In many scientific disciplines, we are interested in inferring the nonlinear
dynamical system underlying a set of observed time series, a challenging task
in the face of chaotic behavior and noise. Previous deep learning approaches
toward this goal often suffered from a lack of interpretability and
tractability. In particular, the high-dimensional latent spaces often required
for a faithful embedding, even when the underlying dynamics lives on a
lower-dimensional manifold, can hamper theoretical analysis. Motivated by the
emerging principles of dendritic computation, we augment a dynamically
interpretable and mathematically tractable piecewise-linear (PL) recurrent
neural network (RNN) by a linear spline basis expansion. We show that this
approach retains all the theoretically appealing properties of the simple
PLRNN, yet boosts its capacity for approximating arbitrary nonlinear dynamical
systems in comparatively low dimensions. We employ two frameworks for training
the system, one combining back-propagation-through-time (BPTT) with teacher
forcing, and another based on fast and scalable variational inference. We show
that the dendritically expanded PLRNN achieves better reconstructions with
fewer parameters and dimensions on various dynamical systems benchmarks and
compares favorably to other methods, while retaining a tractable and
interpretable structure.

本文介绍了一种基于线性样条基函数扩展动态可解释的分段线性循环神经网络（PLRNN）的方法，用于近似任意非线性动态系统。我们采用 BPTT 与教师强制以及快速可接受的变分推理两种框架对系统进行训练，并在各种动态系统基准测试上表明，这种方法具有更好的重建能力和更少的参数和尺寸。

可计算的树突状循环神经网络用于重构非线性动力学系统

Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems

The process of translation is ambiguous, in that there are typically many
valid trans- lations for a given sentence. This gives rise to significant
variation in parallel cor- pora, however, most current models of machine
translation do not account for this variation, instead treating the prob- lem
as a deterministic process. To this end, we present a deep generative model of
machine translation which incorporates a chain of latent variables, in order to
ac- count for local lexical and syntactic varia- tion in parallel corpora. We
provide an in- depth analysis of the pitfalls encountered in variational
inference for training deep generative models. Experiments on sev- eral
different language pairs demonstrate that the model consistently improves over
strong baselines.

通过深度生成模型，我们提供了一种考虑平行 corpus 中局部语义和句法变化的机器翻译方法，并通过多个语言对的实验验证了其相比基准模型的效果提高。