DisParQ: Self-Supervised Part Concepts for Interpretable Vision Foundation Models

1 INTRODUCTION

• Prior approaches leave open combining spatial grounding, one concept per location, attributes for within-concept variation, and no class labels or language supervision.The cited discussion contrasts fixed-label prototypes, language-reliant concept bottlenecks, and overlapping continuous SAE activations.Source: §1 · p. 2
• DisParQ assigns each patch one concept from a learnable dictionary, selects a sparse subset per image, and quantizes within-concept residuals into discrete attributes.Training first learns high-level concepts with continuous residuals, then quantizes them into attributes for a fully discrete inference bottleneck.Source: §1 · p. 2
• On ImageNet linear probing, DisParQ reaches 83.2% versus 83.4% for its frozen backbone, and its concepts are more consistent across images than language-grounded ones.The paper also reports first place among self-supervised methods on most PartImageNet part-quality metrics.Source: §1 · p. 2
• The part-to-part retrieval benchmark tests whether a concept names the same part across categories, with DisParQ consistently leading self-supervised baselines on PartImageNet and CUB.Figure 2 depicts a query region and four regions from other images with the closest DisParQ concept description.Source: §1 · p. 2, Figure 2 · p. 2
• The paper also studies DisParQ across six frozen backbones and choices involving feature extraction, concept budgets, quantization, decoder depth, gradient routes, and training objectives.Source: §1 · p. 3
• DisParQ stays within 0.2 p.p. of its teacher on ImageNet and within 2.2 p.p. on four fine-grained datasets, while leading self-supervised baselines on most part-quality metrics.The same configuration uses at most 16 active concepts per image; the reported retrieval gains reach 3.5 mAP on PartImageNet and 5.9 p.p. R@1 on CUB.Source: §1 · p. 3

2 RELATED WORK

• Prototype models match patches to learned exemplars, while part discovery learns a small fixed part set; DisParQ instead uses a large shared dictionary without class labels or a task-specific classifier.Each image selects a few concepts to describe its parts.Source: §2 · p. 3
• Concept bottleneck models use human-defined or language-generated concepts, while SAE dictionaries use continuous overlapping codes that entangle concept identity with appearance.CFM adds spatial grounding but names concepts through a text vocabulary.Source: §2 · p. 3
• DisParQ assigns each patch exactly one concept and separately encodes concept identity and within-concept attributes using integer indices.Its part-to-part retrieval benchmark tests whether descriptions preserve part identity across images and categories.Source: §2 · p. 3

3.1 FEATURE EXTRACTION

• At each location, shared-query attention fuses features from different VFM blocks, and AnyUp uses the normalized image to guide upsampling for finer concept assignment.The resulting spatial feature vectors provide the input for concept discovery.Source: §3.1 · p. 4

3.2 CONCEPT IDENTIFICATION AND ASSIGNMENT

• A shared bank of 1,024 learned prototypes supplies 16 selected concepts per image by default, whose strongest spatial responses assign each location exclusively.Prototype scores are balanced across images during training before the top-K concepts are selected.Source: §3.2 · pp. 4–5

3.3 ATTRIBUTE ENCODING AND QUANTIZATION

• For each selected concept, the method pools its region, computes a normalized residual from the prototype, and product-quantizes that residual into a discrete appearance attribute.The attribute represents the region’s appearance relative to its concept reference, avoiding a separate prototype for every appearance variation.Source: §3.3 · p. 5

3.4 CONCEPT DECODER

• A spatial decoder combines assigned concept embeddings, appearance attributes, and positional embeddings to predict the frozen VFM’s global representation.The quantized description is fully specified by selected identities, the assignment map, and discrete appearance codes.Source: §3.4 · pp. 5–6

3.5 TRAINING OBJECTIVES AND REGIME

• Training distills each augmented view’s frozen VFM representation without class labels, text descriptions, or region annotations, using assignment regularization and affine equivariance.Training first discovers concepts with continuous attributes, then freezes feature fusion and prototypes while learning product-quantized attributes and the decoder.Source: §3.5 · p. 6

4.1 EXPERIMENTAL SETUP

• Evaluation spans seven datasets, compares frozen DINOv2-B/14 concept baselines, and tests cross-category retrieval by ranking regions using their concept histograms.The retrieval benchmark uses annotated part masks on PartImageNet or visible keypoints on CUB.Source: §4.1 · pp. 6–7

