Concept Bottleneck Models (CBMs) promise predictions that humans can inspect and correct through concepts such as "curved beak". Yet on CUB-200-2011, their standard benchmark, progress is measured like that of ordinary classifiers: by task and concept accuracy. Neither reveals whether the label is predicted from the exposed concept scores, or whether a concept is supported by visual evidence of that concept rather than by co-occurring features such as cues to the species as a whole. We audit where the accuracy of CBMs and Concept Embedding Models (CEMs) on CUB comes from. The CUB annotations are too noisy to explain it: class-level training labels agree with per-image annotations on only ~82% of image--concept pairs, and classifiers trained on per-image annotations reach only ~37% species accuracy. Leakage probes show that CEM predictions cannot be reconstructed from their concept scores; the missing class information sits in internal embeddings. We identify four design axes through which class information can enter concept scores---receptive field, shared versus concept-specific representations, norm-dependent scoring, and task supervision. An ablation shows that most of it enters through non-local features: restricting a ResNet50 backbone to local BagNet patches lowers the accuracy recoverable from concept scores from 72% to 43%, close to what ground-truth annotations support, while joint training raises it again at the cost of concept accuracy. Localization and occlusion show that locality makes grounding measurable but does not guarantee it: under class-level labels, local concept scores use the head as a proxy for body, wing, and tail concepts, and CEM concept scores barely respond to occluding their supporting part. Task and concept accuracy should thus support, not drive, the evaluation of CBMs, and given the noisy annotations, CUB accuracy gaps should not be overinterpreted.
Figures & tables
Figure 1: Comparison of class-level and instance-level annotations for two sample images. Concepts are color-coded by source: class-only ( orange ; not visually observable to the annotator), instance-only ( blue ), and shared ( green ). In yellow , we highlight annotated concepts judged by the authors to be not visually observable. A subset of the concepts is shown for visualization purposes.
Encoding
Best predictor
Test accuracy
Binary ( ±1 )
MLP-2x256
37.50
Table 1: Concept-only reference accuracy on CUB. Classifiers receive only ground-truth instance-level binary concept annotations as input (all certainty levels, i.e., no concept is masked). We report the best test accuracy across concept-to-label predictors. The full table, including certainty-based masking, is available in Appendix C .
Model
Concept Acc.
AUC
Nat.
Cont.
Disc.
Emb.
Δb
Δenc
Δemb
by-instance
CEM
79.83±0.43
66.57±0.19
67.52±2.48
52.21±1.90
38.76±2.15
68.56±1.23
15.31
13.45
16.34
CBM
80.22±0.13
63.97±0.48
58.20±2.67
57.16±1.48
52.06±2.35
–
1.04
5.11
–
LC-CBM †
74.84±0.07
70.20±0.13
–
25.23±0.48
21.84±1.45
–
0.00
3.39
–
by-class
CEM
94.89±0.15
90.23±0.54
76.91±0.18
69.68±0.83
69.54±1.07
74.98±0.74
7.23
0.14
5.30
Table 2: Concept accuracy, AUC, and leakage probe results (% accuracy, mean ± std). Nat.: native task accuracy; Cont./Disc./Emb.: linear probes on continuous, discretized, and internal-embedding concept outputs. Δb , Δenc , Δemb quantify bypass, encoding, and embedding leakage. † : fully constrained configuration of the ablation (Section 5.2 ), shown for reference; its predictions come only from the probe, so Δb=0 by construction. Gaps are computed before rounding.
Concept quality
Task Acc (probe)
Backbone
Heads
Training
Conc. Acc
Conc. AUC
Cont.
Disc.
Head sharing
ResNet50
Shared
Concept-only
82.53±0.16
84.03±0.49
64.66±0.62
60.57±0.57
ResNet50
Specific
Concept-only
95.79±0.13
92.85±0.21
72.11±0.55
72.59±0.68
BagNet-33
Shared
Concept-only
77.21±0.52
70.47±3.79
20.63±5.30
13.40±4.33
Task supervision
Table 3: Systematic ablation of the design axes of Section 5 (mean ± std, by-class annotations). All configurations use the template of Section 5.2 with spherical scoring; task accuracy is measured by linear probes on continuous (Cont.) and discretized (Disc.) frozen concept scores, so no configuration can bypass its scores. † : fully constrained configuration ( LC-CBM ).
Figure 2: Spatial faithfulness ([email protected]) by anatomical region. Models trained with by-class annotations (left) exhibit strong head bias, while by-instance supervision (right) yields more balanced localization across body parts.
