Learning representations through deep generative modeling is a powerful approach for dynamical modeling to discover the most simplified and compressed underlying description of the data, to then use it for other tasks such as prediction. Most learning tasks have intrinsic symmetries, i.e., the input transformations leave the output unchanged, or the output undergoes a similar transformation. The learning process is, however, usually uninformed of these symmetries. Therefore, the learned representations for individually transformed inputs may not be meaningfully related. In this paper, we propose an SO(3) equivariant deep dynamical model (EqDDM) for motion prediction that learns a structured representation of the input space in the sense that the embedding varies with symmetry transformations. EqDDM is equipped with equivariant networks to parameterize the state-space emission and transition models. We demonstrate the superior predictive performance of the proposed model on various motion data.
翻译:通过深层基因模型的学习表现是一种强有力的动态模型方法,目的是发现最简化和压缩的数据基本描述,然后将其用于预测等其他任务。大多数学习任务具有内在的对称性,即输入转换使输出保持不变,或产出发生类似的转变。但是,学习过程通常不了解这些对称性。因此,对个别转换输入的学习说明可能没有有意义的关联。在本文件中,我们提议了一种SO(3)等等异的深层动态模型(EqDDM)用于运动预测,以学习输入空间的结构化代表,即嵌入与对称转换不同。EqDDM配有等式网络,以参数化国家空间排放和转变模型。我们展示了各种运动数据的拟议模型的高级预测性性表现。