Concept Bottleneck Models (CBMs) enhance model interpretability by introducing human-understandable concepts within the architecture. However, existing CBMs assume static datasets, limiting their ability to adapt to real-world, continuously evolving data streams. To address this, we define a novel concept-incremental and class-incremental continual learning task for CBMs, enabling models to accumulate new concepts and classes over time while retaining previously learned knowledge. To achieve this, we propose CONceptual Continual Incremental Learning (CONCIL), a framework that prevents catastrophic forgetting by reformulating concept and decision layer updates as linear regression problems, thus eliminating the need for gradient-based updates. CONCIL requires only recursive matrix operations, making it computationally efficient and suitable for real-time and large-scale data applications. Experimental results demonstrate that CONCIL achieves "absolute knowledge memory" and outperforms traditional CBM methods in concept- and class-incremental settings, establishing a new benchmark for continual learning in CBMs.

The lack of interpretability in the field of medical image analysis has significant ethical and legal implications. Existing interpretable methods in this domain encounter several challenges, including dependency on specific models, difficulties in understanding and visualization, as well as issues related to efficiency. To address these limitations, we propose a novel framework called Med-MICN (Medical Multi-dimensional Interpretable Concept Network). Med-MICN provides interpretability alignment for various angles, including neural symbolic reasoning, concept semantics, and saliency maps, which are superior to current interpretable methods. Its advantages include high prediction accuracy, interpretability across multiple dimensions, and automation through an end-to-end concept labeling process that reduces the need for extensive human training effort when working with new datasets. To demonstrate the effectiveness and interpretability of Med-MICN, we apply it to four benchmark datasets and compare it with baselines. The results clearly demonstrate the superior performance and interpretability of our Med-MICN.