InfoCons: Identifying Interpretable Critical Concepts in Point Clouds via Information Theory

Dear Reviewer LVUY,

We sincerely thank you for your thorough review and valuable comments on our paper. We have summarized your concerns into three parts and provided our responses as follows:

1: Balancing Fidelity and Conceptual Coherence

Thank you for raising an important question. In our work, we examine the balance between fidelity (faithfulness) and conceptual coherence (interpretability) from two perspectives:

• (i) Limitations of existing methods: As discussed in lines 68–87 (left part), existing approaches often lack either conceptual coherence or faithfulness, which we attribute to the absence of a learnable, unbiased prior.
• (ii) Challenges in balancing conceptual coherence: When a learnable prior is introduced (Sec. 3.2, line 193), we observe that feature entanglement among neighboring points leads to a conflict between fidelity and conceptual coherence. To address this issue, in Def. 3.2, we introduce the term $\text{sg}(1-\hat m) \odot \epsilon$ to compensate for information loss caused by selecting critical points while excluding their entangled neighbors. A detailed discussion of this mechanism is provided in lines 201 (right) to 251 (left).

As a result, as shown in Fig. 9, the test accuracy remains stable within a narrow range (92.22% to 92.26%) across different values of $\beta$. It is attributed to the compensation term, which injects Gaussian noise to replace the influence of unimportant yet entangled points, effectively mitigating the conflict.

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2: Clarity of Figures, Mathematical Notation, and Novelty of Attention Bottleneck

• Concerns About Notations and Figure Clarity in Fig. 2: We acknowledge that some implementation-specific notations (e.g., $\hat{m}, \mu_z, \sigma_z, \epsilon$) cause clarity issues in Fig. 2-(b). To improve readability, we will relocate these notations to Fig. 5, which will focus on the detailed workflow.
• Concerns About the Novelty of Attention Bottleneck: Attention Bottleneck (AB) is integrated into InfoCons because it can handle data of varying lengths (e.g., different numbers of points). We want to clarify that the main contribution of InfoCons lies in how AB is integrated into our framework. For example, directly applying AB (as a straightforward "selection strategy" in Def. 3.1) is inappropriate for some PC models, as it introduces conflicts between fidelity and conceptual coherence, as mentioned earlier. As presented in Def. 3.2 and Fig. 2-(b) of the current manuscript, we demonstrate how AB (denoted as $\theta$) serves as a component of our IB-based explanation framework, which constitutes our main contribution. We recognize that relocating the lower-left portion of Fig. 2-(b) to Fig. 5 would present our contributions.

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3: Evaluating on More Recent Point Cloud Models

We appreciate the reviewer’s suggestion to validate our method on more recent point cloud models. In the current manuscript, we evaluate eight PC models spanning three distinct architecture types: non-hierarchical MLP-based, hierarchical MLP-based, and self-attention-based models (details in Appendix C). We conduct a further survey and find that these models encompass the majority of widely adopted point cloud models in both research and practice, including those used in adversarial attacks.

To further assess our method on a recent model, we conduct a pilot study on Sonata [1] (CVPR 2025 accepted), a newly proposed self-supervised pretraining framework for scene understanding. Sonata utilizes a novel hierarchical self-attention-based encoder. Our pilot study extends our method as follows (similar to the object detection experiments in Appendix B.2):

• We follow Sonata’s official setup and re-implement linear probing on the S3DIS dataset for 3D semantic segmentation. Given a test PC, our goal is to explain why the model incorrectly segments part of a table as a chair, as shown in subfig-(I) in this link: https://ibb.co/FqXg3tD1
• The score map based on InfoCons is shown in subfig-(III). Results show that the interaction between the table‘s leg and the chair's seat leads to the incorrect segmentation of the table's leg.
• More specifically, the implementation of InfoCons (Def.3.2) has made the following adaptations: (i) Replace the sample-wise CE loss with an aggregated point-wise CE loss (i.e., I(C; Y)) over points and target labels of interest, and the information loss term (i.e., I(C; X)) remains unchanged. (ii) To reduce computational overhead, we learn the prior using only the target PC, which contains about a million points.

Finally, regarding the reviewer's suggestions, we will correct the formatting inconsistencies in Appendix B. We appreciate the detailed review and are grateful for your comments. We hope this additional analysis addresses your concerns.

[1] Sonata: Self-Supervised Learning of Reliable Point Representations, arxiv25

Best regards,

Authors

Dear Reviewer vGFq,

We sincerely thank you for your thorough review and detailed comments on our paper. In response to your concerns regarding the statement on “Good Explanations” and our qualitative comparison, we provide the following clarifications.

1: Clarification on “Good Explanations”

Our definition of what constitutes a good explanation for point cloud models builds upon widely accepted principles in interpretability research, which we clarify as follows:

• (i) The desiderata of explanation methods, faithfulness and interpretability, date back to LIME [1] (KDD 2016) and have since been widely adopted in subsequent interpretability methods (e.g., LIME3D), as stated in the abstract of the LIME paper:

"...a novel explanation technique that explains the predictions of any classifier in an interpretable and faithful manner ...".

