We present Ordinary Differential Equation Variational Auto-Encoder
(ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential
data. Leveraging the advances in deep generative models, ODE$^2$VAE can
simultaneously learn the embedding of high dimensional trajectories and infer
arbitrarily complex continuous-time latent dynamics. Our model explicitly
decomposes the latent space into momentum and position components and solves a
second order ODE system, which is in contrast to recurrent neural network (RNN)
based time series models and recently proposed black-box ODE techniques. In
order to account for uncertainty, we propose probabilistic latent ODE dynamics
parameterized by deep Bayesian neural networks. We demonstrate our approach on
motion capture, image rotation and bouncing balls datasets. We achieve
state-of-the-art performance in long term motion prediction and imputation
tasks.

本文介绍了 ODE2VAE，一种用于高维序列数据的潜在二阶 ODE 模型，它可以同时学习高维轨迹的嵌入和推断任意复杂的连续时间潜在动力学，并通过深度贝叶斯神经网络参数化概率潜在 ODE 动力学，展示了在动作捕捉、图像旋转和弹跳球数据集上的表现出色，实现了长期运动预测和补全任务的最新性能。

ODE$^2$VAE: 深度生成二阶 ODE 的贝叶斯神经网络

ODE$^2$VAE: Deep generative second order ODEs with Bayesian neural  networks

The Recurrent Neural Networks and their variants have shown promising
performances in sequence modeling tasks such as Natural Language Processing.
These models, however, turn out to be impractical and difficult to train when
exposed to very high-dimensional inputs due to the large input-to-hidden weight
matrix. This may have prevented RNNs' large-scale application in tasks that
involve very high input dimensions such as video modeling; current approaches
reduce the input dimensions using various feature extractors. To address this
challenge, we propose a new, more general and efficient approach by factorizing
the input-to-hidden weight matrix using Tensor-Train decomposition which is
trained simultaneously with the weights themselves. We test our model on
classification tasks using multiple real-world video datasets and achieve
competitive performances with state-of-the-art models, even though our model
architecture is orders of magnitude less complex. We believe that the proposed
approach provides a novel and fundamental building block for modeling
high-dimensional sequential data with RNN architectures and opens up many
possibilities to transfer the expressive and advanced architectures from other
domains such as NLP to modeling high-dimensional sequential data.

通过使用 Tensor-Train 分解来分解 RNN 中的高维输入矩阵，尽管架构比其他模型简单得多，但在分类实验中仍能够实现与最先进的模型相媲美的性能，这为建模高维序列数据提供了一种新的基础模块，并打开了从其他领域（如自然语言处理）传输表达和先进模型的多种可能性。