Digging Deeper: Learning Multi-Level Concept Hierarchies

Modern deep neural networks remain challenging to interpret due to the opacity of their latent representations, impeding model understanding, debugging, and debiasing. Concept Embedding Models (CEMs) address this by mapping inputs to human-interpretable concept representations from which tasks can be predicted. Yet, CEMs fail to represent inter-concept relationships and require concept annotations at different granularities during training, limiting their applicability. In this paper, we introduce Hierarchical Concept Embedding Models (HiCEMs), a new family of CEMs that explicitly model concept relationships through hierarchical structures. To enable HiCEMs in real-world settings, we propose Concept Splitting, a method for automatically discovering finer-grained sub-concepts from a pretrained CEM's embedding space without requiring additional annotations. This allows HiCEMs to generate fine-grained explanations from limited concept labels, reducing annotation burdens. Our evaluation across multiple datasets, including a user study and experiments on PseudoKitchens, a newly proposed concept-based dataset of 3D kitchen renders, demonstrates that (1) Concept Splitting discovers human-interpretable sub-concepts absent during training that can be used to train highly accurate HiCEMs, and (2) HiCEMs enable powerful test-time concept interventions at different granularities, leading to improved task accuracy.

Concept Bottleneck Models (CBMs) enhance interpretability by projecting learned features into a human-understandable concept space. Recent approaches leverage vision-language models to generate concept embeddings, reducing the need for manual concept annotations. However, these models suffer from a critical limitation: as the number of concepts approaches the embedding dimension, information leakage increases, enabling the model to exploit spurious or semantically irrelevant correlations and undermining interpretability. In this work, we propose Concept Flow Models (CFMs), which replace the flat bottleneck with a hierarchical, concept-driven decision tree. Each internal node in the hierarchy focuses on a localized subset of discriminative concepts, progressively narrowing the prediction scope. Our framework constructs decision hierarchies from visual embeddings, distributes semantic concepts at each hierarchy level, and trains differentiable concept weights through probabilistic tree traversal. Extensive experiments on diverse benchmarks demonstrate that CFMs match the predictive performance of flat CBMs, while substantially mitigating information leakage by reducing effective concept usage. Furthermore, CFMs yield stepwise decision flows that enable transparent and auditable model reasoning with hierarchical class structures.

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.