A theoretical design of concept sets: improving the predictability of concept bottleneck models

Concept-based learning, a promising approach in machine learning, emphasizes the value of high-level representations called concepts. However, despite growing interest in concept-bottleneck models (CBMs), there is a lack of clear understanding regarding the properties of concept sets and their impact on model performance. In this work, we define concepts within the machine learning context, highlighting their core properties: 'expressiveness' and 'model-aware inductive bias', and we make explicit the underlying assumption of CBMs. We establish theoretical results for concept-bottleneck models (CBMs), revealing how these properties guide the design of concept sets that optimize model performance. Specifically, we demonstrate that well-chosen concept sets can improve sample efficiency and out-of-distribution robustness in the appropriate regimes. Based on these insights, we propose a method to effectively identify informative and non-redundant concepts. We validate our approach with experiments on CIFAR-10 and MetaShift, showing that concept-bottleneck models outperform the foundational embedding counterpart, particularly in low-data regimes and under distribution shifts. We also examine failure modes and discuss how they can be tackled.