4.2 QUANTITATIVE RESULTS

• 83.2% ImageNet-1k linear-probe accuracy is only 0.2 p.p. below DINOv2; DisParQ also reaches 55.3% on Places365, 0.1 p.p. below its backbone.On ImageNet-1k, it is the highest-scoring concept model in Figure 5.Source: §4.2 · p. 7, Figure 5 · p. 7
• On PartImageNet, DisParQ leads 7/10 self-supervised metrics; across fine-grained datasets, it leads all 10 except tied Flowers LP.On CUB, its PIP purity is 54.5 vs. 37.3; supervised PDiscoFormer scores higher on CUB clustering and keypoint error, but lower on PIP purity.Source: §4.2 · pp. 7–8, Table 2 · p. 8, Table 3 · p. 8
• Across seven configurations of six frozen backbones, DisParQ stays within 2 p.p. of backbone linear-probe accuracy on six, and within 3.5 p.p. on CLIP-DINOiser.At a 16/1024 concept budget, DINOv2 leads the other six configurations on 7/8 concept metrics and part-to-part retrieval.Source: §4.2 · p. 8
• On PartImageNet, part-to-part retrieval reaches R@1 79.7% and mAP 30.5, vs. 79.2% and 27.0 for the best baselines; image-to-image mAP is 76.1 vs. 61.8.DisParQ also leads CUB R@1, 36.8% vs. 30.9%.Source: §4.2 · p. 8, Table 4 · p. 9

4.3 QUALITATIVE RESULTS AND INTERPRETABILITY

• DisParQ’s non-overlapping concept maps follow distinct object parts and stop at object boundaries, while baselines merge parts or spread into the background.For a sail, one DisParQ concept marks the part across four images, whereas a baseline misses instances or covers the whole object.Source: Figure 6 · p. 9, §4.3 · p. 9
• Removing concepts measures their class-logit contribution, with the four largest parts accounting for 56–100% of positive logit drops.In a 120-participant study, correct-part matches were 69% for DisParQ, 60% for PIP-Net and 53% for CFM.Source: Figure 5 · p. 7, §4.3 · p. 9

5 CONCLUSION

• DisParQ describes frozen self-supervised vision features with a few discrete part concepts, one per location, each with a quantized attribute, learned without labels or language.Source: §5 · p. 10
• The representation preserves backbone accuracy, yields parts more consistent across images than language-grounded and sparse-autoencoder dictionaries, and retains concept identity across categories.Source: §5 · p. 10
• The paper proposes that future work could use discrete concepts to search by part and appearance or correct predictions by removing or replacing concepts.Source: §5 · p. 10

• The Clickworker study followed organizational procedures and regulations; participants were informed, compensated, and not personally identified.Source: ETHICS STATEMENT · p. 10
• DisParQ inherits its frozen backbone’s biases, so coherent concepts may still encode spurious correlations.Source: ETHICS STATEMENT · p. 10
• Consequential use requires validation in the intended setting, including assessment of errors and bias.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

• The model and training objectives are described in Section 3, with a highly detailed technical account in Appendix C.Source: REPRODUCIBILITY STATEMENT · p. 10
• Appendix D specifies datasets and splits, pretrained backbones, evaluation metrics, and baseline protocols.Source: REPRODUCIBILITY STATEMENT · p. 10, APPENDIX · p. 16

APPENDIX

• The appendices also cover limitations, ablations, extended results, user-study details, qualitative examples, and automatic concept naming.Source: APPENDIX · p. 16

• DisParQ learns a large shared dictionary without class labels, assigns each patch one concept, and captures cross-image variation with attributes.Earlier prototype and part-discovery approaches generally use class-serving prototypes or a small fixed set of parts per category or dataset.Source: A RELATED WORK · p. 18
• Unlike language-defined bottlenecks or overlapping continuous SAE patch codes, DisParQ uses visual features alone and separates part identity from appearance variation.Its image description uses at most 16 active concepts represented by integer indices alone.Source: A RELATED WORK · p. 18
• The part-to-part retrieval benchmark starts from an annotated region and tests whether its description finds the same part across categories.This differs from semantic-correspondence evaluations that usually match keypoints between images of the same category (Min et al., 2019).Source: A RELATED WORK · p. 18

