{"id":"6e9298ad-a10f-4bab-a847-166f94062ecf","arxiv_id":"2412.06639","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A concept-based alignment analysis using manifold concepts and a partitioned Rand index reveals that increased supervision reduces semantic structure in late-layer ViT representations.","lead":"This paper presents a method to compare how vision transformers organize their internal representations by breaking alignment down into individual concepts modeled as nonlinear manifolds. It reports that models trained with stronger supervision show less semantically structured representations in later layers.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The supervision claim rests on FS layer-11 concept atlases, the exact setting where Fig. 2 shows UMAP fidelity collapses and the text says clustering is less trustworthy; the 'less semantic structure' result may be an embedding artifact.","rationale":"The reader's verdict is CONDITIONAL and I agree with that level. The method is a real contribution: the code is public, the sanity check in Table 2 favors NLMCD on a clear neighboring-layer criterion, and the concept-formation graphs give qualitative evidence that the pipeline captures recognizable structures. Those pieces are independent of the supervision claim and justify conditional acceptance. The load-bearing weakness is the supervision claim itself. The paper defines concepts as manifolds in feature space, but the operational pipeline replaces the 768-d space with a 50-d UMAP embedding for both cluster discovery and proximity scoring. UMAP is a useful visualization and preprocessing tool, but it is not a faithful isometry; its distortion is documented in Fig. 2, and the distortion is largest for FS in late layers, exactly where the paper draws its headline conclusion. The paper honestly flags this ('we can trust the clustering on the embedding less') but does not correct for it. Because the layer-11 'semantic organization' conclusion is qualitative and is made in the same embedding, the correlation with supervision strength could be an artifact. The concrete test above would settle the question by making semantic organization quantitative and by varying or bypassing UMAP. It is a conditional-acceptance checkpoint rather than a rejection: the method and its validation stand, but the central empirical claim needs this robustness check.","tokens_in":18863,"tokens_out":5836,"duration_ms":64273,"concrete_test":"Re-run layer-11 SEQ concept discovery for all four models with a UMAP grid (n_neighbors in {15,30,100}, min_dist in {0.001,0.1}, embedding_dim in {20,50,100}) plus a UMAP-free control that clusters the original 768-d features with approximate HDBSCAN or k-means at matched k. For each variant, compute a quantitative semantic-organization score: adjusted Rand index between cluster assignments and the paper's WordNet supercategories, or a label-free analog using mean within- vs between-category concept-pair distances in the original feature space. If FS is the least organized under most variants, the supervision finding is robust to embedding distortion; if FS becomes comparable to DINO or MAE under any variant, the central claim is an artifact of UMAP.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Concepts are not discovered or scored in the original 768-d feature space: HDBSCAN runs on a 50-d UMAP embedding, and the soft proximity scores P^alpha(phi) in Appendix A are defined from distances to exemplar points and persistence values inside that embedding. Every CBA value and every concept-atlas point therefore inherits UMAP geometry. Fig. 2 shows that the RMSE between original and embedded distance matrices for FS rises strongly from layer 8 onward, and Sec. 4.1 explicitly states 'we can trust the clustering on the embedding less' for FS. Layer 11 is precisely the layer used to conclude that FS is less semantically organized than CLIP/DINO/MAE, and the text adds that FS has high DBCV but low robustness at this point. The central empirical claim is a visual reading of concept atlases built from this same unreliable embedding for the one model that drives the conclusion. No quantitative semantic-organization metric or cross-check in the original feature space is provided; Fig. 5's class-label alignment is reported without error bars and is not tied to the atlas interpretation. If the FS layer-11 clusters are partly noise or geometrically distorted, the observed lack of structure is an artifact, not a finding about supervision.