Beyond Scalars: Concept-Based Alignment Analysis in Vision Transformers

Measuring the alignment between representations lets us understand similarities between the feature spaces of different models, such as Vision Transformers trained under diverse paradigms. However, traditional measures for representational alignment yield only scalar values that obscure how these spaces agree in terms of learned features. To address this, we combine alignment analysis with concept discovery, allowing a fine-grained breakdown of alignment into individual concepts. This approach reveals both universal concepts across models and each representation’s internal concept structure. We introduce a new definition of concepts as non-linear manifolds, hypothesizing they better capture the geometry of the feature space. A sanity check demonstrates the advantage of this manifold-based definition over linear baselines for concept-based alignment. Finally, our alignment analysis of four different ViTs shows that increased supervision tends to reduce semantic organization in learned representations.