发表机构
University of Science and Technology of China（中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该综述提出统一数学视角，通过分类法组织连续时间机器学习各分支，规范其公式并比较算法与权衡，识别开放挑战。
AI 中文摘要
连续时间（CT）机器学习已成为一个原则性框架，用于将时间动态建模为连续过程，特别是在观测在任意时间点采样或跨越长期范围的情况下。然而，CT机器学习的主要分支已在不同的研究社区中成熟，导致其数学关系和设计权衡未被充分刻画。在本综述中，我们通过一个分类法，根据其基础数学公式对主要CT机器学习分支进行组织，开发了一个统一的、概念驱动的视角。我们提出了一个规范的数学公式，通过向量场参数化、随机性、记忆机制和离散化的不同架构选择，将这些分支家族联系起来。我们比较了训练算法、优化策略和失败模式，突出了各家族之间的权衡。我们进一步提供了理论计算复杂性的比较分析，以及每个家族代表性架构的说明性架构控制基准分析。我们还回顾了支持其实现的软件生态系统。最后，我们识别了逼近理论、训练稳定性、硬件高效实现、基准测试、基础模型和科学机器学习中的开放挑战，并讨论了未来研究的议程。
英文摘要
Continuous-time (CT) machine learning has emerged as a principled framework for modeling temporal dynamics as a continuous process, particularly when observations are sampled at arbitrary time points or span long-range horizons. However, major branches of CT machine learning have matured in separate research communities, leaving their mathematical relationships and design trade-offs insufficiently characterized. In this survey, we develop a unified, concept-driven view of major CT machine learning branches through a taxonomy that organizes families according to their underlying base mathematical formulations. We present a canonical mathematical formulation that relates these families through different architectural choices of vector-field parameterization, stochasticity, memory mechanisms, and discretization. We compare training algorithms, optimization strategies, and failure modes, highlighting the trade-offs across families. We further provide a comparative analysis of theoretical computational complexity alongside an illustrative architecture-controlled benchmark analysis on representative architectures from each family. We also review software ecosystems supporting their implementation. Finally, we identify open challenges in approximation theory, training stability, hardware-efficient implementations, benchmarking, foundation models, and scientific machine learning, and discuss an agenda for future research.
