InfoCons: Identifying Interpretable Critical Concepts in Point Clouds via Information Theory
Authors: Feifei Li
Mi Zhang
Zhaoxiang Wang
Min Yang
Venue: ICML 2025 poster (2025)
Keywords: Information Theory
Interpretability
Point Cloud
Primary area: social_aspects->accountability_transparency_and_interpretability
TL;DR: InfoCons is an explanation framework for point cloud models that decomposes inputs into interpretable 3D concepts using information-theoretic principles, ensuring both faithfulness and conceptual coherence.

Abstract: Interpretability of point cloud (PC) models becomes imperative given their deployment in safety-critical scenarios such as autonomous vehicles. 
We focus on attributing PC model outputs to interpretable critical concepts, defined as meaningful subsets of the input point cloud.
To enable human-understandable diagnostics of model failures, an ideal critical subset should be *faithful* (preserving points that causally influence predictions) and *conceptually coherent* (forming semantically meaningful structures that align with human perception).
We propose InfoCons, an explanation framework that applies information-theoretic principles to decompose the point cloud into 3D concepts, enabling the examination of their causal effect on model predictions with learnable priors.
We evaluate InfoCons on synthetic datasets for classification, comparing it qualitatively and quantitatively with four baselines. 
We further demonstrate its scalability and flexibility on two real-world datasets and in two applications that utilize critical scores of PC.

InfoCons:
Identifying Interpretable Critical Concepts in Point Clouds via Information Theory
Feifei Li"
Mi Zhang'
Zhaoxiang Wang'
Min Yang
Abstract
Explanation
Application
inpur x
Interpretability of point cloud (PC) models be- comes imperative given their deployment in safety-critical scenarios such autonomous vehi- cles. We focus on attributing PC model outputs to interpretable critical concepts, defined as mean- ingful subsets of the input point cloud. To en- able human-underse eanntaddddertt diagnostics of model failures, an ideal critical subset should faith- ful (preserving points that causally influence pre- dictions) and conceptually coherent (forming se- mantically meaningful structures that align with human perception). We propose InfoCons, an explanation framework that applies information- theoretic principles to decompose the point cloud into 3D concepts, enabling the examination of their causal effect on model predictions with learn- able priors. We evaluate InfoCons on synthetic datasets for classification, comparing it qualita- tively and quantitatively with four baselines. We further demonstrate its scalability and flexibility on two real-world datasets and in two applications that utilize critical scores of PC.
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Figure 1. Attributing PC model outputs to group of interpretable critical concepts using InfoCons. The derived concepts, which conform to a specific semantically meaningful structure (i.e., con- ceptual cohesion), faithfully. The critical score map can also be integrated into multi- ple applications. Better viewed in color.
reflect their influence the model outputs
safety- scenarios like autonomous vehicles (Geiger et al., 2012). Interpretability has become a crucial issue in assessing the reliability of model decisions, and under- standing complex, nigh-dimensional deep neural networks has been a long-standing challenge. However, despite sub- stantial recent progress in the domains of 2D images and language (Deng al., 2024; Rai et al., 2024), research in the field of 3D data remains lacking. Challenges in developing explanation methods for point clouds arise from the signifi- cant domain gap between point clouds and other modalities, making direct application of 2D) methods less effective (Wu et al., 2015; Tan, 2023). Furthermore, the absence of well- established architectures and diverse modules complicates the development of faithful and broadly effective explana- tion method for various point cloud models.
1. Introduction
Point clouds are unordered sets of points representing the 3D world. Point cloud (PC) models directly take the point cloud as input and perform various downstream tasks such as classification, segmentation and object detection (Chang et al., 2015; Armeni et al., 2016). The advancements in deep learning-basse based PC models (Qi et al., 201 7a;b; Wang al., 2019; Guo et al., 2021: Ma al., 2022; Wu al., 2024) have significantly improved their performance 3D understanding tasks, paving the way for applications in
Previous study of point cloud explanation methods aim to extract point cloud subset critical for model decisions, collectively referred to as Critical Subset Theory (Qi et al., 2017a; Zheng et al., 2019; Kim et al., 2021; Levi Gilboa, 2023). These methods differ in how they define the im- portance of points. For instance, the maxpool- Crit- ical Points (CP) (Qi et al., 2017a) identify points indexed through maxpooling layer applied to features as critical, suggesting that stronger responses indicate greater impor- tance. Meanwhile, the gradient-base point cloud saliency map (PCSAM) (Zheng et al., 2019) utilizes the gradients of the CE loss w.E. spherical coordinates to rank salient
'School of Computer Science, Fudan University, China. Corre- spondence to: Mi Zhang <mi ami.zhang@e fuuan..duu.nn.. Min Yang <m_yang @
Proceedings of the 4dnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Identifying Interpretable Critical Concepts in Point Clouds
points, indicating that sensitivity to a target label reflects importance. Critical subsets can naturally explain model decisions in an interpretable way, mitigating the issue of in- formation redundancy, which arises from the large number of points representing the same amount of information.
We conduct both qualitative and quantitative evaluations of InfoCons using the synthesis dataset ModelNer40 (Chang et al., 2015), explaining eight models covering three types of structures: non non-hierarchical MLP- MLP-based, hierarchical MLP- based, and seff-attention-baseed We apply InfoCons to the saliency-guided mixup method SageMix (Lee et al., 2022) and the sensitivity-guidee attack SIAdv (Huang et al., 2022) to further enhance their performance. We also demonstrate the scalability of InfoCons on more challenging benchmarks, including the real-world object dataset ScanObjectNN (Uy et al., 2019) and outdoor scene dataset KITTI (Geiger et al., 2012).
However, existing methods have limitations in providing interpretable subsets that satisfy both faithfulness and con- ceptual cohesion. As theoretically illustrated in Fig. 2-(a), faithfulness means that the subset has direct causal effect on model predictions, thereby providing sufficient informa- tion about the model's behavior in cases of misclassification (e.g.. why the model confuses 'plant' with 'flower - as shown in Fig. 1). Meanwhile, conceptual cohesion encour- ages the subset to conform to a semantically meaningful structure that aligns with human perceptual priors (e.g., ob- ject parts like flower and pot/vase that can be identified as contributing to the misclassification). From this perspective, existing methods fail to satisfy both criteria. For example, the maxpool-based CP, which relies on the output of the PC encoder, neglects the influence of the subsequent clas- sifier, resulting in a lack of faithfulness to the entire PC model. Moreover, PCSAM approximates points removal by slightly perturbing points towards the PC centroid, introduc- ing a biased shape prior of centroid singularity'. This prior leads to biased attribution, producing critical subsets that are spatially concentrated in corners.
In summary, our main contributions are as follows:
We formalize the problem of extracting interpretable criti- cal subsets for deep PC models and provide an in-depth analysis on the limitations of existing methods in terms of faithfulness and conceptual cohesion.
We propose a novel framework, InfoCons, which applies information-theorett principles to decompose the point cloud into 3D concepts by learning a selective function with unbiased prior.
We conduct comprchensive experiments across three datasets, evaluating InfoCons three types of model structures and two application scenarios. Results show that InfoCons effectively extracts interpretable concepts that satisfy both faithfulness and conceptual coherence.
In our work, we propose a novel framework, InfoCons, principles to decompose a point cloud into 3D concepts with different levels of in- fluence model predictions, where the critical subset is given by the most discriminative concept. To ensure faith- fulness, we leverage mutual information (MI) between the critical subset C and the model decision Y, deriving a crit- ical score map by maximizing I(C, Y). Meanwhile, we introduce a learnable unbiased prior to minimize the MI between the critical subset and input point cloud X, encour- aging a meaningful conceptual structure. Further motivated by variational Information Bottleneck (IB) for Attribution frameworks, which aim to select informative features as model interpretation via a learned selective function (Chen et al., 2018; Schulz et al., 2020; Bang et al., 2021), we formalize the learnable prior as a selective function for crit- ical subsets, optimized using an IB-based objective. The proposed framework for explaining PC models specifically addresses the problem of selecting the most influential sub- sets from an unordered set of points. This contrasts with existing methods for CNNs on 2D images, which focus on selecting relevant pixels of the labeled objects from irrele- vant background pixels.
that applies information-theoree
2. Background
2.1. Point Cloud Models
We focus on category of point cloud models known as point-based models, which directly handle 3D points with- out voxelization or projection. Point- based models can be formalized as consisting of an encoder and a task-specific head. Encoder F extracts point features 2 E Dx from input x E R(3+C)xN N (3D coordinates with C' additional features), and compresses them into a global embedding Eglobul E R using symmetric functions that account for the unordered nature of point clouds, typically via maxpool- ing or combination of max- and avgpooling. For shape classification, the head outputs a shape prediction y. In seg- mentation tasks, the head typically receives a concatenated point- and global-Ievel feature Zeoncat E 2D to output point labels (Qi ct al., 2017a).
Information Redundancy in Point Cloud. Voxel- or projection-based PC models reduce information redundancy at the input level, but this approach often leads to significant information loss, limiting model performance (Liu et al., 2019). bosnt-based models employ a different strategy. Hi- erarchical models use sampling operations in each encoder
'Due to the inductive bias of PC models, PC of singularity (N = 1024 points at the same position) is also shape-informative: an 'origin PC' can be predicted as 'guitar' by PointNet (Qi et al., 2017a) with 99.2% certainty.
2

