Formal Concept Lattices are Good Semantic Scaffolds for Concept-Based Learning

Learning semantics is essential for deep learning models to be interpretable and better aligned with human reasoning. Concept-based models approach this by representing classes through meaningful semantic abstractions, but typically treat all concepts as a flat, unstructured set learned at a single neural network layer. This overlooks a fundamental property of human semantic understanding: concepts being organized hierarchically, from general to specific. While deep networks do learn a hierarchy of visual features, this structure is rarely aligned with explicit semantic hierarchies. Drawing on Formal Concept Analysis, we demonstrate that formal concept lattices provide principled semantic scaffolds to guide neural network learning. These lattices naturally identify where in the network concepts should be learned based on their level of generality. This allows the model to develop staged, semantically grounded representations throughout its depth. Empirical results on real-world datasets show that our models produce more interpretable embeddings, support more effective interventions, and learn concept representations that are both meaningful and hierarchically structured.

Humans view the world through objects, relationships, and meaning. We reason in concepts: a bird has wings, cats are mammals, tree bark is rough. Most vision models, however, process the world as raw pixels, making them black-boxes that are difficult to interpret, reason with, and deploy in high-stakes applications. Concept-based models aim to bridge this gap by learning through human-understandable concepts. For example, a model might learn to use concepts like fur, whiskers and mammal to recognize a cat. Existing approaches typically treat concepts as a flat unstructured set learned only near the final prediction stage. Humans, however, organize concepts hierarchically - from general ideas to increasingly specific ones. Inspired by Formal Concept Analysis, we construct a formal concept lattice: a graph-like structure where nodes are obtained and organized hierarchically from class-attribute associations. We use this lattice to guide the network to learn general concepts early in the network and specific ones later - in effect, aligning the network with an explicit semantic structure. We find that such hierarchical guidance leads to representations that are more meaningful, interpretable and structured.