Towards Robust and Reliable Concept Representations: Reliability-Enhanced Concept Embedding Model

Bihan Wen; Satoshi Tsutsui; Winnie Pang; Xiyu Wang; Yuxuan Cai

REVIEW 3 major objections 8 minor 28 references

Towards Robust and Reliable Concept Representations: Reliability-Enhanced Concept Embedding Model

T0 review · 3 major / 8 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read A new concept-embedding model claims to resist background shifts by disentangling irrelevant features and aligning same-concept embeddings across samples.

desk verdict A solid, well-ablated empirical paper on making concept embeddings robust, but the signature mixup mechanism trains on mean-aligned inputs that differ from test-time inputs, so the gains may be partly a training artifact. read the letter →

arxiv 2502.01191 v1 pith:O4LO4BMK submitted 2025-02-03 cs.CV

Yuxuan Cai , Xiyu Wang , Satoshi Tsutsui , Winnie Pang , Bihan Wen This is my paper · ORCID

classification cs.CV

keywords ConceptBottleneckModelsEmbeddinginterpretablemachinelearningdistributionshiftrobustnessdisentangledrepresentationsemanticalignmentmixupScore

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Concept Bottleneck Models make predictions through human-understandable intermediate concepts, but those concepts are often unreliable: they encode background and other irrelevant content, and the same concept looks different from sample to sample. This paper proposes the Reliability-Enhanced Concept Embedding Model (RECEM), which attacks both failure modes at once. Concept-Level Disentanglement strips concept-irrelevant information out of the embedding with an adversarial gradient-reversal layer and a reconstruction decoder, while Concept Mixup pulls active-concept embeddings toward a per-concept mean embedding so the same concept stays semantically consistent across images. Together the two mechanisms are claimed to make concept representations faithful enough that downstream task accuracy improves on CUB, CelebA, and AwA2 and, on the TravelingBirds background-shift benchmarks, RECEM outperforms all baselines by several points. A sympathetic reading: if this holds, concept-based interpretability no longer has to be bought with robustness.

What carries the argument

The load-bearing objects are the positive and negative concept embeddings $\phi^+_k(h)$ and $\phi^-_k(h)$ of a Concept Embedding Model, which are blended into $\hat{c}_{i,k}$ by the predicted activation probability. RECEM adds two mechanisms on top: (1) Concept-Level Disentanglement, an encoder–decoder pair in which an auxiliary encoder $E_{\mathrm{dis}}$ extracts a concept-irrelevant vector $\hat{z}_i$, a Gradient Reversal Layer plus HSIC penalty pushes task information out of $\hat{z}_i$, and a decoder reconstructs the latent $h_i$ to preserve rich information; and (2) Concept Mixup, which replaces the active part of each concept embedding with a convex combination $\beta\bar{c}^+_k + (1-\beta)\hat{c}^+_{i,k}$ of the per-concept mean and the sample embedding, so the label predictor is trained on semantically aligned concepts. The final objective is $L_{\mathrm{task}} + \alpha L_{\mathrm{concept}} + \lambda_m L_m + \lambda_{\mathrm{cvd}} L_{\mathrm{cvd}} + \lambda_{\mathrm{rec}} L_{\mathrm{rec}}$.

What would settle it

Train RECEM exactly as specified, then evaluate the task classifier on the unadjusted embeddings $\hat{C}$ as the paper does, and compare against a variant trained directly on $\hat{C}$ with the same auxiliary losses. If the two accuracies are equal, Concept Mixup's benefit is real; if the mean-aligned training variant loses most or all of its TravelingBirds gain, the reported robustness is an artifact of the alignment shortcut rather than evidence of more reliable concepts.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the two observed failure modes of Concept Embedding Models—entanglement with concept-irrelevant features and semantic inconsistency of the same concept across samples—can be treated as optimizable objectives rather than accepted limitations. By adding a disentanglement loss (adversarial cross-entropy with a Gradient Reversal Layer plus HSIC regularization) and a mixup loss that aligns active concept embeddings toward their class mean, RECEM produces concept embeddings with higher cosine similarity under background perturbation and higher Concept Alignment Score. On the three TravelingBirds variants, RECEM reaches 64.1%, 64.0%, and 65.0% task accuracy versus roughly 60–62% for the best baselines. The paper's conclusion is that reliability of the intermediate concept representation is the lever: when concepts are faithful, downstream accuracy, human intervention effectiveness, and domain-shift robustness all improve together.

