Title: Concepts' Information Bottleneck Models
Venue: NeurIPS 2025
Accepted: no
Keywords: Concept bottleneck models

Information bottleneck

Variational Inference
Abstract: Concept Bottleneck Models (CBMs) promise interpretable prediction by forcing all information to flow through a human-understandable "concept" layer, but this interpretability often comes at the cost of reduced accuracy and concept leakage. To solve this, we introduce an explicit Information Bottleneck regularizer on the concept layer---penalizing $I(X;C)$---to encourage minimal yet task-relevant concept representations. We derive two variants of this penalty and integrate them into the standard CBM training objective. Across six model families (hard/soft CBMs trained jointly or independently, ProbCBM, AR-CBM, and CEM) and three benchmark datasets (CUB, AwA2, aPY), IB-regularized models consistently outperform their vanilla counterparts---narrowing and in some cases closing the accuracy gap to unconstrained black-box networks. We further quantify concept leakage with two metrics (Oracle Impurity and Niche Impurity Scores) and show that IB constraints reduce leakage significantly, yielding more disentangled concepts. To assess how well concept sets support test-time corrections, we employed two intervention metrics (area under the intervention-accuracy curve and average marginal gain per intervened concept) demonstrating that IB-regularized CBMs retain higher intervention gains even when large fractions of concepts are corrupted. Our results reveal that enforcing a minimal-sufficient concept bottleneck improves both predictive performance and the reliability of concept-level interventions, thereby closing the accuracy gap of CBMs while improving their interpretability and ability to intervene.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a Concept Information Bottleneck model, which addresses the information leakage issue in Concept Bottleneck Models while preserving concept and label prediction accuracy through Information Bottleneck regularization.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The paper is overall well-written and well-organized.\n\n2. The experiments conducted in this paper are comprehensive.\n\n3. The proposed loss function is plug-and-play, making it easily applicable to various CBM models while effectively addressing their leakage issues.\n\nWeaknesses:\n\n1. The performance gains brought by the IB regularization appear to be marginal.\n\n2. Some reported results are inconsistent with prior work. For example, the label accuracy of CBM (SJ) reported in the original CBM paper (ICML 2020, https://arxiv.org/pdf/2007.04612) is around 80% (see Table 1 and Fig. 2), whereas this paper reports a significantly lower value of 70.8%.\n\n3. The authors should provide more detailed evidence to demonstrate how the proposed methods enhance the interpretability of CBMs. The numerical results in Table 2 are insufficient, as it is unclear what the reduction in OIS from 4 to 3 actually implies. For instance, the experiments in https://arxiv.org/pdf/2106.13314 offer a more intuitive demonstration of concept leakage in CBMs. It would be helpful to see a direct comparison between CBM and the proposed CIBM under such experimental setups.\n\nQUESTIONS:\nIf the authors can address the discrepancies in the reported results (Weakness 2) and provide more comprehensive and interpretable evidence of the improvements brought by the CIBM (Weakness 3), I would consider raising my overall evaluation of the paper.\n\nLIMITATIONS:\nThe rationale for why leakage can be mitigated through IB regularization appears to be heuristic, lacking a formal theoretical justification. However, I do not consider such a theoretical proof to be strictly necessary for the contribution of this paper.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes CIBM, an extension of Concept Bottleneck Models (CBMs) that incorporates an informational regularization term that is borrowed from the Information Bottleneck (IB) method of Tishby et al. (1999). The paper evaluates several variants of this method and shows that the BI-regularization term yields improved performance in terms of test time accuracy and concept leakage.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n- The paper proposes an interesting new method, with a substantial set of experiments. Overall, I'm inclined to think that this method has merit and could potentially make a valuable contribution to the NeruIPS community (but see my main question below).\n- This work is original in the sense that it combined existing techniques in a novel way and the motivation for integrating IB with CBMs is clearly conveyed. I find the concept leakage analysis particularly useful and directly related to the IB motivation.\n- The paper is well organized and clearly written.\n\n**Weaknesses**\n- While the paper presents a substantial set of experiments, many of them are not clearly motivated or insightful. For example, the paper considers 12 variants -- two bounds and 6 training settings (HJ / HI / SJ / Prob / CEM / AR ) -- but it's unclear why they are all equally interesting or useful. The current presentation of the paper lacks proper motivation of all these variants, giving an impression they are all considered simply because it's possible, not necessarily because they give unique insight into the problem/solution. \n- Relatedly, the E-CIB bound assumes that the concepts entropy $H(C)$ is constant, while this entropy is not constant given the implementation details in the appendix. Thus, this bound, even though it performs better than the SUB-CIB bound, does not seem to be well motivated, or at least this issue is not addressed in the main text. \n- The choice of $\\beta$ values seems quite arbitrary as well. Why these two particular values? The paper seems to incorrectly treat $\\beta$ as a constant rather than a free (hyper)parameter.