LogicCBMs: Logic-Enhanced Concept-Based Learning
Existing concept bottleneck models (CBMs) rely on linear concept combinations, limiting expressivity and hindering modeling of complex semantic relationships. This paper proposes Logic-CBM, the first differentiable logic-driven CBM that embeds propositional logical operations (e.g., AND, OR, NOT) into an end-to-end trainable framework. Leveraging a neuro-symbolic design—integrating differentiable logic gates, gradient straight-through estimators, and joint optimization—it enables nonlinear logical reasoning over concepts. Evaluated on multiple benchmark and synthetic datasets, Logic-CBM achieves significant improvements in prediction accuracy, supports precise concept-level interventions, and preserves strong interpretability and model transparency. Its core contributions are threefold: (1) introducing the first differentiable logic-based concept learning paradigm; (2) overcoming the fundamental limitations of linear concept composition; and (3) unifying the structural rigor of symbolic logic with the learnability of deep neural networks.