Load-bearing premise

The central premise is that training the label predictor on concept embeddings pulled toward their per-concept means does not harm it when, at test time, it receives the raw unadjusted embeddings—this train/test distribution shift is never examined.

Editorial extensions

If this is right

On the three TravelingBirds background-shift test sets, RECEM holds 63.99–65.00% task accuracy while the best baselines sit near 60–62%, so concept reliability translates directly into distribution-shift robustness.
Concept Alignment Score rises sharply (CUB: 93.2 vs CEM's 86.1; CelebA: 84.4 vs 79.5), meaning the learned concepts line up with human ground-truth labels more faithfully.
Human concept interventions become more effective: at higher intervention ratios RECEM approaches near-perfect task accuracy on CUB and CelebA, and it also leads on CelebA with incomplete concept annotations.
The disentanglement and mixup mechanisms transfer to fuzzy concept bottleneck models, lifting Fuzzy-CBM task accuracy on CelebA by more than 10 points (33.8% to 44.3%), though Bool-CBM gains are marginal.
Ablation confirms both components matter: removing either Concept Mixup or the disentanglement losses consistently degrades task accuracy across datasets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An unexamined gap: the task classifier is trained on mean-aligned embeddings $\dot{C}_i$ from Equations 14–17 but evaluated on unaligned embeddings $\hat{C}$ from Equation 1; if the decision boundary relies on the mean-shifted component, the claimed mixup benefit could shrink or reverse, and the paper does not analyse this mismatch.
A natural extension would be to apply the same mean alignment at test time, or to train the classifier directly on unadjusted embeddings, and compare the two; this would isolate whether the robustness comes from genuinely disentangled concepts or from a train/test alignment shortcut.
The higher OIS on CUB (56.5 vs CEM's 43.5) suggests the method may trade one form of leakage for another on correlated concepts; a leakage metric that does not assume concept independence could settle whether RECEM's representations are truly cleaner.
Since Concept Mixup only aligns active concepts toward their mean, a testable extension would apply the same alignment to inactive concepts or to concept co-occurrence structure, which could further improve consistency in densely correlated attribute datasets like CUB.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First thing you should know: this is a legitimate empirical paper, not a noisemaker. The method is a clean combination of two regularizers, adversarial/HSIC disentanglement and a per-concept mean-alignment mixup, and the authors test it properly: multiple datasets, five seeds, confidence intervals, ablations, and sensitivity analysis. The task-accuracy gains are real in the tables, especially on TravelingBirds background shifts (+4 points over CEM), and the extension to Fuzzy-CBM is a useful sanity check.

The soft spot that matters is the mixup training/inference mismatch. Equation 14 replaces active embeddings with a dot product of the per-concept mean and the sample embedding, and Equation 17 trains the label predictor f on the adjusted vector. At test time f gets the unadjusted embeddings from Equation 1. The paper never discusses this distance. It is not necessarily fatal, because the standard task loss still trains f on the unadjusted embeddings, so the classifier sees both distributions, but the ablation removing L_m removes both the alignment signal and the mismatched training distribution. That means the ablation cannot isolate representation quality, and the robustness gains in Table 3 could partly come from f leaning on the mean-aligned component. The authors should either analyze the train/test discrepancy or release code so reviewers can check it.

The CAS improvements are also partly by construction: training directly pulls active embeddings toward the mean, so cosine similarity and CAS go up. That does not make the method useless, but CAS is not independent evidence for reliability when it is a training target.

Minor issues: the GRL coefficient lambda is never specified; there is no code release; and the abstract says "consistently outperforms" while Table 1 shows AwA2 concept accuracy slightly below CEM (97.849 vs 98.048), though task accuracy wins. The appendix also shows OIS gets worse on CUB for RECEM (56.5 vs 43.5), which the authors attribute to concept correlations. That is an honest note, but it complicates the claim that disentanglement always reduces leakage.

