Invariance and equivariance to the rotation group have been widely discussed
in the 3D deep learning community for pointclouds. Yet most proposed methods
either use complex mathematical tools that may limit their accessibility, or
are tied to specific input data types and network architectures. In this paper,
we introduce a general framework built on top of what we call Vector Neuron
representations for creating SO(3)-equivariant neural networks for pointcloud
processing. Extending neurons from 1D scalars to 3D vectors, our vector neurons
enable a simple mapping of SO(3) actions to latent spaces thereby providing a
framework for building equivariance in common neural operations -- including
linear layers, non-linearities, pooling, and normalizations. Due to their
simplicity, vector neurons are versatile and, as we demonstrate, can be
incorporated into diverse network architecture backbones, allowing them to
process geometry inputs in arbitrary poses. Despite its simplicity, our method
performs comparably well in accuracy and generalization with other more complex
and specialized state-of-the-art methods on classification and segmentation
tasks. We also show for the first time a rotation equivariant reconstruction
network.

本文介绍了一种基于向量神经元的通用框架，用于创建点云处理的 SO（3）- 等变神经网络。通过扩展神经元从 1D 标量到 3D 向量，向量神经元使得我们可以将 SO（3）操作简单地映射到潜在空间中，从而提供了构建常见神经操作的等变性的框架，尽管方法简单，但在准确性和泛化性方面表现出色，是处理任意姿态下的几何输入的一种有效方法。

矢量神经元：一个针对 SO (3)- 等变网络的通用框架

Vector Neurons: A General Framework for SO(3)-Equivariant Networks

The 3D deep learning community has seen significant strides in pointcloud
processing over the last few years. However, the datasets on which deep models
have been trained have largely remained the same. Most datasets comprise clean,
clutter-free pointclouds canonicalized for pose. Models trained on these
datasets fail in uninterpretible and unintuitive ways when presented with data
that contains transformations "unseen" at train time. While data augmentation
enables models to be robust to "previously seen" input transformations, 1) we
show that this does not work for unseen transformations during inference, and
2) data augmentation makes it difficult to analyze a model's inherent
robustness to transformations. To this end, we create a publicly available
dataset for robustness analysis of point cloud classification models
(independent of data augmentation) to input transformations, called
RobustPointSet. Our experiments indicate that despite all the progress in the
point cloud classification, there is no single architecture that consistently
performs better -- several fail drastically -- when evaluated on transformed
test sets. We also find that robustness to unseen transformations cannot be
brought about merely by extensive data augmentation. RobustPointSet can be
accessed through this https URL

本研究旨在探讨如何增加点云分类模型对于未知变换的鲁棒性，通过创建名为 RobustPointSet 的公共数据集，研究表明即使在点云分类领域进展很大，也没有一种单一的架构能够一致地表现得更好。