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

TL;DR

The paper tackles the challenge of interpreting point-cloud models by identifying interpretable, causally influential 3D concepts. It introduces InfoCons, an information-bottleneck–based framework that learns a soft, learnable attention bottleneck to decompose a point cloud into concepts and derive a faithful critical subset by maximizing $I(\mathcal{C},Y)$ while constraining $I(X,\mathcal{C})$. A Gaussian prior and noise are incorporated to decouple neighbor information and promote semantic coherence, producing informative score maps $\hat{m}$ with $\hat{z}=\hat{m}\odot z(x)$. Empirical results across ModelNet40, ScanObjectNN, and KITTI show InfoCons yields more interpretable, less redundant explanations compared to baselines, and its applications to data augmentation and adversarial attacks demonstrate practical benefits in safety-critical settings. The framework is scalable across diverse PC models and tasks, though it incurs computational overhead from the attention bottleneck and requires careful hyperparameter tuning.

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.

Figures (19)

• Figure 1: Attributing PC model outputs to a group of interpretable critical concepts using InfoCons. The derived concepts, which conform to a specific semantically meaningful structure (i.e., conceptual cohesion), can reflect their influence on the model outputs faithfully. The critical score map can also be integrated into multiple applications. Better viewed in color.
• 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 $\mathcal{G}\circ \mathcal{F}$. SymFunc stands for symmetric functions (e.g., maxpooling). Attention Bottleneck $\theta$ is trained with end-to-end objectives. Once trained, $\theta$ uses only the intermediate feature to provide explanations.
• Figure 3: Feature Analysis for four models in (A), and derived Selective 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 $|M|$). However, in hierarchical models, nearly all points are highlighted (Point No. 0,1,and 2 in (B)). We address this problem by proposing InfoCons in Eq. \ref{['eq:infocons']}.
• Figure 4: InfoCons-based critical subsets (200 pts) for four PC models (covering three distinct structure types) are compared with meanpool-based 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 5: The data flow of the bottleneck network $f(\cdot|z(x);\theta)$. The input $z$ is the intermediate feature from $\mathcal{F}$, and the output $\hat{m}$ holds the same dimension as $z$.

Theorems & Definitions (2)

• Definition 3.1: Selective Critical Points
• Definition 3.2: InfoCons