Topo-ADV: Generating Topology-Driven Imperceptible Adversarial Point Clouds

Despite extensive progress in point cloud robustness, existing methods primarily rely on augmentation strategies or defense mechanisms while overlooking the geometric nature 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, potentially leading to misclassifications. 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 under multiple adversarial attacks across several datasets, achieving average robustness gains of +20.02 and +8.83 percentage points over vanilla models on ModelNet40 and ScanObjectNN, respectively.

The advent of deep neural networks has led to remarkable progress in 3D point cloud recognition, but they remain vulnerable to adversarial attacks. Although various defense methods have been studied, they suffer from a trade-off between robustness and transferability. We propose Adversarial Point Counterattack (APC) to achieve both simultaneously. APC is a lightweight input-level purification module that generates instance-specific counter-perturbations for each point, effectively neutralizing attacks. Leveraging clean-adversarial pairs, APC enforces geometric consistency in data space and semantic consistency in feature space. To improve generalizability across diverse attacks, we adopt a hybrid training strategy using adversarial point clouds from multiple attack types. Since APC operates purely on input point clouds, it directly transfers to unseen models and defends against attacks targeting them without retraining. At inference, a single APC forward pass provides purified point clouds with negligible time and parameter overhead. Extensive experiments on two 3D recognition benchmarks demonstrate that the APC achieves state-of-the-art defense performance. Furthermore, cross-model evaluations validate its superior transferability. The code is available at https://github.com/gyjung975/APC.

Persistent Homology (PH) offers stable, multi-scale descriptors of intrinsic shape structure by capturing connected components, loops, and voids that persist across scales, providing invariants that complement purely geometric representations of 3D data. Yet, despite strong theoretical guarantees and increasing empirical adoption, its integration into deep learning for point clouds remains largely ad hoc and architecturally peripheral. In this work, we introduce a unified design space for Persistent-Homology driven learning in 3D point clouds (3DPHDL), formalizing the interplay between complex construction, filtration strategy, persistence representation, neural backbone, and prediction task. Beyond the canonical pipeline of diagram computation and vectorization, we identify six principled injection points through which topology can act as a structural inductive bias reshaping sampling, neighborhood graphs, optimization dynamics, self-supervision, output calibration, and even internal network regularization. We instantiate this framework through a controlled empirical study on ModelNet40 classification and ShapeNetPart segmentation, systematically augmenting representative backbones (PointNet, DGCNN, and Point Transformer) with persistence diagrams, images, and landscapes, and analyzing their impact on accuracy, robustness to noise and sampling variation, and computational scalability. Our results demonstrate consistent improvements in topology-sensitive discrimination and part consistency, while revealing meaningful trade-offs between representational expressiveness and combinatorial complexity. By viewing persistent homology not merely as an auxiliary feature but as a structured component within the learning pipeline, this work provides a systematic framework for incorporating topological reasoning into 3D point cloud learning.