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Concept-Based Alignment (CBA), a representational alignment measure that decomposes the usual scalar alignment into per-concept contributions. Concepts are defined as nonlinear manifolds in feature space, discovered by applying HDBSCAN to UMAP embeddings of ViT hidden features, and represented by soft membership scores. CBA is built on a generalized Rand index with pseudo-metric properties, and the paper provides an upper-bound decomposition into pairwise concept distances. The method is validated through a neighboring-layer sanity check against linear and spherical concept baselines, and it is then applied to compare four ViTs (FS, CLIP, DINO, MAE) across layers, leading to the conclusion that increased supervision correlates with a reduction in the semantic structure of learned representations. The paper includes public code and a detailed appendix describing the HDBSCAN soft-clustering procedure.","tokens_in":19134,"tokens_out":4476,"duration_ms":44075,"significance":"The idea of decomposing scalar representational alignment into concept-level contributions is valuable, and the definition of concepts as arbitrary manifolds is a meaningful generalization of existing linear concept definitions. The upper-bound decomposition in Eq. (4) is mathematically sound, and the paper ships reproducible code and an external sanity check that does not fit any parameter of the proposed method. If the empirical conclusions survive the additional validation requested below, the approach offers a genuinely new tool for comparing vision transformer representations. However, the central empirical claim currently rests on clustering in a low-dimensional embedding whose fidelity is worst for the model and layer that drive the conclusion, so the significance of the paper depends on the robustness checks described in the major comments.","major_comments":[{"comment":"The central empirical claim that the fully supervised (FS) representation at layer 11 is 'notably less semantically organized' than the other models is supported only by visual inspection of concept atlases, which are UMAP embeddings of concept-pair distances derived from clusters in the 50-dimensional UMAP embedding. Fig. 2 shows that the RMSE between the original and embedded distance matrices for FS rises strongly from layer 8 onward, and Sec. 4.1 states that 'we can trust the clustering on the embedding less' for FS. Layer 11 is exactly the layer used to conclude that FS is less semantically structured. Because clusters and soft membership scores are computed inside the embedding, the observed lack of structure may be an embedding artifact. Please provide a quantitative semantic-organization metric computed in the original feature space (e.g., concept-label agreement or a clustering-validity index) for layer 11, and verify that the FS versus CLIP/DINO/MAE difference persists under this metric. The class-label alignment curves in Fig. 5 are also presented without error bars and are not quantitatively connected to the atlas interpretation.","section":"Sec. 4.1 / Fig. 2 vs. Sec. 4.3 / Fig. 4"},{"comment":"All concept proximity scores P^alpha(phi) are defined from exemplar-point distances and persistence values in the UMAP embedding, so every CBA value inherits the embedding geometry. The manuscript defends this choice by the practical infeasibility of density clustering in 768 dimensions, but it provides no evidence that the embedding is faithful for the FS late layers beyond the global RMSE, which is worst in exactly that regime. Please validate the clustering and alignment results against an alternative approach that does not depend on the UMAP geometry, for example by computing CBA on distances in the original feature space to concept exemplars, or by perturbing UMAP hyperparameters and showing that the FS layer-11 conclusion is stable.","section":"Appendix A, Eq. (12) and Sec. 2.2"},{"comment":"The abstract claims to 'confirm the superiority' of the nonlinear concept definition for alignment analysis, but Table 2 shows that for DINO SEQ the PCA baseline achieves a score of 1.0 while NLMCD achieves 0.90, and all scores are reported without error bars. The main-text statement correctly notes this exception, so the abstract overstates the result. Please report variability across clustering/embedding runs and either soften the superiority claim or provide a statistical test showing that NLMCD is significantly better overall.","section":"Sec. 4.2 / Table 2 and Abstract"}],"minor_comments":[{"comment":"The caption states 'CLIP, DINO and FS' in the description of the block structure, but the surrounding text and the figure itself indicate that the third model should be MAE; please correct this typo.","section":"Fig. 4 caption"},{"comment":"The line break and nested absolute values in Eq. (4) make the formula hard to parse; please add parentheses to clarify that the outer absolute value applies to the difference of the two per-cluster absolute differences.","section":"Eq. (4)"},{"comment":"The sentence 'which has a high DBCV but low robustness' is a sentence fragment; it should be integrated into