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arxiv: 2506.05014 · v2 · submitted 2025-06-05 · 💻 cs.LG · cs.AI· stat.ML

Towards Reasonable Concept Bottleneck Models

Nektarios Kalampalikis , Kavya Gupta , Georgi Vitanov , Isabel Valera This is my paper

Pith reviewed 2026-05-19 11:11 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML
keywords concept bottleneck modelsinterpretable machine learningconcept reasoningmodel interventionsmissing conceptsconcept leakage
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The pith

CREAM models let users bake concept relationships directly into the architecture of concept bottleneck models.

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

The paper introduces Concept REAsoning Models (CREAMs) as a flexible way to build concept bottleneck models that explicitly incorporate known relationships among concepts and from concepts to the prediction target. By encoding things like mutual exclusivity, hierarchies, or correlations into the model structure itself, CREAM avoids having to learn these links from data alone and supports direct interventions on concepts. An optional side-channel can fill in for missing concepts without letting the model drift away from concept-based reasoning. Experiments show these models match black-box performance while remaining intervenable and avoiding concept leakage even when the concept set is incomplete.

Core claim

CREAMs extend standard concept bottleneck models by architecturally encoding arbitrary C-C relationships such as mutual exclusivity or hierarchical associations together with potentially sparse C to Y mappings, and they optionally add a regularized side-channel that lets the model reach black-box accuracy under missing concepts while keeping predictions concept-grounded.

What carries the argument

The CREAM architecture that directly wires known concept-concept and concept-task relationships into the model's reasoning layers, plus an optional regularized side-channel for incomplete concept sets.

If this is right

  • Direct interventions on concepts become more efficient because the model already respects the encoded relationships.
  • Concept leakage is reduced because the architecture prevents the model from bypassing the concept layer.
  • Task performance stays competitive with black-box models even when only a subset of concepts is observed.
  • Predictions remain more interpretable because the side-channel is regularized and the core reasoning stays concept-grounded.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same wiring approach could be applied to other bottleneck-style architectures beyond classification, such as regression or generative tasks.
  • If the encoded relationships turn out to be only approximately correct, the side-channel might still allow graceful degradation rather than catastrophic failure.
  • Future work could test whether automatically discovering and then wiring the relationships produces similar gains without requiring manual prior knowledge.

Load-bearing premise

Practitioners already know the correct concept-concept and concept-task relationships and can encode them accurately without adding new errors.

What would settle it

An experiment in which the encoded relationships are deliberately set to incorrect values and the model is then checked for drops in task accuracy, failed interventions, or increased concept leakage compared with a standard CBM.

Figures

Figures reproduced from arXiv: 2506.05014 by Georgi Vitanov, Isabel Valera, Kavya Gupta, Nektarios Kalampalikis.

Figure 1
Figure 1. Figure 1: Reasoning graph for FMNIST from [52]. The white nodes represent concepts used in iFMNIST, while the gray nodes introduce additional seasonality-related concepts to form cFMNIST, addressing concept incompleteness. Concepts and classes within the solid boxes are mutually exclusive. To address these limitations, we propose Concept REAsoning Models (CREAM), a novel family of CBMs, which enforce a desired struc… view at source ↗
Figure 2
Figure 2. Figure 2: Partial illustration of CUB’s reasoning graph is shown, where concepts are represented as [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reasoning graph for predicting “Smiling” (Y ) in CelebA dataset [30]. The graph shows the relationships between most correlated concepts (C) within the face region that directly contribute to smiling. Types of C-C Relationships. AC allows us to capture various types of relationships among the concepts. First, it allows us to capture both the hierarchical and bidirected concept relationships that lead to as… view at source ↗
Figure 4
Figure 4. Figure 4: Sketch of CREAM, where the backbone output is split into concept ( [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Impact of dropout rates on channel importance. Models with complete concept sets require less side-channel regularization. Interpretability in the presence of a side-channel. Given that our model incor￾porates a black-box side-channel, it is crucial to verify that predictions primarily rely on the concepts rather than the side-channel. To quantify this, we introduce a new metric called Concept Channel Impo… view at source ↗
Figure 6
Figure 6. Figure 6: Impact of individual interventions on task accuracy. The baseline model is [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Mean values ± standard deviation of the permutation feature importance of both channels, in all datasets for S-CREAM, averaged over 5 seeds. Increasing p leads to an increase in PCI and decreases PSI. C Dataset Details A summary of the datasets used in our experiments is provided in [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Expanded version of the illustration of CREAM found in the main text, providing additional [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Impact of group interventions compared to individual ones, on task accuracy. Group [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Correlation matrix for the CREAM models reported in Table 2. For each concept we draw [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Correlation matrix for the CREAM models reported in Table 2. For each concept we draw [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Covariance matrix of the outputs of the side-channel for CREAM. On the left, we report [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Concept and Task accuracies across different dropout rates (p [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Concept and Task accuracies across different [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Concept and Task accuracies across different [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Intervenability comparison of H-CREAM and S-CREAM. The latter slightly outperforms [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Correlation matrices of the output of the representation splitter ( [PITH_FULL_IMAGE:figures/full_fig_p026_17.png] view at source ↗
read the original abstract