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Identifying Interpretable Critical Concepts in Point Clouds
block, reducing the number of point from N to N' < N layer-by-layer. Non-hierarchical models address redun- dancy by applying symmetric functions/ f : + RD after extracting point features, ensuring that shape-relevant information is preserved.
(2020) propose to identify the importance of each pixels by optimizing the pixel-wise intensity scale À of a random noise which is applied to the latent feature fa) in an ad- dictive manner: 2 = >f()) + (1 - (1-))c, E~ NN (f..f)) where f denotes intermediate layers, f(x) E D and a s sig id function constraints À E 10.1 À is then interpolated to the input size and averaged along the channel dimension to obtain a pixel-level attribution map A E I Hy xWr (assuming that all channel dimensions are i..dd).. The VIB objectives for attributing (VIB-A) (Schulz et al., 2020) can be formalized as a combination of the classification cross-entropy loss and the information loss:
2.2. Information Bottleneck Theory
The Information Bottleneck (IB) theory (Tishby et al., 2000) provides a theoretic perspective on defining what we mean by a 'good' representation. The IB models the role of deep networks as learning a minimal sufficient statistics (maxi- mally compressed) x = fzz. 9) for predicting the class label y. The IB principle can be formalized
tradeoff between having precise representation (being informative to 2)) and achieving good predictive power (being informative to y):
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where the prior is defined as g(2) = N (u), Intuitively, the VIB-A objectives is optimized to first find the pixels that encode the least information about the label and replace their feature values with random Gaussian noise, resulting in A having low saliency score for background pixels.
where I(.,-) denotes the mutual information, capturing all non-linear relationships between the two random variables; and 3 controls the degree of restraining input-relevant infor- mation. Variational Information Bottleneck (VIB) (Alemi et al., 2016) provides variational approximation to In- formation Bottleneck, allowing us to parameterize the IB objectives by training a neural network. See Appendix A. for details.
In our work, we formalize the desiderata of good critical subset in point cloud attribution: it should be faithful to the model's predictions and conceptually coherent with human priors. To this end, we apply information -hherrrti princi- ples to identify critical concepts that satisfy these properties.
2.3. Attribution Methods
Desiderata of Explanations. The desiderata of explana- tion methods can be traced back to LIME (Ribeiro et al., 2016), which aims to provide explanations for classifier predictions in an interpretable and faithful manner by ap- proximating the behavior of complex model with a local, interpretable surrogate. Grad-CAM (Selvaraju et al., 2017) introduces a principle for what constitutes a good visual explanation in image classification: explanations should be dlassdiicriminntiiee (Faithfully localizing objects of inter- est) and high-re nigh-resolution (capturing fine-grained details that make explanations interpretable).
2.4. Attribution for Point Cloud
Pooling- based Methods. Pooling- methods derive score maps directly from activation maps. For example, Critical Points (CP) (Qi al., 2017a) identifies subset of points as critical if they remain active after the final max- pooling layer of the point encoder, and Critical Points++ (CP++ (Levi & Gilboa, 2023) extends CP to continuous measures by applying meanpooling. Many point cloud mod- cls also use feature map statistics (averages or maxima) to heuristically explain their proposed models. However, these approaches are primarily based on the encoder of point cloud models and often overlook the influence of the downstream classifier, rendering them insufficient for fully explaining model decisions. Besides, FFAM (Liu et al., 2024a) lever- ages the non-negative matrix factorization (NMF) of feature maps tailored for attributing 3D object detection results.
While this principle is well-suited for image data, where clear boundaries often exist between objects of interest and unimportant background pixels, such boundaries are typi- cally absent in point cloud data, which consists of thousands of unordered 3D points. Concept-level explanations offer a more general formulation of interpretability (Koh et al., 2020). In the image domain, concepts can be human-labeled attributes (Koh et al., 2020) or discovered as selective input patches (Brendel& & Bethge, 2019; Zhou et al., 2024).
Gradient-based Methods. PC Saliency Map (PC- SAM) (Zheng al., 2019) identifies critical points based on the negative gradient of the discriminative loss with respect to points' spherical coordinates. Several other works on adversarial attacks also use gradient- based critical points (with C&W loss) as guidance for optimizing point perturba- tions (Xiang et al., 2019; Huang et al., 2022). These methods tend to produce locally aggregated critical points at spatial
VIB for Attribution. Some works have explored the way of utilizing the VIB objectives to solve the problem of at- tributing the black-box decisions of deep models (Liu et al., 2024b). Given a pre-trained image classifier, Schulz et al.
3

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Identifying Interpretable Critical Concepts in Point Clouds
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Steps to derive infocions
(a) Theoretical Illustration
(b) Framework Overview
Figure 2. (a) Theoretical illustration for extracting critical concepts. (b) Overview of our explanation framework to obtain the InfoCons. PC model for shape classification is denoted as 9 o F. SymFune stands for symmetric functions (c.g., maxpooling). Attention Bottleneck / is trained with end-to-end objectives. Once trained, uses only the intermediate feature to provide explanations.
corners, observed across various point cloud models, even those with significantly different architectures (as shown in Fig. 4). This is caused by the biased prior introduced (we refer to as the shape prior of PC centroid), leading to model-independdet explanations (Hong et al., 2023; Feng et al., 2024).
discrete selection of points where m a random variable sampled from multinomial distribution and the selection probability represents the importance of points:
softaax m, (at(softmax(s(()))))
j (L...... .D.,, (3)
Black-box Query-based Methods. LIME3D (Tan & Kot- thaus, 2022) extends LIME (for images) explain point cloud classification by creating set of queries by flipping the original sample and then fitting surrogate model to predict point scores. LIME3D uses point-dropping as the flipping operation, considering the discrete nature of point clouds. Similarly, OccAM (Schinagl et al., 2022) proposes a perturbation-base (point-dropping) method to explain object detection results (e.g., a detected car with bound- ing box), estimating the influence of each point using sampling-and-forward brute-force approach.
where D, represents the reduced size dimension of C, which is bounded by dimension bottleneck?; and s(x); s(x,) R is the probability of point i being selected point. In order to derive soft and continuous score map for x, we use a soft relaxation of m denoted as m E IR x We leverage a neural network with learnable parameters 0 to calculate the soft mask in and apply to point features 2:
critical
m = f(m]==()) 2 = m O 2(x),
(4)
where @ represents element-wise multiplication, and is the intermediate feature of given trained PC model by z(-) _.)(()) at 1-th layer. Noted that 2x) = =(x;)) is the D-dim feature of x;, thereby in optimized for is also applicable for x.
3. Methodology
3.1. Overview: IB for Critical Points
For deriving good critical subset that encodes sufficient shape-relevant information (faithfulnesss) and conforms semantically meaningful structure (conceptualness), we
Definition 3.1 (Selective Critical Points). With the formu- lation above, the objectives in Eq. 2 can be formalized as:
rewrite the IB objectives as follows:
max
E Ey<p(r) log (()(2) p<p(2)
E
3 DRL DKL (flla((m)) (5)
-Los
E,
JIB-CP max I(C,v) v) C),
(2)
where we replace q(ylm @ x)) by q(vl2). Considering <=) is constant for given encoder F, we approxi- mate the upper bound of T(x, C) by Dzz (xillllggmm)
where C C= x C x denotes a predictive critical subset of point cloud x by applying binary mask m, B controls the tradeoff between being predictive and being less redundant.
where (m) is the prior distribution by setting q. (m) = L'(0, 1)
Following the variational approach, we use cross-entropy for classification as a lower bound of (C, y) (Xie et al., 2020), but estimating I(C, x) is non-trivial since we do not have knowledge about the prior (Lin et al., 2023). To address this issue, one straightforward solution formalize as
and we use a sigmoid function to constraint m E 1].
Dimensioo bottleneck proposed by Qi et al. (2017a) refers to the maxpooling layer used to obtain the critical subset where the channel dimension (denoted D) implicitly bounds the size of critical subset. Ncc