• (ii) In our work, we propose a statement on a good critical subset (i.e., an ideal critical subset should be faithful to model predictions and conceptually coherent with human prior, as detailed in line 67, left) in the context of critical-point-based explanations for point cloud data. This aligns with the notion used in Grad-CAM [2] (IJCV 2019). Grad-CAM also introduced a widely accepted principle for what constitutes a good visual explanation in image classification (page 2 of the Grad-CAM paper):

"What makes a good visual explanation? Consider image classification – a ‘good’ visual explanation from the model for justifying any target category should be (a) class-discriminative (i.e. localize the category in the image) and (b) high-resolution (i.e. capture fine-grained detail)."

However, the process of explaining image classification is significantly different from that of explaining point cloud data. For example, *capturing fine-grained detail* in an image often implies a clear boundary between objects of interest and unimportant background pixels, whereas such a boundary may not exist in point cloud data, which consists of thousands of unordered points (as we discussed in the right part of line 60).  

• (iii) We therefore adopt the term conceptual coherence, drawing from concept-level explanations [3-5], where human-understandable concepts provide a more general formulation of interpretability. In the image domain, concept-level explanations can be attributes labeled by humans [3] or selective patches [4, 5]. In our work, critical concepts can be intuitively described as selective sub-PCs that frequently appear in the training dataset and contribute significantly to corresponding labels. Here, we introduce two key adaptations: (i) The human prior is replaced with a learnable prior derived from the training dataset. (ii) Critical concepts are explicitly extracted/selected from the original PC.

To summarize, our claim is consistent with these widely accepted principles and appropriately formulated for point cloud data. We appreciate the reviewer’s suggestion and will include additional discussion in the appendix to clarify this point.

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[1] "Why should I trust you?" Explaining the predictions of any classifier. KDD 2016.

[2] Grad-CAM: Visual Explanations from Deep Networks via Gradient-Based Localization. IJCV 2019.

[3] Concept bottleneck models. ICML 2020.

[4] Approximating cnns with bag-of-local-features models works surprisingly well on imagenet. ICLR 2019.

[5] Explaining generalization power of a dnn using interactive concepts. AAAI 2024.

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2: Additional Qualitative Analyses

In addition to Fig. 6 in Sec. 4.1, we have provided further qualitative comparisons in Appendix-Fig. 14 in the current manuscript.

Furthermore, in response to the reviewer’s suggestion, we conduct additional qualitative comparisons following the same settings as Sec. 4.1 on 20 samples (i.e., all test samples in the 'flower_pot' class of the ModelNet40 dataset) across five approaches. The results are available at this link: https://ibb.co/zhG7KGQs (this may take some time to load due to the image size). We will include these additional examples in Appendix D.1 (Additional Qualitative Results).

Additionally, since our method provides score maps for explanations, we have already conducted quantitative evaluations over the entire test dataset to rigorously assess its effectiveness. Specifically, we have conducted drop attack (Sec. 4.2), adversarial attack (Tab. 1), and data augmentation (Tab. 2) experiments. These quantitative evaluations provide measurable evidence of our method’s effectiveness.

We sincerely appreciate your insightful suggestions and will incorporate the additional qualitative results into our paper.

Best regards,

Authors

Dear Reviewer h8Li,

We sincerely appreciate your thorough review and your positive assessment of our work. Based on your feedback, we will refine the writing and presentation to enhance readability as follows:

1: Expanding the Related Work Section and Adjusting Paper Structure

In the current manuscript, we have integrated methodological comparisons with closely related approaches (e.g., CP, CP++, and PCSAM) within Sec. 3.1 (line 201) and Sec. 3.2 (line 252) to maintain narrative flow while avoiding redundancy. However, we acknowledge that an overview of point cloud interpretability literature in Sec. 2 would further benefit readers. To address this, we will

• (i) Introduce a new subsection in the Background section (Sec. 2) that specifically discusses prior attribution methods for point cloud models, including CP, CP++, and PCSAM.
• (ii) Expand the discussion of these methods in a new appendix section to provide a comprehensive review of existing interpretability methods for point cloud models, considering their architectural characteristics.

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2: Clarification of Figure 2 for Improved Understanding

Thank you for pointing out the clarity issue with Fig. 2. To improve its readability, we will revise the lower-left portion of Fig. 2-(b) to emphasize the high-level framework. We will remove implementation-specific notations (e.g., $\hat{m}, \mu_z, \sigma_z, \epsilon$) from Fig. 2-(b). After formally introducing these notations in Eq. 5 and Eq. 6 on page 4, we will present the implementation-specific details (i.e., $\hat{m}$) in Fig. 5 to clarify the overall data flow. This revision will ensure that Fig. 2 centers on the high-level framework, while Fig. 5 provides a more detailed view.

We greatly appreciate your time and valuable feedback, which will significantly enhance the clarity and presentation of our paper.

Best regards,

Authors