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Robustifying Point Cloud Networks by Refocusing

Meir Yossef Levi, Guy Gilboa

TL;DR

This study develops a general mechanism to increase point clouds neural networks robustness based on focus analysis and proposes a parameter-free refocusing algorithm that aims to unify all corruptions under the same distribution.

Abstract

The ability to cope with out-of-distribution (OOD) corruptions and adversarial attacks is crucial in real-world safety-demanding applications. In this study, we develop a general mechanism to increase neural network robustness based on focus analysis. Recent studies have revealed the phenomenon of \textit{Overfocusing}, which leads to a performance drop. When the network is primarily influenced by small input regions, it becomes less robust and prone to misclassify under noise and corruptions. However, quantifying overfocusing is still vague and lacks clear definitions. Here, we provide a mathematical definition of \textbf{focus}, \textbf{overfocusing} and \textbf{underfocusing}. The notions are general, but in this study, we specifically investigate the case of 3D point clouds. We observe that corrupted sets result in a biased focus distribution compared to the clean training set. We show that as focus distribution deviates from the one learned in the training phase - classification performance deteriorates. We thus propose a parameter-free \textbf{refocusing} algorithm that aims to unify all corruptions under the same distribution. We validate our findings on a 3D zero-shot classification task, achieving SOTA in robust 3D classification on ModelNet-C dataset, and in adversarial defense against Shape-Invariant attack. Code is available in: https://github.com/yossilevii100/refocusing.

Robustifying Point Cloud Networks by Refocusing

TL;DR

This study develops a general mechanism to increase point clouds neural networks robustness based on focus analysis and proposes a parameter-free refocusing algorithm that aims to unify all corruptions under the same distribution.

Abstract

The ability to cope with out-of-distribution (OOD) corruptions and adversarial attacks is crucial in real-world safety-demanding applications. In this study, we develop a general mechanism to increase neural network robustness based on focus analysis. Recent studies have revealed the phenomenon of \textit{Overfocusing}, which leads to a performance drop. When the network is primarily influenced by small input regions, it becomes less robust and prone to misclassify under noise and corruptions. However, quantifying overfocusing is still vague and lacks clear definitions. Here, we provide a mathematical definition of \textbf{focus}, \textbf{overfocusing} and \textbf{underfocusing}. The notions are general, but in this study, we specifically investigate the case of 3D point clouds. We observe that corrupted sets result in a biased focus distribution compared to the clean training set. We show that as focus distribution deviates from the one learned in the training phase - classification performance deteriorates. We thus propose a parameter-free \textbf{refocusing} algorithm that aims to unify all corruptions under the same distribution. We validate our findings on a 3D zero-shot classification task, achieving SOTA in robust 3D classification on ModelNet-C dataset, and in adversarial defense against Shape-Invariant attack. Code is available in: https://github.com/yossilevii100/refocusing.
Paper Structure (22 sections, 1 theorem, 5 equations, 9 figures, 6 tables, 2 algorithms)

This paper contains 22 sections, 1 theorem, 5 equations, 9 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Why rely on less influential inputs?
  3. Related Work
  4. Focus Definition and Refocusing Method
  5. Focus
  6. Why normalized entropy?
  7. Focus distribution, over- and under-focusing
  8. Refocusing
  9. Refocusing - "reign of the less influential"
  10. Adaptive threshold
  11. Applications and Experiments
  12. Robust classification
  13. Adversarial defense
  14. Future Work
  15. Conclusion
  16. ...and 7 more sections

Key Result

proposition thmcounterproposition

For any network $F$, input $X$ of any size $N$ and normalized influence $I_F(X)$, the focus $f(X)$ has the following properties:

Figures (9)

  • Figure 1: High and low focus examples. Samples resulting in low focus distribute influence across a broad spectrum of points, while in the case of high focus, influence becomes concentrated within specific regions. Samples containing flat areas, with some extent of symmetry against the center of the shape, contribute to a decrease in focus. It is possible that samples predominantly spanning a 2D plane prompt the network to prioritize attention towards distinctive regions. Points are color-coded by influence.
  • Figure 2: Variation of focus across different corruptions. Influence maps on corrupted samples from ModelNet-C modelnet_c using DGCNN dgcnn. The presence of outliers predominantly increases focus, while occluded parts decrease it. Points are color-coded according to influence. We denote by $f$ the focus of the network for that sample, as defined in Eq. \ref{['eq:focus']}.
  • Figure 3: Outliers and smooth corruptions often draw high influence. Samples color coded according to influence. The measurement of influence, reasonably distributed in an uncorrupted point cloud, is mainly redistributed to outliers in the corrupted version.
  • Figure 4: Refocusing. Left - Focus distribution on DGCNN dgcnn based on the clean set of ModelNet40 modelnet40 and on corrupted sets (ModelNet-C modelnet_c). Corrupted samples deviate from the in-focus region. Right - Screening out influential points aligns the focus distribution, expanding the in-focus region at the expense of under- and over-focus regions. In the chair example shown, one can observe the network is influenced by similar points after refocusing, resembling roughly the same influence distribution across the shape.
  • Figure 5: In-focus, Under-focus, and Over-focus. Top - Histogram of focus values for the clean set, ModelNet40 modelnet40, defining the in-focus region inside the standard deviation. Histograms collected from corrupted sets in ModelNet-C modelnet_c are clearly out of the training distribution. The trend indicates that the appearance of outliers correlates with over-focusing, while the absence of points correlates with under-focusing. Bottom - Success rate of clean (blue) and corrupted (red) sets. A clear performance drop is observed in the over-focus and under-focus regions.
  • ...and 4 more figures

Theorems & Definitions (2)

  • definition thmcounterdefinition: Focus of a network
  • proposition thmcounterproposition: Focus properties