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Identifying Interpretable Critical Concepts in Point Clouds
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Figure 4. InfoCons-based critical subsets (200 pts) for four PC models (covering three distinct structure types) are compared with mcanpool- -aasod CP++ and gradient-based PCSAM. PCSAM tends to extract similar and spatially aggregated subsets for all models, while InfoCons identifies more interpretable critical subsets that are faithful to model behavior (color distinction not required).
Figure 3. Feature Analysis for four models in (A), and derived Se- lective Scores in (B). For PointNet, points with stronger activation receive higher scores (e.g., Point No. 1,2 in (A), which have larger means of activation maps [MD. However, in hierarchical models, nearly all points are highlighted (Point No. 0,1,and in (B)). We address this problem by proposing InfoCons in Eq. 6.
tive concepts for given PC model can derived follows:
Once the f is trained, the underlying probabilities s(x) E [0, 1]xd for sampling m can be obtained by calculating the expectation of m by s(x) = Dj mj, as shown in Fig. 2- (b).
max E (()) Ey-r(s) log ( 2) x (
9
m o 2(x) sg( - m) Oc (6)
where C denotes element-wise multiplication, sg(-) denotes stop- -raddiintnnt operation. G ~ of) is sampled for each point i. Gaussian prior q(2) N(22, o?) is parame- terized with the D-dimensional mean and variance of point feature 2 = F (z). We reused the neural network to formalize 2 by = f()
Feature Analysis. Selective CP defined in Eq. 5 is effective for non-hierarchical, localized PC models like PointNet (Qi et al., 20)7a). PointNet enables these objectives to effec- tively balance the CE loss and information loss through point-wise masking, largely due to the high sparsity of its point features. As shown in Fig. 3, the features from Point- Net in (A) are significantly sparser than those from Point- Net++. Additionally, the selective scores for PointNet for three selected points (Point No.0,1,2) align with their abso- lute mean feature values |M] (i.e., > 2 > 0). In contrast, in PointNet++, higher M (and thus higher selective scores) do not correspond the points that should be critical (by observing 0 > 1 2). The feature analysis explains why CP++ (meanpool- baased) fails with PointNet++ (in Fig. 4).
As defined in Def. 3.2, to address the problem of entangle- ment, we try to decouple the information from neighbour points and the anchor point, by introducing a Gaussian noise denoted as e. We aim to recover a coarse feature about neigh- bors so that only the information about the anchor point is reduced. More specifically, when we need to rank x, as unimportant (m, - 0) (for the reason that either it is re- dundant or less point has multiple information sources from neighbours together with the point z; itself. then we try to add random variable sampled from a specific distribution determined by 2, avoiding significant degradation on model performance.
and the feature of i-th
3.2. Deep InfoCons
Recent PC models usually enhance the feature extraction process by incorporating with feature grouping operations (e.g., DGCNN), set abstraction (e.g., PointNet++)), or deeper stacked layers with residual connections (c.g., PointMLP), where the information flow from points to intermediate fea- tures becomes highly non-linear, resulting in inaceuracy for approximating I -C.-). More specifically, the score map mn ineffective as most of points are considered with equal importance, shown in Fig. 3. This is mainly due to the entanglement of point features with their neighbours when we try to measure the importance of individual points. We introduce InfoCons as follows to address this problem:
Comparison with PC Saliency Map (Zheng et al., 2019). PC Saliency Map is one of the most representative ex- plaining methods for PC data, which can be formalized as: (i(r) -LCF /ōr; r rt+a (r; denotes the distance of x4 to the spherical core and a is a scale factor for var- ied spatial sizes of PC). This score introduces prior that the points lying in the surface of objects tend to be more salient, resulting in redundant critical points clustered in spatial corners, as shown in Fig. 4-(PCSAM).
Attention Bottleneck. The intermediate features of point encoders are high-correlated and entangled, particularly in
Definition 3.2 (InfoCons). Informative scores with informa-
5

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Identifying Interpretable Critical Concepts in Point Clouds
Nx E I = v1). where Wxx denotes for the size of attack dataset (we use Nxx 2, 468). We con- ducted comparison experiments on eight PC models: Point- Net. CurveNet, GDA, PointMLP, DGCNN, Maskpoint, and PCT (Muzahid et al., 2020; Xu et al., 2021; Ma et al., 2022: Qi et al., 2017b; Wang et al., 2019; Liu et al., 2022; Guo et al., 2021). Model dexcriptions and training details are provided in Appendix C. The source code is available at https: /ttp://gtttbbbbt wtt.ccommlllfff wwt.ffffiinfcoos-Pee.
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Figure 5. The data flow of the bottleneck network f(+1=(x);; f). The input the intermediate feature from F, and the output mn holds the same dimension as
4.1. Qualitative Comparison
We compare InfoCons with four baselines for PC expla- nation in Fig. 6 qualitatively. Critical Points++ (AO, A1), InfoCons (DO, D1), and Critical Points (E) are derived with single forward pass. PCSAM (CO, C1) is implemented by iteratively dropping points over 20 steps (10 points per step), and LIME3D (B0, B1) performs 1,000 queries using point-dropped point clouds.
the hierarchical models and self-attention based models. We introduce a non-linear attention block to learn the unbiased priors based on point-level features, denoted as (m) 2;; 0), as shown in Fig.
The input of attention bottleneck is the intermediate feature of point encoder, denoted as For hierarchical models (e.g., PointNet and DGCNN), z holds the same size dimension as input x (N' = N and we use N = 1024). However, for the hierarchical models, points are down-sampled or pre-processed to form 3D patches, the size dimensions may vary. We apply the channel-wise attention to fit with this property. Formally, the input feature is first transformed as 4: WT' 2, U2= o oW""' 2). where W E DDD,, WT E DD and represents an ELU activation function. Then calculate the output:
In (A0-DO), we demonstrate the soft score maps four PCs for DGCNN. The PCs shown are selected from Mod- elNet40 test split, where the model gives incorrect predic- tions (probabilities of the ground truths and predictions are shown on the far left).
In (E, A1-DI), we visualize the derived critical subset (200 out of 1024 points) from the score maps, except for CP, where the size of the critical subset is determined adaptively by the maxpooling layer.
Att(g=: 2, v.) = softmax (o. </VDD Uz..
Compared to the baselines, our InfoCons method suc- cessfully attributes the incorrect predictions to the cor- responding concepts with greater informativeness and reduced redundancy. Specifically, the mislabeled 'plant" in (R1) arises from missing the 'pot'; and the confused 'flower-po' in (R2) can be attributed to the model's atten- tion on the 'pot'. For samples (R3) and (R4), InfoCons (DO and DI) outperforms baselines by exhibiting less redundancy of similar points and providing richer shape- relevant information.
The output is finally expanded to the dimension D through MLPs with a si sigid activation to constraint m E (0, DxDN,', In order to visualize the score map in the case of N' < N, we further propagate in to N using spatial interpolation (Qi et al., 2017b) (weighted by I.2 distance between N' anchor points and N original points).
4. Experiments
Evaluation Protocol. The example point clouds are se-
lected from the synthetic dataset NedelNet40 (Wu et al., 2015) and two real-world datasets: ScanObjectNN for shape classification (the hardest variant PB. T50 RS (Uy et al., 2019)) and KITTI for objection detection (Geiger et al., 2012). Our evaluations are mainly conducted on Model- Net40, which contains 9, 843 training samples and 2, 468 testing samples. We uniformly sample 1, 022 points from the surface of CAD models and only 3D coordinates are used (i.e., x 3 1024). We compare InfoCons with four baselines: Critical Points (Qi et al., 20)7a), PC Saliency Map (Zheng et al., 2019), Critical Points++ (Levi & Gilboa, 2023) and black-box query-base based LIME3D (Tan & Kot- thaus, 2022). One of the quantitative metrics used is over- all accuracy (OA) under point-drop attacks, calculated as:
In Fig. 11 of Appendix B, we visualize information redun- dancy of given PC by applying K-Means clustering to the InfoCons-based score map, forming a Pritical-Subser Hierarchy. In Fig. 13, we demonstrate the Dynamic Critical Subset by iteratively dropping points and re-constructing score maps, providing a fair qualitative comparison with PCSAM.
4.2. Quantitative Comparison
Effectiveness of InfoCons. Following Zheng et al., we conduct a point-drop attack to evaluate the effectiveness of InfoCons by measuring the accuracy changes of (i) drop- ping out the most critical points (MCD) and (ii) dropping
6