Who this is for: researchers working on concept bottleneck robustness or interpretable ML. It is a practical recipe, not a theoretical breakthrough. The train/test mismatch question is easy to settle, and this paper deserves referee time to settle it.

Referee Report

3 major / 8 minor

Summary. The paper proposes RECEM, an extension of Concept Embedding Models (CEM) with two additional mechanisms: Concept-Level Disentanglement, which uses an encoder-decoder with adversarial gradient reversal and HSIC regularization to remove concept-irrelevant information from concept embeddings, and Concept Mixup, which aligns active concept embeddings toward a per-concept mean during training. The authors evaluate RECEM on CUB, CelebA, AwA2, and TravelingBirds, reporting improved task accuracy, concept accuracy, and Concept Alignment Score over CBM, ProbCBM, Coop-CBM, and CEM, together with ablations and hyperparameter sensitivity experiments.

Significance. If the reported results hold, the paper makes a useful contribution to concept bottleneck models by addressing two concrete failure modes: sensitivity to background changes and intra-concept semantic inconsistency. The experimental study is reasonably thorough in its coverage of datasets and baselines, and the appendix contains meaningful additional checks: per-loss ablations (Table 1), hyperparameter sensitivity (Table 4), intervention curves (Figure 5), and attempts to port the mechanisms to Bool-CBM and Fuzzy-CBM (Appendix A.5). The main unresolved question is whether the gains attributed to Concept Mixup survive a correct train/test protocol, because the training-time input to the label predictor differs from the test-time input; this and the leakage metric result on CUB need to be addressed before the central claim can be accepted.

major comments (3)

[4.4, Eqs. (14) and (17)] The label predictor f is trained on adjusted embeddings ˙C_i that use ground-truth masks and the training-set mean ¯c+_k, but at test time f receives unadjusted embeddings ˆC_i from Eq. (1). The paper never quantifies the distribution shift between ˙C_i and ˆC_i nor studies how f transfers across this shift; if f relies on the mean-aligned component, the task-accuracy gains in Table 3 and the L_m ablation gap in Table 1 could be inflated by the train/test mismatch rather than by improved concept reliability. Please provide an analysis of the input discrepancy, or train f only on unadjusted embeddings while keeping L_m as a regularizer on the concept encoder, or evaluate a test-time version of the alignment (e.g., predicted masks or a running mean) and show that the gains persist.
[A.4, Table 5] On CUB, RECEM has a higher Oracle Impurity Score (56.541) than CEM (43.54), meaning more concept leakage according to this metric. The paper attributes this to correlated concepts and questions the validity of OIS, but this is the only direct leakage measurement reported, and it contradicts the abstract's claim that the disentanglement component isolates concept-irrelevant features. Please either provide an alternative leakage measure that supports the claim on correlated-concept datasets, or explicitly scope the disentanglement claim to datasets with near-independent concepts.
[5.2, Table 2 with Eqs. (14)-(15)] The Concept Alignment Score improvement is partly by construction because L_m directly optimizes active embeddings toward the mean of the model's own embeddings, which mechanically reduces intra-concept variance and can increase alignment measures; the target is self-referential because the mean is computed from the current model. The CAS gap therefore does not by itself establish that the representations are more semantically faithful. Please report an independent evaluation of embedding quality (e.g., intervention accuracy under predicted masks, or a transfer/zero-shot check) and/or show that the improvement is not a collapse to a trivial point embedding.

minor comments (8)

[4.2, Eq. (6)] The inequality asserting that prediction on mean embeddings is always better than on sample-specific embeddings is not generally true and is not proved; it should be presented as a heuristic motivation or empirically validated.
[4.3 and 4.4] The symbol β is used for both the HSIC annealing weight in Eq. (11) and the mixup ratio in Eq. (14); clarify whether these are the same hyperparameter and specify the annealing schedule.
[4.3, Eq. (10)] The gradient reversal coefficient λ is never given a value or schedule; please report it.
[Figure 1 caption] The caption refers to 'CDCEM' while the method is called RECEM; unify the naming.
[Figures 7 and 8] The two figure captions are identical, which appears to be a copy-paste error; make the captions describe the respective panels.
[Table 2] Table 2 reports CAS for only CEM, Fuzzy-CBM, and RECEM; for completeness, report CAS for all baselines listed in Table 1.
[5.1] The paper says all models use identical settings with SGD but does not report learning rate, weight decay, number of epochs, or batch size; include these for reproducibility.
[4.4] The name 'Concept Mixup' is misleading: Eq. (14) implements attraction to a mean embedding, not a mixup between two or more samples; consider renaming the mechanism or clarifying the terminology.

