MCPNet-CLL: Cross-Layer Linking Loss for Coherent Multi-Level Concept Reasoning

Multi-Level Concept Prototype Networks (MCP-Net) learn human-understandable prototypes at every feature layer, yet they leave semantic links between layers largely unconstrained, leading to fragmented or redundant hierarchies. We introduce Cross-Layer Linking Loss (CLL) to weld those layers into a coherent concept ladder. CLL works in three coordinated steps: (i) for every prototype it pulls the most semantically related neighbour in the next layer closer through a temperature-annealed InfoNCE objective; (ii) it selects hard negatives - high-similarity but semantically unrelated prototypes - and pushes them away, preserving layer diversity; and (iii) it adds a margin-based repulsion term that discourages multiple prototypes within the same layer from collapsing onto the same concept. This contrastive formulation replaces earlier heuristic "selective matching"and delivers sharper alignment without extra parameters or labels. On synthetic shapes, AWA2, Caltech-101 and CUB-200, MCPNet-CLL matches or exceeds the baseline's top-1 accuracy while raising completeness, purity and distinctiveness scores of the discovered concepts. Visualisations reveal smooth, non-overlapping concept evolution across layers, confirming that CLL yields a more faithful and interpretable representation of the model's reasoning process.