B LIMITATIONS

• Part annotations may be coarser than learned concepts, while over-segmentation or incorrect grouping can also cause failures.Frozen-backbone biases and contextual features limit causal-locality claims; concepts remain unnamed without examples or alignment, and the K=16 budget covers backgrounds regardless of part count.Source: B LIMITATIONS · p. 18

C ARCHITECTURE AND TRAINING DETAILS

• The canonical model uses frozen DINOv2-B/14, a bank of 1,024 concepts, 16 selected concepts per image, and private 16 × 64 product quantization.Every patch is assigned to one concept.Source: C ARCHITECTURE AND TRAINING DETAILS · p. 19

C.1 FEATURE EXTRACTION

• Fusion pools outputs from the encoder’s last four blocks, and image-guided AnyUp upsamples features to 32 × 32; bilinear scores are broadly comparable but maps are less detailed.Source: §C.1 · pp. 19–20

C.2 CONCEPT IDENTIFICATION AND ASSIGNMENT

• Sinkhorn normalization selects a subset from the concept bank, but top-K hard selections need not be balanced or all own a spatial location.Source: §C.2 · p. 20

C.3 ATTRIBUTE ENCODING AND QUANTIZATION

• Concept-specific product codebooks encode appearance variation as combinations of codewords, separating each part’s identity from its attribute.The codeword indices form the discrete appearance code.Source: §C.3 · p. 21

C.4 CONCEPT DECODER

• The spatial decoder predicts the backbone’s global CLS representation from selected concept IDs, spatial owners, and quantized attributes.Per-image codes are compact, but private codebooks require substantial decoder-side storage.Source: §C.4 · p. 22

C.5 TRAINING OBJECTIVES AND REGIME

• Global and auxiliary distillation preserve target information, while spatial and usage regularizers shape its organization into concepts.The objective combines nine weighted losses and averages view-specific cosine losses; each auxiliary prediction matches its own view’s backbone target.Source: Figure 7 · p. 22, §C.5 · p. 23
• Feature-weighted Potts smoothing favors agreement between neighboring assignments with similar features while weakening smoothing across feature discontinuities.Its adaptive temperature and bandwidth respond to logit confidence and feature-distance scale.Source: §C.5 · pp. 23–24
• The objective also encourages confident spatial ownership, discourages redundant region features, and promotes selected-slot and full-bank prototype presence.Full-bank presence supplies gradients to concepts outside the selected subset; usage diversity regularizes prototype usage toward uniformity rather than quantizer commitment.Source: §C.5 · p. 24

C.6 TRAINING STAGES AND OPTIMIZATION

• Stage 1 jointly learns the continuous concept system; stage 2 starts from its selected checkpoint, freezes fusion and prototypes, and learns new PQ projections and codebooks.Training retains Gumbel noise and batch-balanced selection in both stages, while evaluation removes noise and uses hard PQ lookup.Source: §C.6 · p. 25, Table 7 · p. 25
• Underused prototypes are replaced with current region features when their tracked usage falls below 10^-4.Usage is updated from selected-ID counts across both views and devices; after each optimizer step, inactive prototypes are reset along with their usage, dual, and value embedding.Source: §C.6 · pp. 25–26

D.1 DATASETS AND SPLITS / D.2 BACKBONES / D.3 TRAINING DISPARQ

• The evaluation spans seven datasets, uses frozen vision feature extractors and dataset-specific global targets, and trains one DisParQ model per dataset without class labels or part annotations.The main DINOv2-B/14 setup uses N = 1024 concepts and K = 16 per image; training pairs an augmented view with an affine-transformed view.Source: §D.1 · p. 26, §D.2 · pp. 26–27, §D.3 · p. 27

D.4 TRAINING THE BASELINES

• The main comparison includes sparse autoencoders trained on frozen DINOv2-B/14 patch tokens, a released CFM dictionary, and label-free stages of PIP-Net and ProtoQuant.The evaluation also includes PCA references and supervised reference stages; the CFM dictionary is released rather than refitted.Source: §D.4 · pp. 28, 30
• Baseline configurations are selected by aggregate ranks over reported scores, and the sweep selections use evaluation labels, including annotated-part metrics where available.Retrained supervised PDiscoFormer references select the snapshot with the highest test accuracy.Source: §D.4 · pp. 28, 30