Circularity Check

1 steps flagged · score 4.0 of 10

The concept-consistency evidence is partly by construction: Concept Mixup directly optimizes closeness to the model's own mean embedding, and the same closeness is then reported as a reliability gain.

self definitional [Section 4.2 Eq. (5); Section 4.4 Eqs. (14)-(17); evidence in Section 5.2 and Fig. 7]
"Eri∼D h ∥ˆci,k − ¯ck∥2 2 i ... ˙ci,k = µi,k β¯c+ k + (1 − β)ˆc+ i,k + (1 − µi,k)ˆci,k ... Lm = − 1 N P i P m yi,j log fm [˙ci,1, . . . ,˙ci,K]"

The paper defines concept unreliability as distance from the mean embedding (Eq. 5), then defines Concept Mixup to pull active embeddings toward the training-set mean (Eqs. 14-15) and trains the downstream predictor on these mean-pulled inputs (Eq. 17). It then reports higher cosine similarity between same-concept embeddings and higher CAS as evidence of reliability. Since the reported consistency metric is precisely the quantity being minimized by the objective, the improvement is enforced by construction rather than independently verified. The target mean is computed from the model's own embeddings (Eq. 15), making the reference self-referential.

full rationale

The central circular step is confined to the concept-consistency claims. Eq. 5 defines inconsistency as variance around the mean embedding; Eqs. 14-17 directly minimize that variance by blending active embeddings with the training-set mean and training the classifier on the blended inputs. The paper's later statements that Concept Mixup 'ensures consistent, semantically aligned concept representations' and the Fig. 7 cosine-similarity evidence are therefore partly restatements of the training objective, not independent confirmations. The task-accuracy results in Tables 1 and 3, however, are measured on held-out test sets using the unadjusted embeddings of Eq. 1, so they are not forced by this construction. A separate weakness, which I treat as a correctness risk rather than circularity, is that Eq. 17 trains the label predictor on adjusted embeddings ˙Ci while inference uses unadjusted ˆCi; this train/test input-distribution shift is never analyzed, so attributing all task-accuracy gains to improved concept reliability is not fully supported. There is no load-bearing self-citation: the CEM framework is cited from external authors, and the paper does not invoke any uniqueness theorem from its own prior work. Overall, one metric is self-definitional, but the main benchmark numbers retain independent content, yielding a partial circularity score of 4.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The method rests on five hand-set hyperparameters and four domain assumptions about ground-truth concept supervision, the efficacy of adversarial disentanglement, the stability of the mean embedding, and the transfer from adjusted to unadjusted embeddings. No new external entities are introduced.

free parameters (5)

lambda_m (concept mixup loss weight) = 0.1
Selected by validation performance in preliminary experiments; Table 4 sweeps 0.01 to 1.0.
lambda_cvd (concept vector disentanglement loss weight) = 0.05
Selected by validation; Table 4 sweeps 0.01 to 0.5.
lambda_rec (reconstruction loss weight) = 1.0
Selected by validation; Table 4 sweeps 0.1 to 5.0.
beta (annealing coefficient) = increases from 0, schedule unspecified
Controls both the HSIC weight and the proportion of mean embedding in Concept Mixup; Figure 4 varies it but no formula is given.
lambda (GRL gradient reversal coefficient) = not specified
Appears in Equation 10 as scaling the backward gradient by minus lambda; no value or schedule is provided.