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Identifying Interpretable Critical Concepts in Point Clouds
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Figure 6. Qualitative comparisons of InfoCons with four baselines (CP, CP++, PCSAM, LIME3D) include both score maps (best viewed in color) and critical subsets. The PCs are selected from ModelNet40, where DGCNN gives incorrect predictions.
out the least critical points (LCD). We report the instance accuracy for 1pass score maps and multi-iteration (from 5 to 20) dynamic score maps in Fig. 7. We iteratively drop 10 LC/MC points each iteration, thus InfoCons (20it)-MCD denotes score maps for 824 points (200 most critical points dropped). The accuracy gap between MCD and LCD in- dicates InfoCons captures the assigning them higher scores.
spaica DIGOMNGS
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Figure 7. Accuracy under point-drop attacks against DGCNN, We compare InfoCons with CP++, PCSAM, and LIME3D. In (A). the effectiveness of InfoCons is demonstrated by the accuracy gap between LCD and MCD. In (B) and (C), present comparisons in the most- post-powerful setting and fair-rumning time setting, with efficiency details provided in Table
Comparison with baselines. Based on point-drop attacks, we further compare the proposed method with three base- lines with soft score map (CP++, PCSAM and LIME3D) in Fig. 7-(B,C) Since PCSM is a gradient-basee based method that utilize the ground truth label to calculate the loss, our Info- Cons may not outperform PCSAM when dropping only a small critical subset. However, our method InfoCons (Ipass) achieves better performance when remove larger subset, in- dicating the information redundancy of critical concepts can be appropriately handled by InfoCons. Besides, LIME3D achieves the most substantial drop-attack by significantly de- grading the accuracy to 45.22% and InfoCons (20iter) ranks second with 63.70% (at 500-pts 1000-pts-dmg pts-dropping point). However, LIME3D incurs heavy computational cost (about 4.5s/PC shown in Tab. 3) limiting its applications. The interpretabil- ity of LIME3D also lacks, as it is challenging to interpret the semantics of the derived critical subsets compared to white-box methods. Full evaluations on eight models are in Fig. 18 and Fig. 19 of Appendix D.2.
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Bork 3.0 20
Figure 8. InfoCons-based mixup (left) and adversarial attack (right). InfoCons-based score map can also explain the effec- tiveness of adversarial examples. Better viewed in color.
based saliency score map of SageMix (Lee et al., 2022) with InfoCons, then following SageMix's 'ss dynamic data augmen- tation to generate continuous mixed PC. We re-implement SageMix and report the results in Tab. 1. We use larger batch size and fewer training epochs (96, 300) compared to the original paper (32, 500). Under the same training hyper- parameters, we achieve improved classification performance by integrating InfoCons into the mixup pipeline, primarily because InfoCons mitigates the gradient saturation effect through KL divergence regularization.
4.3. Extensive Evaluations
We integrate InfoCons into two applications by enhanc- ing their salient-region search algorithm, and successfully achieving improved performance (Fig. 8). We also extend In- foCons on two challenging real-world benchmarks ScanOb- jectNN and KITTI (Fig. 10).
InfoCons for Adversarial Attack. We integrate the pro- posed method into SI-Adv (Huang et al., 2022) to gener- ate effective and imperceptible adversarial perturbations. SI-Ady is sensitivity- guided attack, and we enhance its
Cono for Data Augmentation. We replace the gradient-
7

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Identifying Interpretable Critical Concepts in Point Clouds
Test Accuracy, Score Veriance vs. P for DCCKNgS
Table 1. Quantitative evaluations of InfoCons for mixup. Our re- implemented results are shown in black, with SageMix's ' original results displayed in (grey).
30005
0.5224
30004
0.9222
0.9220
30003
Score Var
Model DGCNN
Aug Type
Test OAf (%)
3,0003
Base
92.30 (92.9)
09226
1SST ACCT
DGCNN
SageMix
92.79 (93.6)
0.9214
+30000
+InfoCons
93.19 (+0.4)
10
3DP
101
712
10"
301
6%
Table Quantitative evaluations of InfoCons for adversarial at- tacks. Enhanced with InfoCons, can achieve higher ASR and lower average CD/HD.
Figure 9. Impacts of B. D. and intermediate layer I for DGCNN@ on ModelNet40.
DGCNN (on ModelNet40 testset)
SI-Adv
+InfoCons
A
A- 1P"
Exp a nataion for Mesinn Objects
ASRT (%)
99.76
99.80
(+0.04)
CDJ (10-²)
5.58
5.47
(-0.11)
HDL (10 !)
6.70
6.55
(-0.15)
sensitive-region search by rescaling the gradient from C&W loss using InfoCons' score map. For fair comparison, we use the same step size and normalize the resulting score maps for both SI-Adv (+Sensitive scores, original) and SI- Adv (+InfoCons). We use step size of 0.007 and 80 steps in total. As in Fig. 8 (right) and in Tab. 2, InfoCons provides more effective salient regions that help optimize adversarial perturbations. The score maps derived from InfoCons can also explain the effectiveness of adversarial examples (e.g.. changes in the scores around the leg of a perturbed 'chair' contribute to the success attack that causes the model to misclassify it as 'bed").
Missing Why?
UDAR
Origiaal Detection
Figure 10. Impacts of 3 for DGCNN @5 on ScanObjecINN (left) and the explanation for missing objects of object detector PointPil- lars@1 (right, better viewed in color). The implementation details can be found in Appendix C.2.
mentation and adversarial attacks. The results are derived for DGCNN on ModelNet40 testset. LIME3D achieves the best drop attack performance by querying 10a times and InfoCons (20iter) ranks the second. However, there is limitation in using the drop rate of OA an effectiveness metric, as a larger drop may result from removing points in certain spatial locations that push the point cloud off the data manifold, rather than reflecting true faithfulness in terms of contributions to the predicted labels.
Table 3. Efficiency comparisons of InfoCons with four baselines.
Method
0A(%)L
ET,
ET. (s)
#Param
CP++
75.08
IF
0.01
0
PCSM( pass)
pass)
89.87
I(F+B)
0.05
0
PCSM(20it)
79.86
20(F+B)
0.85
0
LIME3D(10")
67.99
100F
0.54
1K
Parameter Study. The proposed framework is occupied with several hyper-parameters to choose, demonstrate three key hyperparameters of our InfoCons in Fig. 9:
LIME3D(10")
45.22
1000F
4.54
1K
InfoCons(Ipass))
73.50
IF
0.01
2.4M
InfoCons(1On) (1it)
69.08
10F
0.17
2.4M
InfoCons(20it) 63.70
20F
0.29
2.4M
The weighting coefficient | applied to the information loss, which controls the level of retaining point-wise po- sitional information. We utlize the variance of scores as a metrics to measure the quality of the score map, and consider the optimal choice of 3 together with the test set accuracy. We empirically observe that there exists an optimal point for the choice of 3 that reaches relatively high accuracy with high score variance.
1. F: one forward- pass time, B: one backward-par time.
2. Empirical explaining time (ET.) is measured using the s imeit magic command in Jupyter Notebook.
4.4. Efficiency and Parameter Study
Efficiency Study, In Tab. 3, we report (1) test overall accu- racy (OA) after dropping the 500 most critical points, where lower OA indicates a more effective explanation follow- ing Zheng et al. 2019; Tan & Kotthaus 2022; (2) theoretical explanation time for each point cloud (ET;) and empirical explanation time (ET.): and (3) the size of the explain- ers. InfoCons and CP++ require only a single forward pass, making them the most -meeeffficiett methods, which is an important advantage for applications like dynamic data aug-
The reduction dimension D, of attention bottleneck, which impacts the prior distribution. A smaller D, will be more parameter-efficieet We observe that different D, have varying optimal / values but do not significantly alter the optimal score map distribution, and we set D,- = 64 as the default value.
8