D.5 EVALUATION PROTOCOL

• Linear probes use batch normalization and a trained linear classifier, but comparisons retain method-specific augmentation, cached features, and image geometry.Classification and image retrieval use a 224 × 224 center crop for DisParQ, while dictionary baselines and PDiscoFormer use cached square-resized features.Source: §D.5 · pp. 30–31

D.6 METRICS

• Spatial metrics include matched-part mIoU, foreground-only FG-ARI, and locality, consistency, and impurity computed from thresholded concept supports.Mapped NMI and ARI remove the penalty for splitting a part among concepts mapped to the same label, so these scores are descriptive clustering measures.Source: §D.6 · p. 32
• Part-to-part retrieval represents each region with a normalized histogram of global concept identities and ranks regions from other images by cosine similarity.A retrieved region is relevant when it has the query’s part label; the benchmark samples 8,000 regions for ranking and reports recall and mAP.Source: §D.6 · p. 33
• Concept contribution is measured by removing a concept, reassigning its cells among selected concepts, and normalizing positive drops in the predicted-class logit.The resulting weights describe relative positive support under the intervention, not an additive decomposition of the classifier’s logit.Source: §D.6 · p. 33

E ABLATION STUDIES

• Most component ablations use a bilinear-upsampled continuous-stage control on PartImageNet, with each alternative changing one named component and results averaged over three seeds.Backbone, bank-size, and concept-budget sweeps instead report single runs; small differences are interpreted descriptively, not as significance tests.Source: E ABLATION STUDIES · p. 34

E.1 FEATURE EXTRACTION

• DINOv2 retains LP accuracy within 0.1 pp of its frozen target, while DINOv3 leads most part-quality measures in the patch-16 group.The ordering varies by metric: CLIP-DINOiser has higher CFM consistency than DINOv2, and SigLIP2’s pooler improves LP over GAP by 2.7 pp.Source: §E.1 · p. 34, Figure 8 · p. 35
• Removing layer fusion leaves LP and mAP essentially unchanged but lowers foreground purity by 3.16 pp and mIoU by 1.44 pp.The comparison indicates that fusion contributes primarily to concept quality rather than downstream accuracy.Source: §E.1 · p. 34, Figure 9 · p. 35
• At the same 32 × 32 resolution, bilinear interpolation raises foreground purity by 2.07 pp but lowers mIoU by 1.39 pp and locality by 1.47 pp versus AnyUp.LP changes by +0.22 pp and mAP by −0.03 pp; these mixed differences support bilinear as a cheaper ablation control, not equivalence on every metric.Source: §E.1 · p. 34, Figure 10 · p. 36
• Mixed training with AnyUp on 20% of batches stays close in LP and mAP (+0.08 and −0.05 pp) and raises foreground purity by 2.17 pp.This variant uses full AnyUp at evaluation; native 16 × 16 resolution instead lowers foreground purity by 6.55 pp while raising FG-ARI by 2.42 pp.Source: §E.1 · pp. 34–35, Figure 10 · p. 36

E.2 CONCEPT BANK, SELECTION, AND MAINTENANCE

• At N=8192, purity rose 4.05 pp while FG-ARI, mIoU, consistency, and locality fell; K=16, N=1024 had the strongest reported spatial and semantic scores among tested values.Across the joint sweep, the highest observed purity was 86.60% at (K, N) = (32, 8192), while the default had the highest observed consistency (16.30%).Source: §E.2 · pp. 36–37, Figure 11 · p. 36, Figure 13 · p. 37
• Disabling inactive-prototype replacement lowered mAP by 7.51 pp, foreground purity by 13.43 pp, and consistency by 8.52 pp, larger changes than the tested selector alternatives.Peak scoring barely changed LP or mAP but reduced purity by 3.45 pp; direct top-K selection reduced consistency and locality by 1.38 and 1.63 pp versus zero-bias Sinkhorn.Source: §E.2 · pp. 37–38, Figure 14 · p. 38