assumptions (5)

domain assumption Ground-truth concept labels are available for all training samples and are used to build the adjusted embeddings in Equations 8 and 14.
The disentanglement and mixup losses rely on the mask from ground truth; this holds for the used datasets but may not hold in semi-supervised or incomplete annotation scenarios.
domain assumption The Gradient Reversal Layer removes concept-relevant information from the irrelevant feature vector.
Adversarial training is assumed to force classification signals into the concept embeddings; this is a heuristic, not a proven guarantee.
domain assumption The semantic mean embedding is a stable, meaningful reference for each active concept.
The mean is computed from the model's own embeddings, so it could be noisy or collapse if embeddings are highly variable; the paper does not analyze this risk.
domain assumption The classifier trained on adjusted embeddings transfers to unadjusted embeddings at test time.
The mixup loss uses adjusted embeddings, but inference uses the original embeddings; the paper does not analyze this train and test distribution shift.
domain assumption Standard dataset splits and evaluation protocols for CUB, CelebA, AwA2, and TravelingBirds are adopted without modification.
The paper relies on splits from Koh et al. 2020 and Zarlenga et al. 2022, which are standard but not independently revalidated here.

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Cite this review

Pith. "Pith review of Towards Robust and Reliable Concept Representations: Reliability-Enhanced Concept Embedding Model." pith.science (2026). https://pith.science/paper/O4LO4BMK

@misc{pith2026250201191,
  author       = {Pith},
  title        = {Pith review of: Towards Robust and Reliable Concept Representations: Reliability-Enhanced Concept Embedding Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O4LO4BMK}},
  note         = {Machine review of arXiv:2502.01191}
}

read the original abstract

Concept Bottleneck Models (CBMs) aim to enhance interpretability by predicting human-understandable concepts as intermediates for decision-making. However, these models often face challenges in ensuring reliable concept representations, which can propagate to downstream tasks and undermine robustness, especially under distribution shifts. Two inherent issues contribute to concept unreliability: sensitivity to concept-irrelevant features (e.g., background variations) and lack of semantic consistency for the same concept across different samples. To address these limitations, we propose the Reliability-Enhanced Concept Embedding Model (RECEM), which introduces a two-fold strategy: Concept-Level Disentanglement to separate irrelevant features from concept-relevant information and a Concept Mixup mechanism to ensure semantic alignment across samples. These mechanisms work together to improve concept reliability, enabling the model to focus on meaningful object attributes and generate faithful concept representations. Experimental results demonstrate that RECEM consistently outperforms existing baselines across multiple datasets, showing superior performance under background and domain shifts. These findings highlight the effectiveness of disentanglement and alignment strategies in enhancing both reliability and robustness in CBMs.

Figures

Figures reproduced from arXiv: 2502.01191 by the authors.

**Figure 1.** (a) The model predicts cˆ and cˆ ′ , corresponding to the original image and the image with a background shift. Reliable concept representations should be robust to irrelevant variations and exhibit consistent semantic meanings. (b) shows the cosine similarity distribution between embeddings before and after the background change, reflecting model sensitivity to irrelevant features. The results indicate that CEM (b… view at source ↗

**Figure 2.** An intuitive illustration of the proposed mechanisms, Concept-Level Disentanglement and Concept Mixup. intermediate concepts. Despite their significant potential, CBMs face challenges in ensuring reliable concept representations, which can propagate to downstream tasks and undermine robustness and reliability (Furby et al., 2023; Havasi et al., 2022). Inspired by Concept Embedding Models (CEMs) (Zarlenga et al., 20… view at source ↗

**Figure 3.** Overview of the proposed RECEM architecture, highlighting three key components with numbered dashed boxes: (1) ConceptLevel Disentanglement, where Edis extracts concept-irrelevant features zˆi and Drec ensures rich semantic information within the concept embeddings; (2) Concept Mixup, a mechanism aligning and proportionally mixing true concept embeddings (indicated by the green dashed box) across samples to achieve… view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Task accuracy under varying levels of human intervention in concept predictions for different models [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Each pair of heatmaps compares the attention focus of the undecoupled concept encoder (left) and the disentangled concept encoder (right). The images clearly show how our method effectively isolates concept-relevant features, avoiding spurious background correlations. …

**Figure 7.** Figure 7: Cosine similarity distributions of concept embeddings before and after background variations. RECEM maintains higher similarity, showing its robustness against background shifts compared to baseline methods. To provide further evidence of semantic inconsistency, we inc…

**Figure 8.** Figure 8: Cosine similarity distributions of concept embeddings before and after background variations. RECEM maintains higher similarity, showing its robustness against background shifts compared to baseline methods. A.4. Concept Leakage Within RECEM Concept Bottleneck Models o…

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

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