论文标题
通过轨道映射证明不变性的简单策略
A Simple Strategy to Provable Invariance via Orbit Mapping
论文作者
论文摘要
许多应用程序需要神经网络的鲁棒性或理想的不变性，才能对输入数据的某些转换。最常见的是，通过使用对抗性培训或定义包括设计所需不变性的网络体系结构来解决此要求。在这项工作中，我们提出了一种方法，通过根据固定标准从（可能是连续的）轨道中选择一个元素，使网络体系结构对小组操作证明是不变的。简而言之，我们打算在将数据馈送到实际网络之前“撤消”任何可能的转换。此外，我们凭经验分析了通过培训或体系结构结合不变性的不同方法的性质，并在鲁棒性和计算效率方面证明了我们方法的优势。特别是，我们研究了图像旋转的鲁棒性（可以持续到离散化工件）以及3D点云分类的可证明的方向和缩放不变性。
Many applications require robustness, or ideally invariance, of neural networks to certain transformations of input data. Most commonly, this requirement is addressed by training data augmentation, using adversarial training, or defining network architectures that include the desired invariance by design. In this work, we propose a method to make network architectures provably invariant with respect to group actions by choosing one element from a (possibly continuous) orbit based on a fixed criterion. In a nutshell, we intend to 'undo' any possible transformation before feeding the data into the actual network. Further, we empirically analyze the properties of different approaches which incorporate invariance via training or architecture, and demonstrate the advantages of our method in terms of robustness and computational efficiency. In particular, we investigate the robustness with respect to rotations of images (which can hold up to discretization artifacts) as well as the provable orientation and scaling invariance of 3D point cloud classification.