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Identifying Interpretable Critical Concepts in Point Clouds
The intermediate layer impacts the target feature map = =Fld that InfoCons uses to identify informative con- cepts. A basic principle for choosing 1 is that the layer should be as deeper as possible to be tnape--nformative, while ensuring the size dimension of z is not too small (N' > 256) to reduce the entanglement of neighbour fea- tures. This crucial for the visualization quality of the score maps (measured by the variance). Following this, we manually determine the intermediate layer for eight models, listed in Appendix C.4.
help the human inspects to better understand the root cause of accidents unexpected decisions of LiDAR-based deep learning models in the vehicles.
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5. Conclusion
In our work, we propose PC explanation framework called InfoCons, which attributes model predictions to critical con- cepts. We provide an in-depth analysis of the limitations of existing attribution methods and design an IB [B-based objec- tive to derive faithful and interpretable critical score map. This enables humans to identify the concepts that the model correctly or unexpectedly focuses on. We demonstrate the effectiveness of the proposed methods both qualitatively and quantitatively. InfoCons is also scalable across multi- ple structures of point cloud models (eight models in total) and real-world datasets. Furthermore, the application of InfoCons in saliency- based mixup and adversarial attacks further demonstrates its effectiveness.
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Acknowledgement
We are thankful to the shepherd and reviewers for their careful assessment and valuable suggestions, which have helped us improve this paper. This work was supported in part by the National Natural Science Foundation of China (62472096, 62172104, 62172105, 62102093, 62102091, 62302101, 62202106). Min Yang a faculty of the Shang- hai Institute of Intelligent Electronics & Systems and En- gineering Research Center of Cyber Security Auditing and Monitoring, Ministry of Education, China.
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---

Identifying Interpretable Critical Concepts in Point Clouds
A. Theoretical Details
bound of [zz
A.1. Deep Variational Information Bottleneck
[(z,W) v)
f plu, 2) log p(ylz) dydz ply)
The Information Bottleneck (IB) provides the principle of what is a good representation in terms of fundamental tradeoff between being predictive to labels and keeping maximal redundant information of input data (Alemi al., 2016). Let æ denotes inputs and y denotes the corresponding target labels, we can regard the output of intermediate layers of a network as a stochastic encoding z w.e. the input x. For correctly classify the input x as y, our primary goal is to learn a encoding function that maximize the information about y in
=
/ plu, 2) log pogp( :ddd
plu: =) log ply)dyds
= / p(u. 2) log 2 dyddz
p(v) log log p(y)dy
/ p(u, 2) log + (2)
2 / plu. =) log glu ddyd=
(8)
max [2,, y),
The second term [(2, can also he expanded by definition:
[(2,x)= / p(2,ar) log p(2, dzdæ
p(z)p(z)
which upper bound given by the dataset (xr, y) indepen- dent the network and the encoding z. To prevent the trivial solution (z = z), the IB principle apply constraint Le to 2z, and can use the Lagrange multiplier 3 to get the objective functions:
/ p(2,z)log log
p(=|z) dzdr
p(z)
Introducing a prior (22) with learnable parameters approx- imate the unknown true distribution of latent representations p(z), we can derive the variational upper bound of / (2,
max ((2,y) v) s.t. s.L.( <= la
DkIlp(=)]l<(=]] 20
max ((2,0) (x,,2),
I p(z) logp(z)dz >/-
/ p(z) log g(2)dz
[(2,x) S p(2, 2l2 log p(2|z) dedr
where the hyper-parameter 3 > 0 controls the degree of restraining information about the input. The first item can be expressed as follows:
((2)
= / p(z)))p(z) log p(2|z) dadx
(9)
q(2)
E x<p(xx)
T(z,y) / p(z, v) log ply.2) dydz
p(u)p(2)
Combining the lower bound of T(z, y) (Eq. 8) and the up- per bound of [22, (Eq. 9), the objective of Information Bottleneck can be reformulated as
/ plu. 2) log
p(ulz) dydz
p(y)
J plus 2) log glvl=)dydz -3 E x>p(x))
D (p(2 (x<)
For the intractable term of likelihood p(y]z), we can intro- duce (yy|)) to approximate p(y|z) by a classifier g Z Y. With the nonnegativity of the Kullbach-Leibler diver- gence:
E,
(10)
Note that p(u.2)
E Eppple p(u, 2|x)
(e=set>p(ul))p(((z)>>) then the first item can be written as (Schulz et al., 2020):
DxI/w//)]ldwlb))200 / p(y, 2) log p(ul=)dy
f ((0)))(()))))())) log (dylz)d (11)
f plu,
o(g d(y)=)dy,
log log
===p()))=p(=lz)) / p(ul=) log ((vl))dg)
(12)
E -CCE]
(13)
then we can replace p(y|z) with ())(2) and derive the lower
==p(st),e-((=lz))
12