E.3 APPEARANCE ATTRIBUTES AND QUANTIZATION

• Removing continuous appearance attributes during discovery lowered LP by 8.98 pp and mAP by 6.22 pp, while their removal after assignment freezing lowered them by 12.24 and 11.14 pp.At the reference 96-bit rate, shared PQ16×64 was competitive with private PQ16×64: LP changed by −0.17 pp, mAP by +0.03 pp, and kNN by +0.07 pp.Source: Figure 15 · p. 38, §E.3 · pp. 38–39, Figure 16 · p. 40
• At 12 bits per concept, shared VQ4096 had the highest mean LP and mAP among the three tested shared quantizers, though all trailed the 96-bit reference.The low-rate private VQ64 and PQ2×8 alternatives lost 1.69 and 2.05 pp LP against private PQ16×64; these comparisons also changed quantizer structure and capacity.Source: §E.3 · p. 39, Figure 16 · p. 40

E.4 CONCEPT DECODER

• Mean pooling instead of spatial attention lost 1.26 pp LP and 2.06 pp mAP; three decoder blocks improved over one, while six blocks added little and reduced consistency.Moving from three to six blocks roughly doubled parameters from 23.42M to 44.68M for 0.11 pp higher mean scores in each downstream metric, with consistency falling by 2.07 pp.Source: §E.4 · p. 40, Figure 17 · p. 41
• The auxiliary-only readout changed LP by −0.75 pp and mAP by +0.35 pp, but a same-readout comparison showed changes of approximately 0.00 ± 0.82 pp and −0.05 ± 0.15 pp.The system comparison changes training and readout; the auxiliary head uses continuous pooled region features, unlike the spatial decoder's concept identities, spatial assignments, and appearance attributes.Source: §E.4 · p. 40, Figure 18 · p. 41

E.5 GRADIENT ROUTES

• Removing the identity surrogate modestly lowered LP by 0.28 pp, FG-ARI by 0.79 pp, and consistency by 1.00 pp; restoring residual gradients did not uniformly help concept quality.With residual gradients restored, FG-ARI, mIoU, and foreground purity fell by 1.10, 0.67, and 0.69 pp.Source: §E.5 · p. 41, Figure 19 · p. 42

E.6 TRAINING OBJECTIVES

• Usage-diversity removal barely changed LP (+0.01 pp) but lowered foreground purity by 7.04 pp and locality by 4.82 pp; bank-presence removal had smaller declines.Removing bank presence lowered foreground purity by 0.68 pp and locality by 0.19 pp.Source: §E.6 · p. 42
• Removing feature-weighted Potts regularization lowered mIoU by 6.94 pp and consistency by 7.91 pp, while removing auxiliary distillation lowered foreground purity and locality by 1.38 and 1.51 pp.Removing entropy regularization improved FG-ARI, mIoU, consistency, and locality but lowered purity; removing affine equivariance or selected-region presence also produced mixed metric changes.Source: §E.6 · p. 42, Figure 20 · p. 43

F.1 LARGE-SCALE CLASSIFICATION IN FULL

• DisParQ is the only compared method with both full spatial grounding and a full discrete bottleneck, where indices alone define what the predictor reads.The property columns describe method construction, not localization performance.Source: §F.1 · p. 44

F.2 FULL PARTIMAGENET COMPARISON

• The full PartImageNet comparison spans supervised methods, self-supervised methods, sparse-autoencoder settings, concept budgets, backbones, and DisParQ’s other backbones.The figures report method-minus-DisParQ differences for supervised comparisons and also include self-supervised methods scored with differing downstream representations and budget protocols.Source: Figure 21 · p. 45, §F.2 · p. 45, Figure 22 · p. 46

F.3 FULL CUB CONCEPT METRICS

• On CUB, DisParQ led self-supervised methods by 3.5–8.5 points on clustering metrics and by 17.2 on PIP purity, while supervised PDiscoFormer scored higher on clustering for K ≥ 8.CUB’s keypoint annotations make mIoU, FG-ARI, and grounding metrics undefined; PDiscoFormer also had lower keypoint error at every tested K.Source: Table 16 · p. 48, §F.3 · p. 48

