Empirically, PGCMs achieve similar predictive performance as state-of-the-art CBMs while substantially improving transparency, interpretability, and intervenability.

Recently impressive performance has been achieved in Concept Bottleneck Models (CBM) by utilizing the image-text alignment learned by a large pre-trained vision-language model (i.e. CLIP). However, there exist two key limitations in concept modeling. Existing methods often suffer from pre-training biases, manifested as granularity misalignment or reliance on structural priors. Moreover, fine-tuning with Binary Cross-Entropy (BCE) loss treats each concept independently, which ignores mutual exclusivity among concepts, leading to suboptimal alignment. To address these limitations, we propose Concept-wise Attention for Fine-grained Concept Bottleneck Models (CoAt-CBM), a novel framework that achieves adaptive fine-grained image-concept alignment and high interpretability. Specifically, CoAt-CBM employs learnable concept-wise visual queries to adaptively obtain fine-grained concept-wise visual embeddings, which are then used to produce a concept score vector. Then, a novel concept contrastive optimization guides the model to handle the relative importance of the concept scores, enabling concept predictions to faithfully reflect the image content and improved alignment. Extensive experiments demonstrate that CoAt-CBM consistently outperforms state-of-the-art methods. The codes will be available upon acceptance.

Catastrophic forgetting remains a fundamental challenge in continual learning, in which models often forget previous knowledge when fine-tuned on a new task. This issue is especially pronounced in class incremental learning (CIL), which is the most challenging setting in continual learning. Existing methods to address catastrophic forgetting often sacrifice either model interpretability or accuracy. To address this challenge, we introduce ClassIncremental Concept Bottleneck Model (CI-CBM), which leverage effective techniques, including concept regularization and pseudo-concept generation to maintain interpretable decision processes throughout incremental learning phases. Through extensive evaluation on seven datasets, CI-CBM achieves comparable performance to black-box models and outperforms previous interpretable approaches in CIL, with an average 36% accuracy gain. CICBM provides interpretable decisions on individual inputs and understandable global decision rules, as shown in our experiments, thereby demonstrating that human understandable concepts can be maintained during incremental learning without compromising model performance. Our approach is effective in both pretrained and non-pretrained scenarios; in the latter, the backbone is trained from scratch during the first learning phase. Code is publicly available at github.com/importAmir/CI-CBM.

We introduce Graph Concept Bottleneck (GCB) as a new paradigm for self-explainable text-attributed graph learning. GCB maps graphs into a subspace, concept bottleneck, where each concept is a meaningful phrase, and predictions are made based on the activation of these concepts. Unlike existing interpretable graph learning methods that primarily rely on subgraphs as explanations, the concept bottleneck provides a new form of interpretation. To refine the concept space, we apply the information bottleneck principle to focus on the most relevant concepts. This not only yields more concise and faithful explanations but also explicitly guides the model to "think" toward the correct decision. We empirically show that GCB achieves intrinsic interpretability with accuracy on par with black-box Graph Neural Networks. Moreover, it delivers better performance under distribution shifts and data perturbations, showing improved robustness and generalizability, benefitting from concept-guided prediction.

Concept Bottleneck Models (CBMs) introduce interpretability to black-box deep learning models by predicting labels through human-understandable concepts. However, unlike humans, who identify objects at different levels of abstraction using both general and specific features, existing CBMs operate at a single semantic level in both concept and label space. We propose HIL-CBM, a Hierarchical Interpretable Label-Free Concept Bottleneck Model that extends CBMs into a hierarchical framework to enhance interpretability by more closely mirroring the human cognitive process. HIL-CBM enables classification and explanation across multiple semantic levels without requiring relational concept annotations. HIL-CBM aligns the abstraction level of concept-based explanations with that of model predictions, progressing from abstract to concrete. This is achieved by (i) introducing a gradient-based visual consistency loss that encourages abstraction layers to focus on similar spatial regions, and (ii) training dual classification heads, each operating on feature concepts at different abstraction levels. Experiments on benchmark datasets demonstrate that HIL-CBM outperforms state-of-the-art sparse CBMs in classification accuracy. Human evaluations further show that HIL-CBM provides more interpretable and accurate explanations, while maintaining a hierarchical and label-free approach to feature concepts.