We propose a novel, flexible, and efficient framework for designing Concept Bottleneck Models (CBMs) that enables practitioners to explicitly encode and extend their prior knowledge and beliefs about the concept-concept ($C-C$) and concept-task ($C \to Y$) relationships within the model's reasoning when making predictions. The resulting $\textbf{C}$oncept $\textbf{REA}$soning $\textbf{M}$odels (CREAMs) architecturally encode arbitrary types of $C-C$ relationships such as mutual exclusivity, hierarchical associations, and/or correlations, as well as potentially sparse $C \to Y$ relationships. Moreover, CREAM can optionally incorporate a regularized side-channel to complement the potentially {incomplete concept sets}, achieving competitive task performance while encouraging predictions to be concept-grounded. To evaluate CBMs in such settings, we introduce a $C \to Y$ agnostic metric that quantifies interpretability when predictions partially rely on the side-channel. In our experiments, we show that, without additional computational overhead, CREAM models support efficient interventions, can avoid concept leakage, and achieve black-box-level performance under missing concepts. We further analyze how an optional side-channel affects interpretability and intervenability. Importantly, the side-channel enables CBMs to remain effective even in scenarios where only a limited number of concepts are available.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes Concept REAsoning Models (CREAMs), a flexible extension of Concept Bottleneck Models that architecturally encodes prior knowledge on arbitrary C-C relationships (mutual exclusivity, hierarchies, correlations) and sparse C→Y links. It introduces an optional regularized side-channel to handle incomplete concept sets while encouraging concept-grounded predictions, along with a new C→Y agnostic metric for interpretability. Experiments claim that CREAM supports efficient interventions, avoids concept leakage, achieves black-box-level task performance under missing concepts, and remains effective with limited concepts, all without added computational overhead.

Significance. If the central claims hold, this work offers a practical way to inject domain knowledge into CBMs via architecture rather than post-hoc constraints, addressing a key limitation when concept sets are incomplete. The side-channel plus regularization and the new metric could improve both performance and evaluable interpretability in real-world settings. The manuscript's strengths include explicit handling of prior relationships and analysis of side-channel effects on intervenability.

major comments (2)
  1. [§3] The central claim that architectural encoding of C-C and C→Y priors plus side-channel regularization forces predictions to remain concept-grounded (even with missing concepts) is load-bearing for the 'avoid concept leakage' and 'black-box-level performance' assertions, yet §3 provides no derivation or constraint showing that the chosen regularization term mathematically prevents the side-channel from learning non-concept shortcuts.
  2. [§4.3] Table 2 and §4.3: the reported competitive performance and intervention results lack quantitative baselines, effect sizes, and cross-dataset behavior of the new C→Y agnostic metric, leaving the claim of black-box-level performance under missing concepts insufficiently verified.
minor comments (2)
  1. [Abstract] The abstract states 'without additional computational overhead' but this is not supported by explicit runtime or parameter counts in the experiments section.
  2. [§3.2] Notation for the side-channel regularization strength (listed as a free parameter) should be defined consistently with the loss term in Eq. (X) of §3.2.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address the major concerns regarding the theoretical justification for the side-channel regularization and the empirical validation of our results and metric.

read point-by-point responses

  1. Referee: [§3] The central claim that architectural encoding of C-C and C→Y priors plus side-channel regularization forces predictions to remain concept-grounded (even with missing concepts) is load-bearing for the 'avoid concept leakage' and 'black-box-level performance' assertions, yet §3 provides no derivation or constraint showing that the chosen regularization term mathematically prevents the side-channel from learning non-concept shortcuts.

    Authors: We agree that a formal mathematical derivation would provide stronger theoretical support. The regularization term is designed to minimize the side-channel's influence on the final prediction by penalizing deviations from concept-based reasoning. While we do not claim a hard constraint that completely eliminates shortcuts, the combination with the architectural priors encourages grounded predictions, as evidenced by our intervention experiments and leakage analyses. We will revise §3 to include a more detailed explanation of the regularization's intended effect and discuss its limitations in preventing all possible shortcuts. revision: partial

  2. Referee: [§4.3] Table 2 and §4.3: the reported competitive performance and intervention results lack quantitative baselines, effect sizes, and cross-dataset behavior of the new C→Y agnostic metric, leaving the claim of black-box-level performance under missing concepts insufficiently verified.

    Authors: We appreciate this point and will enhance the presentation in §4.3 and Table 2 by including quantitative baselines from standard CBMs and black-box models, along with effect sizes for the performance differences. Additionally, we will report the behavior of the C→Y agnostic metric across multiple datasets to better substantiate the interpretability claims under incomplete concept sets. revision: yes

Circularity Check

0 steps flagged

CREAM proposal introduces explicit architectural priors and a new agnostic metric; performance claims rest on external benchmarks rather than self-referential fits or definitions.

full rationale

The paper's core contribution is a new modeling framework that takes practitioner-provided C-C and C-Y relationships as explicit inputs and encodes them directly into the architecture (mutual exclusivity, hierarchies, sparse links, optional regularized side-channel). These encodings are not derived from the evaluation data; they are user-specified priors. The introduced C→Y agnostic metric is defined to measure reliance on the side-channel and is not fitted to the same performance numbers used to claim black-box-level results. Experiments compare against baselines on standard datasets, with no evidence that any reported prediction or grounding property reduces by construction to a parameter fit on the test set or to a self-citation chain. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on the assumption that domain experts can supply accurate relational constraints and that the side-channel regularization can be tuned without destroying concept grounding.

free parameters (1)
  • side-channel regularization strength
    Hyperparameter balancing the contribution of the optional side-channel against the concept bottleneck path.
axioms (1)
  • domain assumption Practitioners can accurately specify C-C and C-to-Y relationships
    The entire encoding mechanism depends on this input being correct and complete.

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