\n- The main text is not self-contained and relies too much on the appendix for key details and results. For example, the dataset are not explained at all in the main text, the main results for sections 4.5 and 4.6 are only in the appendix. \n\n**Minor points and suggestions**\n- I think the main text would benefit from a concrete example to motivate and illustrate the method.\n- Table 1 is pretty hard to digest, I would consider visualizing these results with bar plots and then maybe moving the detailed table to the appendix.\n- Typos:\n   - lines 56-57: use either $K$ or $k$ in both instances\n   - line 125: shouldn't this be $I(X;Z)$? as in Eq.1?\n   - Eq 3: missing $E_{p(c)}$ for the third term\n\nQUESTIONS:\nMy main concern is that it's not entirely clear what is the big-picture contribution and/or deep new insight that this method can offer, beyond the technical results that seem somewhat incremental. If the authors can clarify this matter, that would be extremely helpful for assessing whether this paper merits publication at a top-tier ML venue like NeurIPS.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the issue of concept leakage in Concept Bottleneck Models (CBMs), which are representative interpretable models. To mitigate this problem, the authors propose applying an Information Bottleneck (IB) regularizer to the concept layer. The proposed method is shown to be effective across various CBM families.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths:\n- The paper clearly identifies the problem and proposes a well-motivated solution.\n- It explores multiple design choices and supports them with theoretical justifications.\n- The proposed method improves both prediction performance and mitigates concept leakage, as demonstrated through comprehensive experiments.\n- The authors also identify limitations in existing evaluation metrics and propose a new metric that better assesses the quality of the concept set, analyzing the results thoroughly.\n\n## Weaknesses:\n- While the method demonstrates effectiveness when applied to basic CBM families, there is no experimental comparison with CBMs that use other forms of information bottleneck techniques. Although the differences in approach are discussed conceptually, empirical comparisons would strengthen the evaluation of information leakage mitigation.\n\nQUESTIONS:\n- Can the authors provide a comparison with previous methods that also aim to reduce information leakage in CBMs or similar models?\n\n## Additional Suggestions:\n- In Figure 3, the improved TTI performance due to the IB regularizer is clearly visible for CEM, but less so for other methods. Consider revising the visualization to make this improvement more apparent across models.\n- In Figure E.1, the fact that the first and second columns correspond to different datasets is only indicated in the last row, which may be confusing. It would help to clarify this more explicitly.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes Concept Information Bottleneck Models (CIBM), a new theoretically inspired architecture to improve concept bottleneck models and reduce concept leakage by directly Incentivizing large mutual information between C and Y, while minimizing mutual information between X and C. With a range of experiments, they show this improves many features of CBMs across different architectures such as Class and concept accuracy and intervention effectiveness.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- Paper is well motivated and theoretically justified\n- Overall clearly written and easy to follow, but a few places could be improved\n- Impressive results on concept leakage and intervention effectiveness\n- Pretty good results in terms of accuracy improvement\n\n\nMajor Weaknesses:\n- Some weirdness in experimental results (see Questions), for example baseline CBM performance is lower than reported on the original CBM paper [12].\n\nMinor Weaknesses:\n- Not convinced by the measure of concept-set goodness(4.4), seems like this is closely connected to CBM quality and in the paper it is used to compare different CBMs with the same concept sets, not different concept sets. If the goal is to measure the concept set quality I think the metric should not depend on a particular CBM model.\n- Brief introduction in main text would be useful for several things introduced such as the datasets and the Concept Leakage metrics would be helpful.\n- The introduction categorization into four groups is confusing, what exactly are the four groups? Also seems like these groupings are not mutually exclusive, one method could belong to multiple of these groups, for example post-hoc explanations can be model-agnostic or model-specific.\n- Fig 3 has too many plots in one small fig making it impossible to see all the lines\n- Some qualititative examples showing interpretable decisions on different datasets would be helpful\n\nQUESTIONS:\n- In eq. 5 I don’t see any term corresponding to the I(X; C) term, is this correct? If yes why is this the case?\n- Why is the black-box accuracy so high on CUB? This seems higher than ones reported in other papers, for example the original CBM[12] paper reports 82.5% class accuracy. This leaves a large gap between CBM methods and black-box methods. \n- Similarly, why are the CBM results reported(SJ) much lower than original CBM paper (70.8% vs 80.1%)?\n- How are the results on sequential CBMs? I think the most commonly used CBM type is soft sequential but I don’t see any results on that.\n- What are the leakage results (Table 2) of IB_E?\n- Is the number for Table 3 AUC IB_B with 8 corrupt correct? Seems not in line with the trends?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-06"}