Model
Pairs
Target drop
Target–random
Target–unrelated
Flip rate
LC-CBM
69,228
0.437
0.355
0.153
29.1
CEM
25,994
0.034
0.017
0.003
19.4
Table 4: Part-occlusion audit under class-level CUB supervision. Scores are macro-averages over mapped anatomical groups. Target drop is the change in the exposed concept score when the mapped part is blurred; target–random and target–unrelated are specificity contrasts against control masks. Flip rate reports changes in the native class prediction after target occlusion. Backbone, preprocessing, score scale ( [−1,1] for LC-CBM , [0,1] for CEM), and evaluated pairs differ between rows, so contrasts should be read within each row.
Appendix figures & tables14 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 3: Additional analysis of the class–instance annotation mismatch on CUB. (a) Increasing the certainty threshold substantially reduces coverage, dropping to roughly 55% at the highest threshold. (b) Disagreement direction reveals two sources of mismatch: class-positive concepts that are not visible in individual images, and instance-positive concepts suppressed by class-level aggregation.
Figure 4: Annotation mismatch in CUB. (a) Agreement between instance-level and class-level concept labels remains bounded around 82 – 84% across certainty thresholds, showing that filtering uncertain annotations only marginally improves alignment. class_label=0 denotes disagreement between class-level (green) and instance-level annotations, while class_label=1 denotes agreement; results over both cases are shown in blue. (b) Non-visibility rates vary substantially across concept groups, especially for fine-grained attributes, indicating that limited observability is a major source of mismatch.
Unconstrained
g normalized
w normalized
Both normalized
Concept score decomposition
Norm product contribution
0.997
0.651
0.995
0.000
Cosine contribution
0.003
0.349
0.005
1.000
Norm–saturation correlation
Feature norm vs. saturation
0.575
−0.017
0.520
<0.001
Weight norm vs. saturation
0.197
0.382
−0.039
<0.001
Appendix
Table 5: Controlled normalization study on CUB. We independently normalize g and w and report score decomposition, norm-saturation correlations, and downstream performance. In the standard configuration, ∼ 99.7% of score variance is explained by the norm product. Fixing one norm shifts the dependency to the other, while fixing both removes norm-driven variability.
Figure 5: Feature norm ∥g(x)∥ versus the number of saturated concepts across the four ablation settings. Top-left: standard CBM. Top-right: g-fix, where ∥g(x)∥=1 . Bottom-left: w-fix, where ∥wi∥=1 . Bottom-right: both-fix, where both norms are constrained. The standard model exhibits a strong positive relation between feature norm and saturation. Fixing ∥g(x)∥ removes this dependency, while fixing only ∥wi∥ leaves it largely intact. When both norms are fixed, saturation disappears entirely.
Encoding
Model
t=1
t=2
t=3
t=4
Masked sign
Linear
32.46
32.46
31.50
19.62
MLP (2x256)
37.50
37.50
35.45
25.34
XGBoost
36.02
36.02
34.05
22.82
Appendix
Table 6: Concept-only task accuracy on CUB using ground-truth concepts. We report test accuracy (%) for different concept encodings, certainty thresholds t , and concept-to-label predictors. The best result per encoding is highlighted in bold.
α
LC-CBM (class-level)
LC-CBM (instance-level)
0.05
0.113
0.130
0.10
0.284
0.326
0.15
0.422
0.476
0.20
0.541
0.596
0.30
0.748
0.777
0.35
0.829
0.841
Appendix
Table 7: PCK across thresholds α for LC-CBM trained with class-level and instance-level annotations. Instance-level supervision consistently improves localization, particularly at stricter thresholds.
Region
Koh
Instance
Δ
Head / Bill
0.80
0.59
−0.21
Body
0.18
0.46
+0.28
Wing
0.21
0.39
+0.18
Tail
0.01
0.08
+0.07
Leg
0.03
0.04
+0.01
Appendix
Table 8: [email protected] by anatomical region. Instance-level supervision reduces head bias and improves localization on body parts.
Metric
LC-CBM
CEM
Mean Hamming distance
5.35
3.93
Nearest-code / native agreement
0.03
79.50
Nearest-code / true-class match
45.05
70.50
Appendix
Table 9: Codebook-fidelity diagnostics.
Figure 6: Fully constrained configuration of the ablation template ( LC-CBM ). A BagNet-33 backbone extracts local features, projects them into concept-specific representations, compares them with learned concept vectors via cosine similarity, and aggregates them via global max pooling into concept scores. The other configurations of Table 3 replace the backbone, the heads, the scoring, or the training objective.
Hyperparameter
Value
epochs
150
learning_rate
1×10−4
weight_decay
1×10−4
batch_size
32
image_size
224×224
bbox_center_crop
True
Appendix
Table 10: LC-CBM hyperparameters used for all reported experiments.
Concept prefix
CUB part IDs
Bilateral?
bill_*
beak (2)
No
belly_*
belly (3)
No
breast_*
breast (4)
No
crown_*
crown (5)
No
forehead_*
forehead (6)
No
eye_color
left eye (7), right eye (11)
Yes
Appendix
Table 11: Concept-to-CUB-part mapping used in the C5 spatial faithfulness evaluation. Concepts has_size_* , has_shape_* , and has_primary_color_* are excluded (no anatomical anchor).