Deep learning models have achieved strong performance in medical image analysis, but their internal decision processes remain difficult to interpret. Concept Bottleneck Models (CBMs) partially address this limitation by structuring predictions through human-interpretable clinical concepts. However, existing CBMs typically overlook the contextual dependencies among concepts. To address these issues, we propose an end-to-end interpretable framework DCG-Net that integrates multimodal alignment with structured concept reasoning. DCG-Net introduces a Dual Cross-Attention module that replaces cosine similarity matching with bidirectional attention between visual tokens and canonicalized textual concept-value prototypes, enabling spatially localized evidence attribution. To capture the relational structure inherent to clinical concepts, we develop a Parametric Concept Graph initialized with Positive Pointwise Mutual Information priors and refined through sparsity-controlled message passing. This formulation models inter-concept dependencies in a manner consistent with clinical domain knowledge. Experiments on white blood cell morphology and skin lesion diagnosis demonstrate that DCG-Net achieves state-of-the-art classification performance while producing clinically interpretable diagnostic explanations.

Concept Bottleneck Models (CBMs) are interpretable models that route predictions through a layer of human-interpretable concepts. While widely studied in vision and, more recently, in NLP, CBMs remain largely unexplored in multimodal settings. For their explanations to be faithful, CBMs must satisfy two conditions: concepts must be properly detected, and concept representations must encode only their intended semantics, without smuggling extraneous task-relevant or inter-concept information into final predictions, a phenomenon known as leakage. Existing approaches treat concept detection and leakage mitigation as separate problems, and typically improve one at the expense of predictive accuracy. In this work, we introduce f-CBM, a faithful multimodal CBM framework built on a vision-language backbone that jointly targets both aspects through two complementary strategies: a differentiable leakage loss to mitigate leakage, and a Kolmogorov-Arnold Network prediction head that provides sufficient expressiveness to improve concept detection. Experiments demonstrate that f-CBM achieves the best trade-off between task accuracy, concept detection, and leakage reduction, while applying seamlessly to both image and text or text-only datasets, making it versatile across modalities.

Concept Bottleneck Models (CBMs) are a prominent framework for interpretable AI that map learned visual features to a set of meaningful concepts for task-specific downstream predictions. Their sequential structure enhances transparency by connecting model predictions to the underlying concepts that support them. In medical imaging, where transparency is essential, CBMs offer an appealing foundation for explainable model design. However, discrete concept representations often overlook broader clinical context such as diagnostic guidelines and expert heuristics, reducing reliability in complex cases. We propose MedCBR, a concept-based reasoning framework that integrates clinical guidelines with vision-language and reasoning models. Labeled clinical descriptors are transformed into guideline-conformant text, and a concept-based model is trained with a multitask objective combining multimodal contrastive alignment, concept supervision, and diagnostic classification to jointly ground image features, concepts, and pathology. A reasoning model then converts these predictions into structured clinical narratives that explain the diagnosis, emulating expert reasoning based on established guidelines. MedCBR achieves superior diagnostic and concept-level performance, with AUROCs of 94.2% on ultrasound and 84.0% on mammography. Further experiments on non-medical datasets achieve 86.1% accuracy. Our framework enhances interpretability and forms an end-to-end bridge from medical image analysis to decision-making.

