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Beyond Scalars: Concept-Based Alignment Analysis in Vision Transformers
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Combines concept discovery (HDBSCAN soft clustering of UMAP-embedded ViT activations, with manifold-shaped concepts) with a generalized fuzzy Rand index to break representational alignment into per-concept contributions across layers and four ViTs.
Problem
Scalar representational alignment measures (e.g., CKA) collapse similarity between representations into one number, hiding which concepts are shared or unique across layers and models of vision transformers.
Approach
Defines concepts as nonlinear manifolds discovered by density-based soft clustering (NLMCD) of UMAP embeddings, represents tokens by concept membership scores, and measures alignment with a pseudo-metric generalized Rand index (Concept-Based Alignment) that can be partitioned into pairwise concept distances.
Key results
- In a sanity check, NLMCD concepts achieve the highest neighbor-layer alignment ratio on most models, e.g., 1.0 for CLS on FS and CLIP, except DINO SEQ where PCA reaches 1.0 versus NLMCD 0.90.
- Concept atlases show that at layer 11 the supervised FS model is less semantically organized than CLIP, DINO and MAE, which show clearer grouping (e.g., canine concepts).
- Alignment heatmaps show higher alignment between DINO and MAE than with CLIP or FS, and earlier layers align more across models.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use nonlinear manifold concepts (NLMCD) instead of linear/spherical concept methods | FS SEQ concept alignment · Concept alignment sanity check (SEQ, FS) | neighboring-layer-best ratio: 0.90 vs 0.90 | No clear effect |
| Use nonlinear manifold concepts (NLMCD) instead of linear concept methods | CLIP SEQ concept alignment · Concept alignment sanity check (SEQ, CLIP) | neighboring-layer-best ratio: 1. vs 0.90 | Helped |
| Use nonlinear manifold concepts (NLMCD) instead of PCA | DINO SEQ concept alignment · Concept alignment sanity check (SEQ, DINO) | neighboring-layer-best ratio: 1. vs 0.90 | Hurt |
| Use nonlinear manifold concepts (NLMCD) instead of MCD | DINO SEQ concept alignment · Concept alignment sanity check (SEQ, DINO) | neighboring-layer-best ratio: 0.90 vs 0.81 | Helped |
| Use nonlinear manifold concepts (NLMCD) instead of linear concept methods | MAE SEQ concept alignment · Concept alignment sanity check (SEQ, MAE) | neighboring-layer-best ratio: 1. vs 1. | No clear effect |
| Use nonlinear manifold concepts (NLMCD) instead of KMeans concepts | FS CLS concept alignment · Concept alignment sanity check (CLS, FS) | neighboring-layer-best ratio: 1. vs 0.83 | Helped |
| Use nonlinear manifold concepts (NLMCD) instead of KMeans concepts | CLIP CLS concept alignment · Concept alignment sanity check (CLS, CLIP) | neighboring-layer-best ratio: 1. vs 0.91 | Helped |
| Use nonlinear manifold concepts (NLMCD) instead of KMeans concepts | DINO CLS concept alignment · Concept alignment sanity check (CLS, DINO) | neighboring-layer-best ratio: 0.83 vs 0.50 | Helped |
| Use nonlinear manifold concepts (NLMCD) instead of KMeans concepts | MAE CLS concept alignment · Concept alignment sanity check (CLS, MAE) | neighboring-layer-best ratio: 0.75 vs 0.66 | Helped |
| Increase supervision during ViT training | ViT representations · ImageNet-1k representation analysis, layer 11 | semantic organization | Hurt |
Surprising findings
- Higher supervision correlates with less semantic structure in late-layer representations, with the supervised FS model showing the least organized concepts.
- PCA outperforms NLMCD on the sanity check for DINO SEQ tokens.
Limitations
- HDBSCAN scalability limits the number of sampled feature vectors, so sparse concept regions appear as noise (high noise rates).
- ImageNet-1k's limited variability may obscure the meaning of concepts, and the WordNet-based category labels are only a proxy.
- Concept discovery quality is moderate (medium DBCV), and robustness drops in later layers (around 0.84).
Experimental setup
Datasets: ImageNet-1k
Benchmarks: ImageNet-1k
Metrics: concept-based alignment (CBA) DBCV RMSE noise rate sanity-check layer-neighbor alignment ratio intrinsic dimensionality
Baselines: PCA linear concepts MCD KMeans CKA
Builds on: HDBSCAN UMAP Centred Kernel Alignment multi-dimensional concept discovery (MCD)
Closest papers by meaning
- Probabilistic Conceptual Explainers: Trustworthy Conceptual Explanations for Vision Foundation Models (ICML 2024 · similarity 0.88)
- LVLM-Aided Alignment of Task-Specific Vision Models (CVPR 2026 · similarity 0.87)
- VL-SAE: Interpreting and Enhancing Vision-Language Alignment with a Unified Concept Set (NeurIPS 2025 · similarity 0.87)
- ConceptBed: Evaluating Concept Learning Abilities of Text-to-Image Diffusion Models (AAAI 2024 · similarity 0.87)
- Beyond the Doors of Perception: Vision Transformers Represent Relations Between Objects (NeurIPS 2024 · similarity 0.86)
- Topology-Aware Representation Alignment for Semi-Supervised Vision-Language Learning (NeurIPS 2026 · similarity 0.86)
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