the preceding clause for readability.","section":"Sec. 4.1"},{"comment":"The concept formation graph is described as 'binary, unidirectional'; 'directed' is the standard term here, and the binary property should be defined explicitly.","section":"Appendix C"}],"recommendation":"major_revision","confidential_remarks":"The paper's core methodology is sound and the code availability is a plus, but the main empirical conclusion is vulnerable to the UMAP fidelity issue that the authors themselves document. I recommend major revision rather than rejection because the claim is testable and could be fixed with additional analyses. There is no circularity problem: the sanity check is external, and the authors' own MCD is used only as a comparison baseline. The fit with the journal's scope is appropriate for a computer-vision audience interested in model comparison and interpretability."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things worth knowing. The methodological package — nonlinear manifold concepts via UMAP+HDBSCAN, soft proximity scores, and a partitioned generalized Rand index — is a genuine extension of the earlier linear MCD work, and it is honestly evaluated against PCA, MCD, and KMeans in the sanity check. The code is public. That part is solid and citable.\n\nThe empirical claim that increased supervision reduces semantic structure is not as solid. The paper's own Fig. 2 shows UMAP distance-preservation RMSE rising steeply for the fully supervised model from layer 8 onward, and Sec. 4.1 explicitly says the clustering on the embedding can be trusted less there. The central visual contrast between FS and the other models is drawn at layer 11 — exactly that regime. The concept atlases are the only evidence for 'less semantically organized,' they are read by eye, and no quantitative semantic-organization metric or error bar is attached. This is a real gap, and the stress-test note is right: the conclusion could be an embedding artifact. It is not a fatal flaw in the method, but it should be fixed before the paper is leaned on.\n\nA few smaller points. The decomposition in Eq. (4) is an upper bound, not an exact partition; the text says so, but it is easy to miss that the concept-pair distances are not additive. The sanity check is a reasonable proxy, but Table 2 has no variance and the DINO SEQ case where PCA beats NLMCD is just noted, not discussed. Hyperparameters are tuned to maximize DBCV, but there is no sensitivity analysis. None of these are load-bearing criticisms of the method, and the sanity check is genuinely external, so there is no circularity.\n\nWho should read this: anyone working on representational alignment or concept-based interpretability. The method deserves referee time. If I were editor I'd send it out, and ask for a quantitative semantic-structure measure computed in the original feature space, or at least an error bar over UMAP/HDBSCAN runs, before accepting. The claim about supervision should be softened to a hypothesis until that is done.","headline":"The method is a real step forward for concept-level alignment, but the headline claim about supervision and semantic structure rests on the one layer where the paper's own UMAP-fidelity check fails.","tokens_in":19656,"tokens_out":1850,"would_cite":true,"duration_ms":18684,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper proposes a concept-decomposed alignment measure and reports that increased supervision correlates with reduced semantic structure in the late layers of vision transformers.","keywords":["representational alignment","concept discovery","vision transformers","nonlinear manifold concepts","UMAP and HDBSCAN","generalized Rand index","supervision and semantic structure","concept atlas"],"falsifier":"Compute the same concept-based alignment using clusters obtained directly in the original 768-dimensional feature space, or with an embedding whose distance-preservation error is verified to be low at every layer, and check whether the fully supervised model's layer-11 representation is still less semantically organized than CLIP, DINO, and MAE. If the supervision-structure gradient disappears under this check, the paper's central finding fails.","tokens_in":18672,"feed_emoji":"🔍","tokens_out":12746,"duration_ms":126774,"temperature":0.7,"pith_summary":"Existing representational alignment measures, such as Centered Kernel Alignment (CKA), return a single scalar and cannot say which features two layers or models share. This paper replaces the scalar with a concept-level description: concepts are defined as arbitrary nonlinear manifolds in a network's feature space, discovered by density-based clustering on a UMAP embedding, and alignment is measured with a generalized Rand index that splits into per-concept distances. Applied to four same-architecture vision transformers