---

Identifying Interpretable Critical Concepts in Point Clouds
A.2. VIB for Critical Points
Cresial makes level
crntoal meets Lewd
Ontic ieets Lnael
Dif Noats Lean
Following Eq. 8 for deriving lower bound of ((2, and Eq. for an upper bound for [22, we can formalize the objectives (C, y) (1, C') defined in Eq. 2 to variational form:
Hoore Pap, 1004 pls
(137p50))
205ppe
p03gm
/ plu. C) log ((vl))
/ p(Cl=))(x) log p(C|z) dCda, (C)
Figure II. Decompose point cloud redundancy by visualizing the Critical Points Hierarchy.
(14)
where parameterize C as m and further approxi- mate it as in @ 2(x). nn is derived from neural network f()(((()); 0) with learnable parameter 0, as proposed in 5..5. 5. We omit the intermediate steps z(x) = Fl)(()), = [(m])(()); 0) and denote (x)) as & = [(]]=;; 0) for sim- plicity. Therefore, objectives in Eq. 14 can be rewritten as:
f p(v, 2) log (y)ld)dd
p(2/z)) dēdı, B f p((())p(z) log (2)
Figure 12. Additional samples for Critical Points Hierarchy.
clustering (K = 4). We observe that the hicrarchy of In- foCons suggests the most critical concept is the contour of a 'sofa' (as the model incorrectly predicts), and the least critical concept the seat (a common attribute between 'sofa' and 'bench').
(15)
where the first term can be represented by -Lor- The second term can be reformulated as a KL divergence and further simplified as:
Eg DKL (p(s)=))la = E. (D(
(16)
Dynamic Critical Subset. The dynamic process of itera- tively dropping points and constructing gradients to derive score maps is vital for PC Saliency Map (PCSAM) (Zheng et al., 2019). The number of iterations should be large enough to fit the size of the required critical subsets (e.g., 20 iterations for 200-point critical subset), demonstrated in Fig. 13. Different from PCSM, InfoCons can produce an effective score map with one-pass score map, and addi- tional iterations (20-iteration) do not significantly change the distribution of the most critical concepts. Therefore InfoCons is more faithful as the PC is not modified during explanation. (Examples for eight models can be found in Fig. 15 and more examples are shown in Fig. 16).
considering = f(] 0). Moreover, since z(x) is deter- mined by the trained encoder F. we consider the upper bound based on á in Eq. as follows:
I(C, x) S Ez (Dxx((lll(
(17)
For the calculation of KL divergence, we use the Monte Carlo algorithm to approximate the value at the point level (i.e. we assume that each point feature is i.i.d., so the large number of points in single point cloud, together with relatively small batch size, provides good approximation performance).
InfoCons for DGCNNeS One pass 20 Itaraioons
PC Saliency Map for DGCNN 10 Iterations
B. Quantitative Comparisons
One pass
20 harations
Critical Subset Hierarchy. Due to information redun- dancy, a point cloud can be split into different levels of subsets, with each level holding a certain geometric struc- ture. In Fig. 11 and 12, we compare the Critical Subset Hierarchy of InfoCons with Critical Poin In CP, the four-level bierarchical subsets are constructed by iteratively dropping critical points over four iterations. For InfoCons, we construct the hierarchical subsets by applying K-Means
Figure 13. Dynamic critical subset (200 points) with one-pass and multi-iteration score maps, compared with PCSAM.
13

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Identifying Interpretable Critical Concepts in Point Clouds
C. Experimental Details
tion module, Attention is trained on the entire training dataset, find it costly to train explainer KITTI. Therefore, we directly optimize the explainer on single-sample (test scene PC) for 60 steps.
C.1. Training Details
For point cloud models involved our experiments, we follow their official training pipeline24507 or open-source re- implementation in Pytorch*910 Our experiments of training InfoCons conducted using NVIDIA GeForce RTX 2080Ti (1IG) GPU, using Python 3.11 and PyTorch 2.1, with CUDA 12.2. For each model, we use batch size of k = 8, and training DGCNN for 50 epochs takes about one hour.
As shown in Fig. 10, the score map particularly highlights a short segment of the LiDAR beam located directly beneath the car. Our method reveals that this segment of the ground causes the model to fail in detecting the car.
C.3. Implementation Details
C.2. InfoCons for Object Detection
Spatial Interpolation. Spatial interpolation is widely used in hierarchical point models for tasks such as point cloud segmentation. We implement our score map interpo- lation from scored subset (x', ,m') with points set size N' (a sub-sampled result) to the input score map (ar, m) with points set size N (the size of input) following KNN-based feature propagation (Qi et al., 2017b). Here, we remove the non-linear learnable transformations for direct attribution, which can be formalized follows:
We extend the InfoCons framework to explain challenging 3D object detection tasks. The results demonstrate that InfoCons is also effective for object detection. We conduct the study on PointPillars (Lang al., 2019). and we use the pretrained weights from OpenPCDet! and the detection code from the official codebase from OccAM
Given a 3D object detector with point cloud encoder (e.g., PointPillars which contains a Pillar Feature Net) and PC from KITTI test split, we can derive a score map for explain- ing missing objects as follows:
my = Σ/ (6) W m
where is =
Σ/= wj
(w m())) index[[d(xx,, m'), sortid(2;,
Firstly, we focus how to explain the missing cases that may cause serious consequences. For example, missing front-near car (as shown in Fig. 10). Since the KITTI test samples lack ground truth labels, we randomly select data, obtain detection results from the detector, and manually identify the target missing objects.
Reparameterizatioon Tricks. The sampling result m from multinomial distribution is a set of discrete one-hot vectors in our reformulation Eq. 2 and the process of sampling is undifferentiable. For differentiable optimization, we use Gumbel reparameterization tricks follows:
For the objectives in Eq.6, we replace LC with the de- tection score of target objects as the surrogate objective for (C;; v). The information loss remains the same in classification (KL divergence). Specifically, we use the negative of the similarity loss defined in OccAM(Schinagl al., 2022), as we are explaining the missing object rather than the detected one.
m = f(ml 2; 0) gumbel-ssffmax/ 0)
E. softmax + log ((z, 0)
] (18)
where 9x = log( log ex U(0, 1) is the Gumbel noise and 7 is the temperature. We set r = 0.7 (larger for smoother distribution) and sample the noise for t = 32 times to calculate the expectation.
Unlike InfoCons for classification, where the explana-
"https://githin hwtp://////aainn//////aeea. Relation-Shape-CMI
C.4. Point Cloud Models Details
'nttpe://github.comt/
Model Architectures. We provide detailed information about the architectures of the point cloud models, as well as the intermediate layers where we apply the Attention Bottleneck in Tab. 4.
pointMiP-pytorch
MaskPoint
hhtrop://gttabb.oommmmm//////d/
Pointnet2.pyttorch
List of available layers in PC models encoder We pro- vide detailed information about the official architectures of the point cloud models involved in our work in Tab. 5, 6, 7. Additionally, we specify the intermediate layers of these models that we targeted.
PCT Fytorch
"https://gitie thtbb httptttt.ccoooepeemmmaaaa////e/e
Phttps://gff thub. com wht.hh.com/.cchiagg///ccoo.
14

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Identifying Interpretable Critical Concepts in Point Clouds
Table 4. Model descriptions with point feature information.
PC Model
Size Dim.
Structure
Sparsity/%
Channel Dim.
@ @layer
N'
of Model
1 L(2 0)((D' N')
D
@ointNet@3 (Qi et al., 2017a)
1024
N-H
62.30
1024
CurveNet@2 (Muzahid et al., 2020)
1024
H N-H
60.19
128
GDA @4 (Xu et al., 2021)
1024
53.94
512
PointMLP@4 (Ma et al., 2022)
64
H
24.24
1024
PointNet++@) I (Qi et al., 2017b)
512
H
2.31
128
DGCNN@5 (Wang et al., 2019)
1024
N-H
0.00
1024
MaskPoint@ 10 (Liu al., 2022)
64
SA
0.00
384
PCT@4 (Guo al., 2021)
256
SA, H
0.00
1024
Table Non-hicrarchical Structure
@ @layer
#points
#channels
PointNet (Qi et al., 2017a)
encoder.2
1024
128
encoder.3
1024
1024
maxpooling
1024
DGCNN (Wang al., 2019)
encoder.3
1024
128
encoder.4
1024
256
encoder.5
1024
1024
maxpooling
1024
avgpooling
1024
GDA (Xu et al., 2021)
encoder:2
1024
64
encoder.3
1024
128
encoder.4
1024
512
maxpooling
512
avgpooling
512
Table 6. Hierarchical Structure
@layer
#points
#channels
PointNet++ (Qi al., 2017b)
encoder.1 I
512
128
encoder.2
128
256
encoder.3
1
1024
PointMLP (Ma et al., 2022)
encoder.2
256
256
encoder.3
128
512
encoder.4
64
1024
maxpooling
/
1024
CurveNet (Muzahid al., 2020)
encoder:2
1024
128
encoder.3
256
256
encoder.4
64
512
encoder.5
64
1024
maxpooling
/
1024
avgpooling
1024
15