F.4 PDISCOFORMER ON CARS AND DOGS

• Retrained PDiscoFormer matched DisParQ’s Cars linear probe (91.1 vs. 91.0) and trailed it by 2.3–4.9 p.p. on the other three Cars and Dogs columns.The retraining used the authors’ code and recipe at 224 × 224 with K=16 parts on the same training splits as DisParQ.Source: §F.4 · p. 48, Table 17 · p. 49

F.5 PROTOQUANT AND PIP-NET: FROZEN VS. FINE-TUNED BACKBONE

• Fine-tuning improved classification but generally hurt part quality: ProtoQuant’s PartImageNet probe rose from 85.2 to 89.1 as part mIoU fell from 33.7 to 9.3.PIP-Net also lost part quality and, unlike ProtoQuant, lost accuracy; the passage attributes the difference to whether backbone fine-tuning receives class-label signal.Source: §F.5 · p. 49
• The frozen rows keep all methods on the same features, while fine-tuned arms also see target-dataset labels through the backbone and classifier.Fine-tuned ProtoQuant reproduced its reported accuracy: 87.0 top-1 on bounding-box-cropped CUB versus 86.9 in its Table 3.Source: §F.5 · p. 49

F.6 RETRIEVAL RESULTS

• On PartImageNet, attribute codes alone achieved R@1 78.9 versus 79.7 for concept identities but mAP 16.3 versus 30.5; using attributes to rerank same-concept candidates raised mAP to 57.3.On CUB, attribute-based reranking raised mAP from 9.3 to 28.1; concatenating attributes and identities changed nothing.Source: §F.6 · p. 49
• Part-to-part R@1 exceeds the category-only oracle on PartImageNet (79.7 vs. 43.9), while class-wise PCA reaches R@1 52.4 at mAP 8.9.Per-image PCA is near chance for part-to-part retrieval, with R@1 5.3 versus 4.6.Source: §F.6 · pp. 49–50
• DisParQ has the best self-supervised part-to-part R@1 on both datasets: 79.7 on PartImageNet and 36.8 on CUB.On CUB it also leads part-to-part R@5 at 73.7, against an oracle R@1 of 22.7 and chance of 7.1.Source: §F.6 · p. 50, Table 19 · p. 51

F.7 WHAT THE QUANTIZED ATTRIBUTES KEEP

• Quantized attributes retain class information: occurrences of one concept cluster by the class of their image.The attribute encoder quantizes a residual with a concept-specific codebook, so an attribute vector carries no concept identity by construction and its codes are comparable only within the same concept.Source: §F.7 · p. 52

F.8 USER STUDY DETAILS AND RESULTS

• Participants rated DisParQ prototypes most consistent overall, significantly above PIP-Net and CFM (p < 0.001 for each); ratings were similarly low across methods on PartImageNet.The gap was largest on CUB, where DisParQ significantly exceeded both baselines.Source: §F.8 · p. 53, Figure 26 · p. 53
• 69% retrieval accuracy for DisParQ exceeded PIP-Net’s 60% and CFM’s 52%; its advantage was significant except against PIP-Net on CUB.On PartImageNet, DisParQ outperformed PIP-Net by 16 percentage points.Source: Table 20 · p. 54, §F.8 · p. 54

G.1 INTERACTIVE CONCEPT VISUALIZER

• The interactive visualizer lets users browse image concept maps, the strongest concept matches, and each concept’s strongest, typical, and weakest examples.Its galleries can be filtered by class or concept and show concept co-occurrences.Source: §G.1 · pp. 54–55

G.2 PARTIMAGENET

• On PartImageNet, DisParQ maps follow annotated parts and object boundaries, while baselines sometimes merge parts or extend into the background.Close-ups with one large annotated part can score DisParQ as over-segmented when its finer concepts divide that part.Source: §G.2 · p. 57

G.3 FINE-GRAINED DATASETS

• Across four fine-grained datasets, DisParQ’s maps stay on objects and recurring regions, and its concepts mark the same parts across images.These datasets have no part masks; PDiscoFormer is shown as a class-label-trained reference.Source: §G.3 · p. 61

G.4 PART-TO-PART RETRIEVAL

• In all six scored retrieval panels, DisParQ’s four retrieved regions carry the query part, while ProtoQuant or MSAE retrieve at most two matching regions.On unscored Cars, Dogs, and Flowers examples, DisParQ retrieves visually corresponding regions such as grilles, muzzles, and petals.Source: §G.4 · p. 63, Figure 38 · p. 64