We are concerned with the challenge of reliably classifying and assessing intracranial aneurysms using deep learning without compromising clinical transparency. While traditional black-box models achieve high predictive accuracy, their lack of inherent interpretability remains a significant barrier to clinical adoption and regulatory approval. Explainability is paramount in medical modeling to ensure that AI-driven diagnoses align with established neurosurgical principles. Unlike traditional eXplainable AI (XAI) methods -- such as saliency maps, which often provide post-hoc, non-causal visual correlations -- Concept Bottleneck Models (CBMs) offer a robust alternative by constraining the model's internal logic to human-understandable clinical indices. In this article, we propose an end-to-end 3D Concept Bottleneck framework that maps high-dimensional neuroimaging features to a discrete set of morphological and hemodynamic concepts for aneurysm identification. We implemented this pipeline using a pre-trained 3D ResNet-34 backbone and a 3D DenseNet-121 to extract features from CTA volumes, which were subsequently processed through a soft bottleneck layer representing human-interpretable clinical concepts. The model was optimized using a joint-loss function to balance diagnostic focal loss and concept mean squared error (MSE), validated via stratified five-fold cross-validation. Our results demonstrate a peak task classification accuracy of 93.33% +/- 4.5% for the ResNet-34 architecture and 91.43% +/- 5.8% for the DenseNet-121 model. Furthermore, the implementation of 8-pass Test-Time Augmentation (TTA) yielded a robust mean accuracy of 88.31%, ensuring diagnostic stability during inference. By maintaining an accuracy-generalization gap of less than 0.04, this framework proves that high predictive performance can be achieved without sacrificing interpretability.

Concept Bottleneck Models (CBMs) aim for ante-hoc interpretability by learning a bottleneck layer that predicts interpretable concepts before the decision. State-of-the-art approaches typically select which concepts to learn via human specification, open knowledge graphs, prompting an LLM, or using general CLIP concepts. However, concepts defined a-priori may not have sufficient predictive power for the task or even be learnable from the available data. As a result, these CBMs often significantly trail their black-box counterpart when controlling for information leakage. To address this, we introduce a novel CBM pipeline named Mechanistic CBM (M-CBM), which builds the bottleneck directly from a black-box model's own learned concepts. These concepts are extracted via Sparse Autoencoders (SAEs) and subsequently named and annotated on a selected subset of images using a Multimodal LLM. For fair comparison and leakage control, we also introduce the Number of Contributing Concepts (NCC), a decision-level sparsity metric that extends the recently proposed NEC metric. Across diverse datasets, we show that M-CBMs consistently surpass prior CBMs at matched sparsity, while improving concept predictions and providing concise explanations. Our code is available at https://github.com/Antonio-Dee/M-CBM.

Ensuring fairness in image classification prevents models from perpetuating and amplifying bias. Concept bottleneck models (CBMs) map images to high-level, human-interpretable concepts before making predictions via a sparse, one-layer classifier. This structure enhances interpretability and, in theory, supports fairness by masking sensitive attribute proxies such as facial features. However, CBM concepts have been known to leak information unrelated to concept semantics and early results reveal only marginal reductions in gender bias on datasets like ImSitu. We propose three bias mitigation techniques to improve fairness in CBMs: 1. Decreasing information leakage using a top-k concept filter, 2. Removing biased concepts, and 3. Adversarial debiasing. Our results outperform prior work in terms of fairness-performance tradeoffs, indicating that our debiased CBM provides a significant step towards fair and interpretable image classification.

Concept Bottleneck Models (CBMs) ground predictions in human-understandable concepts but face fundamental limitations: the absence of a metric to pre-evaluate concept relevance, the "linearity problem" causing recent CBMs to bypass the concept bottleneck entirely, an accuracy gap compared to opaque models, and finally the lack of systematic study on the impact of different visual backbones and VLMs. We introduce CBM-Suite, a methodological framework to systematically addresses these challenges. First, we propose an entropy-based metric to quantify the intrinsic suitability of a concept set for a given dataset. Second, we resolve the linearity problem by inserting a non-linear layer between concept activations and the classifier, which ensures that model accuracy faithfully reflects concept relevance. Third, we narrow the accuracy gap by leveraging a distillation loss guided by a linear teacher probe. Finally, we provide comprehensive analyses on how different vision encoders, vision-language models, and concept sets interact to influence accuracy and interpretability in CBMs. Extensive evaluations show that CBM-Suite yields more accurate models and provides insights for improving concept-based interpretability.