---

Identifying Interpretable Critical Concepts in Point Clouds
Table Multi-head Self-attention--axe
layer
#points
#channels
MaskPoint (Liu et al., 2022)
sa.6
64
384
sa.8
64
384
sa.10
64
384
maxpooling
384
<cls>
384
PCT (Guo et al., 2021)
encoder.2
256
256
encoder.3
256
1024
encoder.4
256
1024
maxpooling
1024
D. Additional Results
in the 'flower.por class of the ModelNet40 dataset five approaches.
D.1. Failure Cases
We demonstrate the failure cases for PCT Fig. 14, where appropriate layer critical and the changes of D,- (rescale by a) and / is unable derive critical concept which conforming a meaningful structure.
D.3. Additional Quantitative Results
In Fig. 17, additionally demonstrate InfoCons eight models.
In Fig. 18, we provide the accuracy degradation of point- drop attack, additionally comparing InfoCons on eight models with PC Saliency Map.
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In Fig. 19, we compare InfoCons on eight models with CP++.
Successful Cases PCT@33
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Figure 14. Failure for PCT@4 with varying 3x E (10' /k, 102 /k, 10 /k, 10" 10"/k/ /k}, where k = N x D and a with D/a.
D.2. Additional Qualitative Results
In Fig. 15, we visualize the score map of a 'monitor' across eight PC models, together with the critical subsets derived from iteratively dynamic score maps (namely one- pass score maps, 10-iteration score maps/critical subsets, 20-iteration score maps/critical subsets).
In Fig. 16, compare InfoCons with dynamic PC- SAM (Zheng et al., 2019) and CP++ (Levi & Gilboa, 2023) on more samples.
this link, we provide additional qualitative comparisons following the same settings as Fig. all test samples
16

---

Identifying Interpretable Critical Concepts in Point Clouds
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Figure 15. InfoCons on the PC labeled as 'monitor' for PC models (from left to right: (i)the 1024 points score map, (ii)the dynamic critical points with 10 iterations and 10 points dropped each iteration. 100 points in total, (iii) dynamic critical points with 20 iteration, 200 points in total, and (iv)-(v) is the least critical points for 10 iterations and 20 iterations).
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Figure 16. InfoCons compared with two baselines on DGCNN (Wang et al., 2019). and demonstrate 200 points critical subset. From
left to right, (i) InfoCons, (ii) Critical Points++ (Levi & Gilboa, 2023), (iii)-(v) PC Saliency Map (Zheng et al., 2019) with a dynamic process of point-droppinn dropping and and-then-aee then-reet reeereecalullaiing gradient, and we highlight the dropped points in earlier iterations high scores.
17

---

Identifying Interpretable Critical Concepts in Point Clouds
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Figure 17. Effectiveness evaluation of InfoCons on eight PC models by point-drop attack, where 10 500 points are dropped. We report the changes of accuracy under two settings: (i) dropping out the most critical points (MCD) and (ii) dropping out the least critical points (LCD). The accuracy gap between MCD and LCD indicates InfoCons captures the shape-relovant points by assigning them higher scores.
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Figure 18. Additional comparisons of InfoCons and PC Saliency Map for Fig. 7.
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Figure 19. Quantitative comparisons between our proposed objectives (Eg. 5 and Eq. 6) and Critical Points++ (Levi & Gilboa, 2023) for eight PC models. We observe an abnormal trend for PointNet+++, where CP++ assigns critical points as unimportant, resulting in a rapidly dropping curve for LCD.
18