trained with different objectives (fully supervised, CLIP, DINO, MAE), the analysis shows a consistent pattern: more supervision correlates with less semantic structure in the final layers, with the fully supervised model undergoing a sharp 'nucleation' into class-specific concepts around layers 9-10. The payoff for practitioners is a way to see, rather than only score, how a model organizes what it has learned.","feed_headline":"More supervision means less semantic structure in vision transformers","feed_subtitle":"Concept-level alignment shows self-supervised ViTs keep concepts more semantically organized than supervised ones.","key_machinery":"The key machinery is the concept manifold paired with a decomposable alignment distance. A concept $C^\\alpha$ is defined as a manifold in the $F$-dimensional feature space, represented by the point cloud of feature vectors lying on it; this generalizes earlier definitions of concepts as linear directions or linear subspaces. The discovery pipeline embeds feature vectors with UMAP, clusters them with HDBSCAN, and converts cluster structure into soft concept-proximity scores $P^\\alpha(\\phi)$. Alignment between two such fuzzy clusterings is measured by the generalized Rand index $CBA = 1 - d_{\\mathrm{cross}}(P,Q)$, and because the pairwise disagreement can be written per concept pair, the scalar alignment becomes a full pairwise distance matrix between concepts. This matrix is what produces the 'concept atlases' showing which concepts are universal, unique, or internally structured.","core_discovery":"The paper's central claim is that alignment can be meaningfully decomposed by concept, and that this decomposition exposes a supervision-structure gradient in vision transformers. Using soft concept proximity scores obtained from nonlinear manifold clustering, it shows that the fully supervised (FS), CLIP, DINO, and MAE models all look similar in early layers, the first half of the network being the most aligned between any pair of models, but diverge strongly in later layers. At layer 11 the concepts of CLIP, DINO, and MAE form semantically coherent atlases, such as separated canine concepts or grouped human body parts, while the FS representation is markedly less semantically organized. The paper reads this as evidence that increased supervision correlates with a reduction in the semantic structure of learned representations, and it ties the FS model's sudden reorganization between layers 9 and 10 to a nucleation process.","pith_inferences":["Inference beyond the paper: the same pipeline could be run on convolutional backbones and larger ViT variants to test whether the supervision-structure relationship is architectural or general.","Inference: the concept atlas suggests a model-selection criterion, namely to prefer a pretrained model whose late-layer concepts remain semantically organized, since that organization may transfer better than raw accuracy alone.","Inference: one could fine-tune a self-supervised model with increasing amounts of label supervision and track the layer-11 atlas, which would test whether the loss of semantic structure is a continuous function of supervision strength.","Inference: because ImageNet-1k's label distribution can bias which concepts appear, the paper's own limitation example being a color concept visible only as dog patches, a test on a less biased image collection would sharpen the semantic-structure claim."],"forward_implications":["Concept-based alignment can identify which concepts are universal across models or layers and which are unique, for example low-distance pairs like zebra stripes and high-distance pairs like complex high-frequency textures between DINO and MAE.","The sanity check indicates that nonlinear-manifold concepts give more faithful alignment than PCA, MCD, or KMeans concepts, especially for CLS-token representations.","The fully supervised model's sharp reorganization between layers 9 and 10 is a nucleation event into class-specific concepts, implying that its last blocks are highly specialized and poorly aligned with earlier blocks.","Early layers of different ViTs are much more aligned than late layers, so foundational visual features are learned similarly across training objectives while task-specific specialization appears in the second half.","CBA makes layer-wise concept atlases directly inspectable, allowing practitioners to see semantic separation such as canine concepts or body parts rather than reading a single number."],"supporting_citations":[{"why":"supplies the scalar alignment measure (CKA) that concept-based alignment replaces and compares against.","marker":"[25]"},{"why":"supplies the prior multidimensional linear subspace concept definition that NLMCD generalizes and outperforms in the sanity check.","marker":"[39]"},{"why":"defines the generalized