G.5 CLASS EVIDENCE OF DISPARQ AND INTERPRETABILITY

• Across 25 examples, a few concepts account for 56–100% of positive logit drops, and concepts retrieve the same parts across images, often across classes.The four largest contributions account for 56 to 100% of total positive logit drops; the largest alone accounts for 17 to 52%.Source: §G.5 · p. 65

G.6 WHAT QUANTIZATION KEEPS

• Quantized attributes preserve 55–78% of 5-nearest-neighbor relations from continuous attributes, retaining which occurrences of a concept look alike.Concept keys identify the shared concept, while attributes restore each region’s appearance.Source: §G.6 · p. 71, Figure 44 · p. 72, Figure 45 · p. 73

G.7 HOW ONE CONCEPT VARIES ACROSS IMAGES

• The occurrence maps use quantized attributes for concepts selected in held-out images; their PCA plane captures only 12–20% of variance, so positions are approximate.The exact nearest and farthest examples are ranked by cosine distance in the full 768-dimensional attribute space.Source: §G.7 · p. 77
• Within a concept, quantized-attribute occurrences group by object kind, and nearest examples can share species, make, or breed despite no class labels in training.Concept identity names a shared part, while the attribute distinguishes its kind.Source: §G.7 · p. 77, Figure 49 · p. 78, Figure 50 · p. 79
• The figures show that quantized codes preserve class-separating structure within a concept, but do not show that quantization creates it because frozen DINOv2 features already separate classes.The authors attribute part of that structure to the backbone.Source: §G.7 · p. 77

H AUTOMATIC ALIGNMENT OF CONCEPT NAMES

• The naming study aligns concept descriptions to language-aligned visual features, retrieves names from a fixed vocabulary, and tests whether names recover region labels.Naming methods use the same regions within each model and evaluation dataset.Source: H AUTOMATIC ALIGNMENT OF CONCEPT NAMES · p. 82

H.1 CONCEPT DESCRIPTIONS AND ALIGNMENT TARGETS

• For each concept occurrence, its description combines the fixed prototype with its image-dependent quantized attribute, and a frozen CLIP-DINOiser teacher supplies the alignment target.Teacher patch features are pooled over the concept region and normalized.Source: §H.1 · p. 82

H.2 CONCEPT DESCRIPTIONS TO NAMES

• Naming compares fixed concept descriptions with attribute-dependent adapters in the same teacher space and vocabulary; the joint MLP lets attribute contributions depend on the prototype.Fixed descriptions include region means and mapped keys; attribute-dependent methods add the quantized attribute to adapter inputs.Source: §H.2 · pp. 82–83

H.3 EVALUATING THE RETRIEVED NAMES

• Name-to-class evaluation ranks annotated labels from predicted names, macro-averages accuracy and MRR over concepts, and evaluates only regions with clear foreground labels.The same text encoder selects names and scores label correspondence, so this is not an independent semantic judgment; intervals reflect sampled concepts, not training seeds.Source: §H.3 · p. 83, Table 21 · p. 84, Table 22 · p. 84

H.4 RESULTS

• Top-1 retrieval improves by 23.05, 20.26, and 18.21 percentage points over region means for ImageNet/DINOv2, PartImageNet/DINOv2, and PartImageNet/CLIP-DINOiser, respectively.The joint MLP yields these gains on VOC object names.Source: §H.4 · p. 84
• Part-label gains are uneven: joint-MLP changes versus region means are +8.46 points for ImageNet/DINOv2, −1.44 for PartImageNet/DINOv2, and −0.02 for PartImageNet/CLIP-DINOiser.For PartImageNet/DINOv2, joint-MLP teacher cosine similarity rises from 0.8169 to 0.8615 while top-1 retrieval falls from 23.18 to 21.74.Source: §H.4 · p. 84

H.5 QUALITATIVE EXAMPLES

• Curated naming figures show selected concepts and top-one predictions across closest and visually similar examples, illustrating method differences rather than estimating naming accuracy.The displayed examples are screened for foreground overlap and labels.Source: §H.5 · p. 85, Figure 53 · p. 86, Figure 54 · p. 87