Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive and time-consuming. Additionally, assessing the networks' generalization abilities or predicting how the inferred output changes under input transformations is complicated since the networks are usually treated as a black box. Both of these problems can be mitigated by incorporating prior knowledge into the neural network. One promising approach, inspired by the success of convolutional neural networks in computer vision tasks, is to incorporate knowledge about symmetric geometrical transformations of the problem to solve that affect the output in a predictable way. This promises an increased data efficiency and more interpretable network outputs. In this survey, we try to give a concise overview about different approaches that incorporate geometrical prior knowledge into neural networks. Additionally, we connect those methods to 3D object detection for autonomous driving, where we expect promising results when applying those methods.

翻译：深度神经网络通过利用大量训练数据，在许多不同问题设置中取得了最先进的结果。然而，收集、存储数据，以及在监督学习情况下对数据进行标注，既昂贵又耗时。此外，由于网络通常被视为黑箱，评估其泛化能力或预测推断输出在输入变换下的变化较为复杂。通过将先验知识融入神经网络，这两个问题都可以得到缓解。受卷积神经网络在计算机视觉任务中取得成功的启发，一种有前景的方法是融入关于待解决问题的对称几何变换知识，这些变换以可预测的方式影响输出。这有望提高数据效率并增强网络输出的可解释性。在本综述中，我们力求简洁概述将几何先验知识融入神经网络的不同方法。此外，我们将这些方法与自动驾驶中的三维物体检测联系起来，并预期在这些方法的应用中会取得有前景的结果。