Reviews:
[{"review_id": "SoPGMQIBEv", "reviewer": "Reviewer_h8Li", "summary": "This paper addresses the problem of explaining decisions made by point cloud classification models, which is particularly important in applications such as autonomous vehicles. Current methods mainly focus on mathematical values like gradients or neuron activations. However, the authors break down the 3D point cloud into concepts that are more understandable to humans, allowing for a better evaluation of how the data influences the decision from a human perspective. The authors propose a novel framework, InfoCons, that applies information-theoretic principles to decompose a point cloud into 3D concepts with varying levels of influence on model predictions. The critical subset is determined by the most discriminative concept. The proposed method, InfoCons, attributes model predictions to key concepts, offering more precise and less redundant explanations. Comparative experiments show that InfoCons effectively identifies significant points in point clouds.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Dear Reviewer h8Li,**\n\nWe 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:\n\n### **1: Expanding the Related Work Section and Adjusting Paper Structure**\nIn 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. \nHowever, we acknowledge that an overview of point cloud interpretability literature in Sec. 2 would further benefit readers. To address this, we will \n- (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.\n- (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.\n\n---\n\n### **2: Clarification of Figure 2 for Improved Understanding**\n\nThank you for pointing out the clarity issue with Fig. 2. \nTo improve its readability, we will revise the lower-left portion of Fig. 2-(b) to emphasize the high-level framework.\nWe will remove implementation-specific notations (e.g., $\\hat{m}, \\mu_z, \\sigma_z, \\epsilon$) from Fig. 2-(b).\nAfter 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. \nThis revision will ensure that Fig. 2 centers on the high-level framework, while Fig. 5 provides a more detailed view.\n\nWe greatly appreciate your time and valuable feedback, which will significantly enhance the clarity and presentation of our paper.\n\nBest regards,\n\nAuthors", "claims_and_evidence": "The claims made in the submitted paper are supported by clear and convincing evidence. The authors conduct comprehensive experiments. The example point clouds are selected from the synthetic dataset ModelNet40 and two real-world datasets: ScanObjectNN for shape classification and KITTI for object detection. They compare their model with four baselines: Critical Points, PC Saliency Map, Critical Points++, and LIME3D. Additionally, they perform comparative experiments on PC models: PointNet, CurveNet, GDA, PointMLP, DGCNN, Maskpoint, and PCT.\nThe qualitative comparison in Figure 6 is helpful, showing how InfoCons assigns importance to critical points in point clouds, which is key for interpretability in applications like autonomous vehicles. They also perform Adversarial Attack, demonstrating how InfoCons compares to other methods. Additionally, the authors provide useful insights on the key hyperparameters of their model.", "methods_and_evaluation_criteria": "The authors propose appropriate methods and evaluation criteria. They use benchmark datasets, both synthetic and real-world. In addition, they compare their approach with baseline methods. They also utilize various metrics such as ASR, CD, and HD.", "theoretical_claims": "In the methodology chapter, the authors present theoretical claims and mathematical formulas. In particular, they refer to the Information Bottleneck (IB) approach for critical points. I have reviewed the mathematical formulas and their notations, and I found no errors. However, some of the introductions and explanations of the theoretical concepts could have been more clearly presented.", "experimental_designs_or_analyses": "The authors logically present their experiments, providing clear and detailed descriptions. They use multiple datasets, various baseline methods, and evaluate the results from different perspectives. The obtained results are supported not only by metric values in tables but also by visualizations in graphs. Based on the presented findings, it can be concluded that the method has been thoroughly tested.", "relation_to_broader_scientific_literature": "The paper’s contributions build upon existing point cloud explanation methods, such as Critical Points and Critical Points++ . It also addresses the bias in gradient-based methods like PC Saliency Map  and improves upon query-based methods like LIME3D by providing more interpretable critical point selection. Overall, the paper enhances existing approaches, offering more accurate and conceptually meaningful interpretations of point cloud models.", "essential_references_not_discussed": "I am not certain about any specific essential works that should have been included but were not.", "other_strengths_and_weaknesses": "Strengths:\n- The problem is well-described and well-justified\n- A new method is proposed that takes into account additional factors, such as human-eye interpretability\n- Detailed experiments are conducted\n- Justification for the use of the work, such as its application to autonomous driving\n- Key hyperparameters are clearly presented\n\nWeaknesses:\n- The related work section is too brief\n- The structure is a bit unusual. I would suggest placing the related works section at the beginning, perhaps after the introduction, rather than after the experimental results\n- Figure 2 is not very clear to me; it’s easier to understand the method from the description than from the figure itself", "other_comments_or_suggestions": "No additional comments or suggestions.", "questions_for_authors": "I do not have any questions for the authors", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "FKH81PotIm", "reviewer": "Reviewer_vGFq", "summary": "This paper mainly focuses on how to extract interpretable key concepts in point cloud models to enhance the interpretability of the models. This work addresses the issue that existing methods often fail to simultaneously meet the two criteria of \"faithfulness\" and \"conceptual cohesion\" when providing interpretable subsets. It proposes a framework named InfoCons based on information theory. By maximizing the mutual information between the key subsets and the model decisions, it ensures faithfulness. Meanwhile, it introduces a learning unbiased prior to minimize the mutual information between the key subsets and the input point cloud, thereby encouraging the formation of meaningful conceptual structures. A large number of experiments have verified the effectiveness of the method.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Dear Reviewer vGFq,**\n\nWe sincerely thank you for your thorough review and detailed comments on our paper. \nIn response to your concerns regarding the statement on “Good Explanations” and our qualitative comparison, we provide the following clarifications.\n\n### 1: **Clarification on “Good Explanations”**\n\n\nOur definition of *what constitutes a good explanation for point cloud models* builds upon **widely accepted principles** in interpretability research, which we clarify as follows:\n\n- (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: \n> \"...a novel explanation technique that explains the predictions of any classifier **in an interpretable and faithful manner** ...\".\n\n- (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**. \nThis 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):\n> \"**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).\" \n\n    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).  \n- (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.\nIn the image domain, concept-level explanations can be attributes labeled by humans [3] or selective patches [4, 5].\nIn 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.\n\nTo 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.\n\n--- \n\n[1] \"Why should I trust you?\" Explaining the predictions of any classifier. KDD 2016.\n\n[2] Grad-CAM: Visual Explanations from Deep Networks via Gradient-Based Localization. IJCV 2019.\n\n[3] Concept bottleneck models. ICML 2020.\n\n[4] Approximating cnns with bag-of-local-features models works surprisingly well on imagenet. ICLR 2019.\n\n[5] Explaining generalization power of a dnn using interactive concepts. AAAI 2024.\n\n---\n### 2: **Additional Qualitative Analyses**\n\nIn addition to Fig. 6 in Sec. 4.1, we have provided further qualitative comparisons in Appendix-Fig. 14 in the current manuscript.\n\nFurthermore, 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). \n\nAdditionally, 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.\n\nWe sincerely appreciate your insightful suggestions and will incorporate the additional qualitative results into our paper.\n\nBest regards,\n\nAuthors", "claims_and_evidence": "Most of the author's propositions are supported by clear quantitative or qualitative analyses. However, regarding the starting point of this article, \"an ideal critical subset should be faithful (preserving points that causally influence predictions) and conceptual coherent\n(forming semantically meaningful structures that align with human perception)\". This claim seems to have no explanation provided for it. I'm not quite sure whether this is a definition that others have proved or is a widly-used consensus, or a definition put forward by the author in this article. I think this statement should be substantiated and explained.)", "methods_and_evaluation_criteria": "The method InfoCons proposed from the perspective of information theory is useful.", "theoretical_claims": "I have checked the author's theoretical claims. In my opinion, they are correct, especially in the section about the deep variational information bottleneck.", "experimental_designs_or_analyses": "In Section 4.1, the qualitative analysis experiment conducted by the author merely relied on the performance of different methods on a few small samples to demonstrate the validity of his/her method. I think this experiment seems rather insufficiently rigorous and should have more or the entire dataset performance as supplementary evidence.", "relation_to_broader_scientific_literature": "This paper mainly applies information theory to conduct interpretable analysis on point clouds. I believe this idea can also be further extended to other research fields.", "essential_references_not_discussed": "There is no obvious lack of references.", "other_strengths_and_weaknesses": "I think the merit of this paper lies in its analysis of model interpretability from the perspective of information theory, which provides certain theoretical basis. Meanwhile, the paper has conducted numerous experiments to prove the effectiveness of the proposed method. Regarding the drawbacks, at present, one aspect is the aforementioned concerns about the initial statement \"an ideal critical subset should be faithful and conceptually coherent\" and the qualitative analysis.", "other_comments_or_suggestions": "no comments", "questions_for_authors": "see Other Strengths And Weaknesses", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ksM9UW7b4E", "reviewer": "Reviewer_LVUY", "summary": "The author proposes a novel InfoCons framework based on the principle of information theory. The framework divides point clouds into different 3D concepts with different influences by using the mutual information principle. It also learns meaningful concept structures by combining learnable prior knowledge. The effectiveness of this method is verified on multiple point cloud models.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Dear Reviewer LVUY,**\n\nWe 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:\n\n### 1: **Balancing Fidelity and Conceptual Coherence**\n\nThank you for raising an important question. In our work, we examine the balance between fidelity (faithfulness) and conceptual coherence (interpretability) from two perspectives:\n- (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.\n- (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). \n\nAs 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.\n\n---\n### 2: **Clarity of Figures, Mathematical Notation, and Novelty of Attention Bottleneck**\n\n- **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. \n- **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.\n\n---\n### 3: **Evaluating on More Recent Point Cloud Models**\n\nWe 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.\n\nTo 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):\n\n- 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\n- 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.\n- 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.\n\nFinally, 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.\n\n\n[1] Sonata: Self-Supervised Learning of Reliable Point Representations, arxiv25\n\nBest regards,\n\nAuthors", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "The authors propose an approach inspired by information theory and clearly establish the connection between their goals and theoretical considerations. The mathematical derivations in Sections 3.1-3.3 provide a clear path from theoretical principles to practical implementation.", "experimental_designs_or_analyses": "Yes. The authors evaluated InfoCons on multiple datasets (ModelNet40, ScanObjectNN, KITTI), eight different point cloud models, and two application scenarios.", "relation_to_broader_scientific_literature": "The author provides a background introduction to InfoCons from the perspective of point cloud interpretability, information theory, etc. In addition, the author provides a comprehensive review of pooling-based, gradient-based, and black-box query-based methods.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "Strengths:\n1、The authors proposed a method to solve the interpretability of 3D point cloud models from the perspective of information theory.\n2、Extensive experimental evaluations on multiple model architectures, datasets, and applications demonstrate the versatility and effectiveness of InfoCons.\nWeakness:\n1、The mechanisms behind balancing fidelity and conceptual coherence in explanations remain unclear.\n2、The article lacks an introduction to some mathematical symbols.\n3、The figure shown by the author is too unclear and the quality of the figure needs to be improved.\n4、Although the author used multiple models to verify the effectiveness of the method, these models are too old. It is recommended that the author verify the effectiveness of the model based on the latest method.\n5、The Attention Bottleneck lacks some novelty.", "other_comments_or_suggestions": "The author needs to check the writing of the entire article. For example, the font of the link in the lower left corner of page 11 is inconsistent.", "questions_for_authors": "See Weakness.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a novel interpretability method for point clouds grounded in information-theoretic principles. The contribution is timely and relevant, addressing a less-explored yet important aspect of 3D deep learning. The overall reception from the reviewers is positive, with appreciation for the originality of the approach and the soundness of the experimental protocol.

The authors provide a consistent evaluation aligned with their methodology, and the experiments are generally well-conducted. Reviewers raised concerns regarding the inclusion of certain important baselines—particularly Sonata—which were appropriately addressed during the rebuttal phase. This responsiveness is commendable and strengthens the empirical foundation of the work.

However, one of the key remaining concerns, raised by reviewer LVUY, is the limited scope of model applicability. Specifically, the effectiveness of the proposed method is not demonstrated on more recent or widely-used self-supervised models such as PointMAE, ReCon, or PointGPT. This raises questions about the generalizability and practical relevance of the method in contemporary settings.

Additionally, reviewers noted issues with presentation clarity, which affects the accessibility of the paper. Some parts of the text require refinement to improve the overall readability and ease of understanding.

In summary, the work presents a promising and original contribution to the interpretability of point cloud models. While there are areas for improvement—particularly in presentation and broader applicability—the core idea is compelling, and the authors have demonstrated a willingness to engage with reviewer feedback.
Decision: Accept (poster)