Obstructive sleep apnea (OSA) is a sleep disorder that affects nearly one billion people globally and significantly elevates cardiovascular risk. Traditional diagnosis through polysomnography is resource-intensive and limits widespread access, creating a critical need for accurate and efficient alternatives. In this paper, we introduce KindSleep, a deep learning framework that integrates clinical knowledge with single-channel patient-specific oximetry signals and clinical data for precise OSA diagnosis. KindSleep first learns to identify clinically interpretable concepts, such as desaturation indices and respiratory disturbance events, directly from raw oximetry signals. It then fuses these AI-derived concepts with multimodal clinical data to estimate the Apnea-Hypopnea Index (AHI). We evaluate KindSleep on three large, independent datasets from the National Sleep Research Resource (SHHS, CFS, MrOS; total n = 9,815). KindSleep demonstrates excellent performance in estimating AHI scores (R2 = 0.917, ICC = 0.957) and consistently outperforms existing approaches in classifying OSA severity, achieving weighted F1-scores from 0.827 to 0.941 across diverse populations. By grounding its predictions in a layer of clinically meaningful concepts, KindSleep provides a more transparent and trustworthy diagnostic tool for sleep medicine practices.

Despite their success in various domains, the growing dependence on GNNs raises a critical concern about the nature of the combinatorial reasoning underlying their predictions, which is often hidden within their black-box architectures. Addressing this challenge requires understanding how GNNs translate topological patterns into logical rules. However, current works only uncover the hard logical rules over graph concepts, which cannot quantify the contribution of each concept to prediction. Moreover, they are post-hoc interpretable methods that generate explanations after model training and may not accurately reflect the true combinatorial reasoning of GNNs, since they approximate it with a surrogate. In this work, we develop a graph concept bottleneck layer that can be integrated into any GNN architectures to guide them to predict the selected discriminative global graph concepts. The predicted concept scores are further projected to class labels by a sparse linear layer. It enforces the combinatorial reasoning of GNNs' predictions to fit the soft logical rule over graph concepts and thus can quantify the contribution of each concept. To further improve the quality of the concept bottleneck, we treat concepts as "graph words" and graphs as "graph sentences", and leverage language models to learn graph concept embeddings. Extensive experiments on multiple datasets show that our method GCBMs achieve state-of-the-art performance both in classification and interpretability.

Concept Bottleneck Models (CBMs) enhance the interpretability of end-to-end neural networks by introducing a layer of concepts and predicting the class label from the concept predictions. A key property of CBMs is that they support interventions, i.e., domain experts can correct mispredicted concept values at test time to improve the final accuracy. However, typical CBMs apply interventions by overwriting only the corrected concept while leaving other concept predictions unchanged, which ignores causal dependencies among concepts. To address this, we propose the Causal Neural Probabilistic Circuit (CNPC), which combines a neural attribute predictor with a causal probabilistic circuit compiled from a causal graph. This circuit supports exact, tractable causal inference that inherently respects causal dependencies. Under interventions, CNPC models the class distribution based on a Product of Experts (PoE) that fuses the attribute predictor's predictive distribution with the interventional marginals computed by the circuit. We theoretically characterize the compositional interventional error of CNPC w.r.t. its modules and identify conditions under which CNPC closely matches the ground-truth interventional class distribution. Experiments on five benchmark datasets in both in-distribution and out-of-distribution settings show that, compared with five baseline models, CNPC achieves higher task accuracy across different numbers of intervened attributes.

