论文标题
重新访问神经网络中旋转表示的连续性
Revisiting the Continuity of Rotation Representations in Neural Networks
论文作者
论文摘要
在本文中，我们仔细分析了与神经网络中旋转表示相关的以前的作品中遇到的Euler角度和单位季节的某些病理行为。特别是，我们表明，对于某些问题，这两种表示将为某些输入产生完全错误的结果，并且这种行为是问题本身的拓扑特性固有的，并且不是由不合适的网络体系结构或培训程序引起的。我们进一步表明，先前提出的$ \ mathrm {so}（3）$的嵌入到更高维的欧几里得空间中，旨在固定这种行为，这不是普遍有效的，这是由于输入导致输入空间拓扑的变化的可能对称性。我们提出了一个合奏技巧作为替代解决方案。
In this paper, we provide some careful analysis of certain pathological behavior of Euler angles and unit quaternions encountered in previous works related to rotation representation in neural networks. In particular, we show that for certain problems, these two representations will provably produce completely wrong results for some inputs, and that this behavior is inherent in the topological property of the problem itself and is not caused by unsuitable network architectures or training procedures. We further show that previously proposed embeddings of $\mathrm{SO}(3)$ into higher dimensional Euclidean spaces aimed at fixing this behavior are not universally effective, due to possible symmetry in the input causing changes to the topology of the input space. We propose an ensemble trick as an alternative solution.
