标题： 连续性丢弃用于神经微分方程 显示英文标题

标题： Continuum Dropout for Neural Differential Equations

摘要： 神经微分方程（NDEs）在建模连续时间动态方面表现出色，能够有效处理不规则观测、缺失值和噪声等挑战。 尽管具有优势，NDEs 在采用 dropout 这一深度学习正则化的基石技术时面临根本性挑战，使其容易过拟合。 为解决这一研究空白，我们引入了连续体 dropout，这是一种基于交替更新过程理论的通用 NDE 正则化技术。 连续体 dropout 将 dropout 的开关机制形式化为一个在连续时间中在活跃（演化）和非活跃（暂停）状态之间交替的随机过程。 这提供了一种防止过拟合并增强 NDE 一般化能力的方法。 此外，连续体 dropout 提供了一个结构化的框架，通过测试时的蒙特卡洛采样来量化预测不确定性。 通过广泛的实验，我们证明连续体 dropout 超过了现有的 NDE 正则化方法，在各种时间序列和图像分类任务中取得了更优的性能。 它还产生了更校准且更可信的概率估计，突显了其在感知不确定性的建模中的有效性。 显示英文摘要

摘要： Neural Differential Equations (NDEs) excel at modeling continuous-time dynamics, effectively handling challenges such as irregular observations, missing values, and noise. Despite their advantages, NDEs face a fundamental challenge in adopting dropout, a cornerstone of deep learning regularization, making them susceptible to overfitting. To address this research gap, we introduce Continuum Dropout, a universally applicable regularization technique for NDEs built upon the theory of alternating renewal processes. Continuum Dropout formulates the on-off mechanism of dropout as a stochastic process that alternates between active (evolution) and inactive (paused) states in continuous time. This provides a principled approach to prevent overfitting and enhance the generalization capabilities of NDEs. Moreover, Continuum Dropout offers a structured framework to quantify predictive uncertainty via Monte Carlo sampling at test time. Through extensive experiments, we demonstrate that Continuum Dropout outperforms existing regularization methods for NDEs, achieving superior performance on various time series and image classification tasks. It also yields better-calibrated and more trustworthy probability estimates, highlighting its effectiveness for uncertainty-aware modeling.