Machine learning accelerates molecular property prediction, yet state-of-the-art Large Language Models and Graph Neural Networks operate as black boxes. In drug discovery, where safety is critical, this opacity risks masking false correlations and excluding human expertise. Existing interpretability methods suffer from the effectiveness-trustworthiness trade-off: explanations may fail to reflect a model's true reasoning, degrade performance, or lack domain grounding. Concept Bottleneck Models (CBMs) offer a solution by projecting inputs to human-interpretable concepts before readout, ensuring that explanations are inherently faithful to the decision process. However, adapting CBMs to chemistry faces three challenges: the Relevance Gap (selecting task-relevant concepts from a large descriptor space), the Annotation Gap (obtaining concept supervision for molecular data), and the Capacity Gap (degrading performance due to bottleneck constraints). We introduce GlassMol, a model-agnostic CBM that addresses these gaps through automated concept curation and LLM-guided concept selection. Experiments across thirteen benchmarks demonstrate that \method generally matches or exceeds black-box baselines, suggesting that interpretability does not sacrifice performance and challenging the commonly assumed trade-off. Code is available at https://github.com/walleio/GlassMol.

Concept Bottleneck Models (CBMs) provide inherent interpretability by first mapping input samples to high-level semantic concepts, followed by a combination of these concepts for the final classification. However, the annotation of human-understandable concepts requires extensive expert knowledge and labor, constraining the broad adoption of CBMs. On the other hand, there are a few works that leverage the knowledge of large language models (LLMs) to construct concept bottlenecks. Nevertheless, they face two essential limitations: First, they overlook the uncertainty associated with the concepts annotated by LLMs and lack a valid mechanism to quantify uncertainty about the annotated concepts, increasing the risk of errors due to hallucinations from LLMs. Additionally, they fail to incorporate the uncertainty associated with these annotations into the learning process for concept bottleneck models. To address these limitations, we propose a novel uncertainty-aware CBM method, which not only rigorously quantifies the uncertainty of LLM-annotated concept labels with valid and distribution-free guarantees, but also incorporates quantified concept uncertainty into the CBM training procedure to account for varying levels of reliability across LLM-annotated concepts. We also provide the theoretical analysis for our proposed method. Extensive experiments on the real-world datasets validate the desired properties of our proposed methods.

Concept Bottleneck Models (CBMs) aim to deliver interpretable predictions by routing decisions through a human-understandable concept layer, yet they often suffer reduced accuracy and concept leakage that undermines faithfulness. We introduce an explicit Information Bottleneck regularizer on the concept layer that penalizes $I(X;C)$ while preserving task-relevant information in $I(C;Y)$, encouraging minimal-sufficient concept representations. We derive two practical variants (a variational objective and an entropy-based surrogate) and integrate them into standard CBM training without architectural changes or additional supervision. Evaluated across six CBM families and three benchmarks, the IB-regularized models consistently outperform their vanilla counterparts. Information-plane analyses further corroborate the intended behavior. These results indicate that enforcing a minimal-sufficient concept bottleneck improves both predictive performance and the reliability of concept-level interventions. The proposed regularizer offers a theoretic-grounded, architecture-agnostic path to more faithful and intervenable CBMs, resolving prior evaluation inconsistencies by aligning training protocols and demonstrating robust gains across model families and datasets.