Family
Koh-trained → Instance GT
Instance-trained → Koh GT
Koh → Koh (matched)
Instance → Instance (matched)
LC-CBM
0.800
0.777
0.904
0.748
CEM
0.812
0.841
0.949
0.798
CBM
0.811
0.841
0.946
0.800
Appendix
Table 12: Cross-label concept accuracy (mean across 3 splits). Matched-label baselines are shown for reference only.
Figure 7: Top-5 highest-activation patches for selected concepts under class-level (top) and instance-level (bottom) supervision. Class-level training shows a strong bias toward head regions, while instance-level supervision produces more spatially aligned activations.
Figure 8: Qualitative visualization of concept localization. For each sample, we show the keypoint (center) and the corresponding receptive field (bounding box) used by the network to infer the concept. We compare class-level (Koh) and instance-level supervision across two examples. Instance-level supervision yields activations that are more spatially aligned with the expected anatomical regions.
Concept Bottleneck Models (CBMs) ground predictions in human-understandable concepts but face fundamental limitations: the absence of a metric to pre-evaluate concept relevance, the "linearity problem" causing recent CBMs to bypass the concept bottleneck entirely, an accuracy gap compared to opaque models, and finally the lack of systematic study on the impact of different visual backbones and VLMs. We introduce CBM-Suite, a methodological framework to systematically addresses these challenges. First, we propose an entropy-based metric to quantify the intrinsic suitability of a concept set for a given dataset. Second, we resolve the linearity problem by inserting a non-linear layer between concept activations and the classifier, which ensures that model accuracy faithfully reflects concept relevance. Third, we narrow the accuracy gap by leveraging a distillation loss guided by a linear teacher probe. Finally, we provide comprehensive analyses on how different vision encoders, vision-language models, and concept sets interact to influence accuracy and interpretability in CBMs. Extensive evaluations show that CBM-Suite yields more accurate models and provides insights for improving concept-based interpretability.
Merve Tapli, Quentin Bouniot, Wolfgang Stammer +2
Middle East Technical University (METU) · Helmholtz Munich · Munich Center for Machine Learning +5
Concept-bottleneck models (CBMs) are neural classifiers that compute predictions from high-level concepts extracted from the input. CBMs ensure stakeholders can understand the concepts -- and the predictions they entail -- by learning these from concept-level annotations, which are however seldom available. Recent CBM architectures work around this issue by obtaining annotations from Vision-Language Models (VLMs). While greatly broadening applicability, doing so can yield lower quality concepts and therefore less interpretable models. We strike for a middle ground by introducing Vision-plus-Human-guided CBM (VH-CBM), a hybrid approach that exploits both VLMs and a small amount of dense annotations. VH-CBM employs a Gaussian Process in the VLM's embedding space, which captures useful global information about the target domain, to propagate the expert's supervision to any target data point. Our empirical evaluation shows how VH-CBM predicts more accurate concepts than VLM-guided CBMs even when annotating as little as 1% of the data, while sporting better concept calibration and supporting active learning.
Nicola Debole, Andrea Passerini, Stefano Teso +2
DISI, University of Trento, Italy · CIMeC, University of Trento, Italy
Concept bottleneck models (CBMs) predict a layer of human-named attributes before predicting a class, which makes their decisions auditable. On fine-grained recognition tasks the concept heads are usually free to attend anywhere in the image, so a head named for one body region can be satisfied by evidence on another. This work studies a part-factorized CBM that removes that freedom by construction. The method has three components built on a frozen DINOv3 vision transformer. A learned foreground gate, trained on DINOv3 patch features, suppresses background patches inside the part attention. A set of part queries cross-attends to patch features and each of the 312 CUB attributes is routed, through a fixed concept-to-part map, to read only from the part token its name implies. A learnable two-dimensional Gaussian prior, injected additively in log space into the attention logits, breaks the permutation symmetry among part queries; its means are initialized from the dataset-average keypoint location of each part, which requires no per-image keypoint supervision at training or test time. On CUB-200-2011 the spatial-prior model matches a fully supervised baseline (88.85% versus 88.95% top-1) while raising pointing accuracy by 16 points (52.6% versus 36.4%). Replacing bounding-box supervision with a PCA foreground target and combining it with the Gaussian prior removes all per-image supervision and reaches 88.6% top-1 at about 70% pointing accuracy. A keypoint-fraction sweep shows that 0.5% of the training set (about 27 images) suffices to initialize the prior with no measurable loss. Removing part identity entirely is the harder case: without any spatial prior, pointing accuracy collapses to 2.9%.