Auditing Where Concept Bottleneck Accuracy Comes From on CUB

Sascha Saralajew; Eleonora Poeta; Eliana Pastor; Ammar Shaker

cs.CVOct 20, 2026

Auditing Where Concept Bottleneck Accuracy Comes From on CUB

Authors: Sascha Saralajew, Eleonora Poeta, Eliana Pastor, Ammar Shaker

Organizations: Politecnico di Torino Turin, Italy

Abstract

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 ( $\pm 1$ )	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.	$\Delta_{b}$	$\Delta_{enc}$	$\Delta_{emb}$
by-instance
CEM	$79.83$ $\pm 0.43$	$66.57$ $\pm 0.19$	$67.52$ $\pm 2.48$	$52.21$ $\pm 1.90$	$38.76$ $\pm 2.15$	$68.56$ $\pm 1.23$	$15.31$	$13.45$	$16.34$
CBM	$80.22$ $\pm 0.13$	$63.97$ $\pm 0.48$	$58.20$ $\pm 2.67$	$57.16$ $\pm 1.48$	$52.06$ $\pm 2.35$	–	$1.04$	$5.11$	–
LC-CBM †	$74.84$ $\pm 0.07$	$70.20$ $\pm 0.13$	–	$25.23$ $\pm 0.48$	$21.84$ $\pm 1.45$	–	$0.00$	$3.39$	–
by-class
CEM	$94.89$ $\pm 0.15$	$90.23$ $\pm 0.54$	$76.91$ $\pm 0.18$	$69.68$ $\pm 0.83$	$69.54$ $\pm 1.07$	$74.98$ $\pm 0.74$	$7.23$	$0.14$	$5.30$

Table 2: Concept accuracy, AUC, and leakage probe results (% accuracy, mean

\pm

std). Nat.: native task accuracy; Cont./Disc./Emb.: linear probes on continuous, discretized, and internal-embedding concept outputs.

\Delta_{b}

\Delta_{enc}

\Delta_{emb}

quantify bypass, encoding, and embedding leakage.

\dagger

: fully constrained configuration of the ablation (Section 5.2 ), shown for reference; its predictions come only from the probe, so

\Delta_{b}=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	$82.53$ $\pm 0.16$	$84.03$ $\pm 0.49$	$64.66$ $\pm 0.62$	$60.57$ $\pm 0.57$
ResNet50	Specific	Concept-only	$95.79$ $\pm 0.13$	$92.85$ $\pm 0.21$	$72.11$ $\pm 0.55$	$72.59$ $\pm 0.68$
BagNet-33	Shared	Concept-only	$77.21$ $\pm 0.52$	$70.47$ $\pm 3.79$	$20.63$ $\pm 5.30$	$13.40$ $\pm 4.33$
Task supervision

Table 3: Systematic ablation of the design axes of Section 5 (mean

\pm

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.

\dagger

: 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

Panel of Figure 3 — 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.

Panel of Figure 4 — 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,

\sim

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.

Panel of Figure 5 — 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 $\|w_{i}\|=1$ . 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 $\|w_{i}\|$ 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.

$\alpha$	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

\alpha

for LC-CBM trained with class-level and instance-level annotations. Instance-level supervision consistently improves localization, particularly at stricter thresholds.

Region	Koh	Instance	$\Delta$
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	$1\times 10^{-4}$
weight_decay	$1\times 10^{-4}$
batch_size	32
image_size	$224\times 224$
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 $\to$ Instance GT	Instance-trained $\to$ Koh GT	Koh $\to$ Koh (matched)	Instance $\to$ 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.

Panel of Figure 7 — 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.

Panel of Figure 8 — 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.

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