In recent years, VAD (Visual Anomaly Detection) has attracted significant attention due to its high interpretability, as it provides visual explanations by highlighting anomalous regions within an image. However, although these visual explanations can be helpful, they lack a direct and semantically meaningful interpretation for users. To address this limitation, we propose extending CBMs (Concept Bottleneck Models) to the VAD setting. By learning meaningful concepts, the network can provide human-interpretable descriptions of anomalies, offering a novel and more insightful way to explain them. Our main contributions are: (i) we introduce a concept-based framework for anomaly explanation by extending CBMs to the VAD setting for the first time; (ii) we evaluate multiple supervision regimes, ranging from supervised to unsupervised anomaly settings; (iii) we propose a dual-branch architecture that combines a CBM-based Concept branch for concept-level explanations with a Visual branch for pixel-level anomaly localization, bridging semantic and spatial interpretability. When evaluated across three well-established VAD benchmarks, our approach, Concept-Aware Visual Anomaly Detection (\ourmethod), achieves performance comparable to classic VAD methods (up to 0.97 I-AUROC on MVTec AD) while providing richer, concept-driven explanations. A user study (582 responses) shows that \ourmethod{} explanations are rated effective in 73.5% of cases (vs. 60.7% for the SOTA VLM-based explainer Anomaly-OV) and misleading in only 3.1% (vs. 11.7%). Beyond explanation quality, CBMs enable human-in-the-loop correction: concept-level interventions further boost detection in the challenging unsupervised setting, closing part of the gap to fully supervised performance.

In many machine learning problems, there may exist multiple models that achieve nearly identical predictive performance while relying on fundamentally different internal logic. However, standard training procedures produce a single model, offering no practical way to explore alternatives that may better suit downstream needs. The set of these equally accurate models is known as the Rashomon set. Exploring the Rashomon set is particularly challenging in large and complex hypothesis spaces, such as Concept Bottleneck Models (CBMs), which are widely used in computer vision to make predictions through intermediate, human-understandable concepts. In this paper, we provide a method for efficiently exploring the Rashomon set of CBMs. Our framework introduces a specialized parallel parameter-efficient adaptation module, combined with a checkpointing scheme and a concept diversity objective, to generate multiple equally accurate CBMs from a single training process. Empirical results show that our method finds models with better diversity than baselines while using much less memory. We further demonstrate that access to these diverse yet accurate CBMs enables trustworthy model selection, resolution of inter-class confusion, and reliable abstention in decision-making.

We propose a novel, flexible, and efficient framework for designing Concept Bottleneck Models (CBMs) that enables practitioners to explicitly encode and extend their prior knowledge and beliefs about the concept-concept ($C-C$) and concept-task ($C \to Y$) relationships within the model's reasoning when making predictions. The resulting $\textbf{C}$oncept $\textbf{REA}$soning $\textbf{M}$odels (CREAMs) architecturally encode arbitrary types of $C-C$ relationships such as mutual exclusivity, hierarchical associations, and/or correlations, as well as potentially sparse $C \to Y$ relationships. Moreover, CREAM can optionally incorporate a regularized side-channel to complement the potentially {incomplete concept sets}, achieving competitive task performance while encouraging predictions to be concept-grounded. To evaluate CBMs in such settings, we introduce a $C \to Y$ agnostic metric that quantifies interpretability when predictions partially rely on the side-channel. In our experiments, we show that, without additional computational overhead, CREAM models support efficient interventions, can avoid concept leakage, and achieve black-box-level performance under missing concepts. We further analyze how an optional side-channel affects interpretability and intervenability. Importantly, the side-channel enables CBMs to remain effective even in scenarios where only a limited number of concepts are available.

Explainability is an important requirement for machine learning models in high-risk domains such as medicine. We introduce HierViT, a hierarchical Vision Transformer that combines competitive predictive performance with multiple mechanisms to support the interpretation of its predictions. The model first predicts clinically relevant visual appearance attributes, which are then used to infer the final target prediction through a hierarchical reasoning process. To facilitate understanding of the intermediate representations, attribute-specific prototypes are visualized as representative image examples, while attribute-specific attention maps highlight image regions associated with each visual feature. Together, these attribute-level components provide complementary views of the model's reasoning by linking representative image examples and spatial attention to semantically defined visual features. We evaluate HierViT on two medical benchmark datasets: LIDC-IDRI for lung nodule assessment and derm7pt for skin lesion classification. Across both datasets, HierViT achieves competitive predictive performance while providing attribute-level prototypes and attention visualizations that support the interpretation of its predictions.