Rand index with pseudo-metric properties used to compute concept-based alignment and its pairwise decomposition.","marker":"[23]"},{"why":"provides HDBSCAN, the density-based clustering algorithm used to discover concept manifolds.","marker":"[4]"},{"why":"provides UMAP, the dimensionality reduction embedding on which clustering and distance preservation are evaluated.","marker":"[27]"},{"why":"provides the soft-clustering membership scores used as concept proximity descriptors of the feature vectors.","marker":"[28]"},{"why":"provides the fully supervised ViT (FS) whose late-layer organization is compared against self-supervised models.","marker":"[37]"},{"why":"provides the CLIP ViT, one of the four training paradigms compared.","marker":"[33]"},{"why":"provides the DINO ViT, one of the four training paradigms compared.","marker":"[5]"},{"why":"provides the MAE ViT, one of the four training paradigms compared.","marker":"[20]"}],"fun_headline_variants":["Concept-level alignment reveals supervision shrinks ViT semantic structure","ViT study: more supervision, less semantic organization in features","Breaking alignment into concepts shows supervised ViTs lose structure","Supervision vs. semantics: concept-based view of ViT feature spaces","New metric: self-supervised ViTs keep concepts more organized than supervised"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the UMAP embedding preserves the feature-space geometry well enough that clusters found in the embedding correspond to real concept manifolds; the paper itself reports that for the fully supervised model the embedding starts distorting distances after layer 8, so the layer-11 structural claim inherits that risk.","fun_headline_variants_meta":{"raw":{"variants":["Concept-level alignment reveals supervision shrinks ViT semantic structure","ViT study: more supervision, less semantic organization in features","Breaking alignment into concepts shows supervised ViTs lose structure","Supervision vs. semantics: concept-based view of ViT feature spaces","New metric: self-supervised ViTs keep concepts more organized than supervised"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000174,"raw_usage":{"total_tokens":1289,"prompt_tokens":956,"completion_tokens":333,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":572,"completion_tokens_details":{"reasoning_tokens":256}},"tokens_in":572,"tokens_out":333,"duration_ms":4294,"temperature":1.0,"reasoning_tokens":256,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T19:26:24.467432+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the same concept-based alignment using clusters obtained directly in the original 768-dimensional feature space, or with an embedding whose distance-preservation error is verified to be low at every layer, and check whether the fully supervised model's layer-11 representation is still less semantically organized than CLIP, DINO, and MAE. If the supervision-structure gradient disappears under this check, the paper's central finding fails.","supporting_citations":[{"cited_title":"Similarity of neural network represen- tations revisited","cited_arxiv_id":null,"evidence_quote":"supplies the scalar alignment measure (CKA) that concept-based alignment replaces and compares against."},{"cited_title":"Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees","cited_arxiv_id":null,"evidence_quote":"supplies the prior multidimensional linear subspace concept definition that NLMCD generalizes and outperforms in the sanity check."},{"cited_title":"Comparing fuzzy partitions: A generalization of the rand index and related measures","cited_arxiv_id":null,"evidence_quote":"defines the generalized Rand index with pseudo-metric properties used to compute concept-based alignment and its pairwise decomposition."},{"cited_title":"hdbscan: Hierarchical density based clustering","cited_arxiv_id":null,"evidence_quote":"provides the soft-clustering membership scores used as concept proximity descriptors of the feature vectors."},{"cited_title":"How to train your vit? data, augmentation, and regularization in vision transformers","cited_arxiv_id":null,"evidence_quote":"provides the fully supervised ViT (FS) whose late-layer organization is compared against self-supervised models."},{"cited_title":"Learning transferable visual models from natural language supervision","cited_arxiv_id":null,"evidence_quote":"provides the CLIP ViT, one of the four training paradigms compared."},{"cited_title":"Emerg- ing properties in self-supervised vision transformers","cited_arxiv_id":null,"evidence_quote":"provides the DINO ViT, one of the four training paradigms compared."},{"cited_title":"Masked autoencoders are scalable vision learners","cited_arxiv_id":null,"evidence_quote":"provides the MAE ViT, one of the four training paradigms compared."}],"review_version":1}