In many applications of geometric deep learning, the choice of global
coordinate frame is arbitrary, and predictions should be independent of the
reference frame. In other words, the network should be equivariant with respect
to rotations and reflections of the input, i.e., the transformations of O(d).
We present a novel framework for building equivariant message passing
architectures and modifying existing non-equivariant architectures to be
equivariant. Our approach is based on local coordinate frames, between which
geometric information is communicated consistently by including tensorial
objects in the messages. Our framework can be applied to message passing on
geometric data in arbitrary dimensional Euclidean space. While many other
approaches for equivariant message passing require specialized building blocks,
such as non-standard normalization layers or non-linearities, our approach can
be adapted straightforwardly to any existing architecture without such
modifications. We explicitly demonstrate the benefit of O(3)-equivariance for a
popular point cloud architecture and produce state-of-the-art results on normal
vector regression on point clouds.

建立等变消息传递框架，实现几何深度学习中的任意维度欧几里得空间上的等变信息传递，通过局部坐标框架和张量对象在消息中保持几何信息一致性，并展示了 O (3) 等变性在点云架构上的优势及在法向量回归中的最新成果。

Tensor Frames -- 如何使任何消息传递网络是等变的

Tensor Frames -- How To Make Any Message Passing Network Equivariant

Point cloud architecture design has become a crucial problem for 3D deep
learning. Several efforts exist to manually design architectures with high
accuracy in point cloud tasks such as classification, segmentation, and
detection. Recent progress in automatic Neural Architecture Search (NAS)
minimizes the human effort in network design and optimizes high performing
architectures. However, these efforts fail to consider important factors such
as latency during inference. Latency is of high importance in time critical
applications like self-driving cars, robot navigation, and mobile applications,
that are generally bound by the available hardware. In this paper, we introduce
a new NAS framework, dubbed LC-NAS, where we search for point cloud
architectures that are constrained to a target latency. We implement a novel
latency constraint formulation to trade-off between accuracy and latency in our
architecture search. Contrary to previous works, our latency loss guarantees
that the final network achieves latency under a specified target value. This is
crucial when the end task is to be deployed in a limited hardware setting.
Extensive experiments show that LC-NAS is able to find state-of-the-art
architectures for point cloud classification in ModelNet40 with minimal
computational cost. We also show how our searched architectures achieve any
desired latency with a reasonably low drop in accuracy. Finally, we show how
our searched architectures easily transfer to a different task, part
segmentation on PartNet, where we achieve state-of-the-art results while
lowering latency by a factor of 10.

本研究提出了一个新的神经网络架构搜索框架 ——LC-NAS，该框架可以在指定延迟内搜索点云网络结构，并平衡了精度和延迟之间的权衡，实验结果表明，该框架在计算成本最小化的同时，能够找到具有最先进性能的点云分类体系结构。