We introduce a class of neural controlled differential equation inspired by
quantum mechanics. Neural quantum controlled differential equations (NQDEs)
model the dynamics by analogue of the Schr\"{o}dinger equation. Specifically,
the hidden state represents the wave function, and its collapse leads to an
interpretation of the classification probability. We implement and compare the
results of four variants of NQDEs on a toy spiral classification problem.

引入一类受量子力学启发的神经控制微分方程，称为神经量子控制微分方程（NQDEs）。通过类比薛定谔方程，NQDEs 模拟动力学。具体地，隐藏状态代表波函数，其塌缩解释了分类概率。我们在一个玩具螺旋分类问题上实现和比较了四个 NQDEs 变体的结果。

带有量子隐藏演化的神经控制微分方程

Neural Controlled Differential Equations with Quantum Hidden Evolutions

Neural ordinary differential equations are an attractive option for modelling
temporal dynamics. However, a fundamental issue is that the solution to an
ordinary differential equation is determined by its initial condition, and
there is no mechanism for adjusting the trajectory based on subsequent
observations. Here, we demonstrate how this may be resolved through the
well-understood mathematics of \emph{controlled differential equations}. The
resulting \emph{neural controlled differential equation} model is directly
applicable to the general setting of partially-observed irregularly-sampled
multivariate time series, and (unlike previous work on this problem) it may
utilise memory-efficient adjoint-based backpropagation even across
observations. We demonstrate that our model achieves state-of-the-art
performance against similar (ODE or RNN based) models in empirical studies on a
range of datasets. Finally we provide theoretical results demonstrating
universal approximation, and that our model subsumes alternative ODE models.

本研究介绍了一个新的神经模型：神经控制微分方程模型，解决了利用常规微分方程对时间动态进行建模时无法针对后续观察调整轨迹的问题，并通过实验和理论结果展示其在较多数据集上实现了与其他神经网络模型相当的最佳性能