Beyond Defenses: Manifold-Aligned Regularization for Intrinsic 3D Point Cloud Robustness

TL;DR

This paper introduces MAPR, a geometric regularization framework that aligns latent and intrinsic surface geometries to enhance 3D point cloud robustness without adversarial training.

Contribution

It formalizes the geometric cause of adversarial vulnerability in 3D networks and proposes MAPR to improve robustness by aligning predictions across intrinsic perturbations.

Findings

MAPR improves robustness by +20.02% on ModelNet40.

MAPR improves robustness by +8.58% on ScanObjectNN.

MAPR enhances invariance to geometry-preserving perturbations.

Abstract

Despite extensive progress in point cloud robustness, existing methods primarily improve performance through augmentation or defense mechanisms, while overlooking the geometric root cause of adversarial fragility. We hypothesize that adversarial vulnerability in 3D networks arises from a manifold misalignment between the latent geometry learned by the model and the intrinsic geometry of the underlying surface. Small, geometry-preserving perturbations along the input manifold often induce disproportionate distortions in feature space, revealing a misalignment between latent and intrinsic geometries. We formalize this phenomenon by developing a geometric interpretation of 3D robustness that links classical adversarial theory to the intrinsic structure of point clouds. Motivated by this analysis, we introduce Manifold-Aligned Point Recognition (MAPR), a framework that regularizes the latent geometry by aligning predictions across intrinsic perturbations. MAPR augments each point cloud with intrinsic features capturing local curvature and diffusion structure, and applies a consistency loss that preserves invariance to intrinsic, geometry-preserving perturbations. Without relying on adversarial training or additional data, MAPR consistently improves robustness across multiple adversarial attacks on both the ModelNet40 and ScanObjectNN datasets, achieving average robustness gains of +20.02% and +8.58% on ModelNet40 and ScanObjectNN, respectively.