用神经随机微分方程建模连续时间序列，统一处理复杂动态数据。
Neural SDEs as a Unified Approach to Continuous-Domain Sequence Modeling
- 将时序数据视为连续动力系统的离散采样，用神经SDE建模演化过程。
- 提出无需模拟的高效训练方法，实现端到端最大似然学习。
- 在具身与生成类任务中表现优异，适用于高维复杂时序场景。
受微分方程在科学与工程中广泛建模连续动态的启发，我们提出一种新颖且直观的连续序列建模方法。该方法将时间序列数据视为潜在连续动力系统的离散采样，并使用神经随机微分方程（Neural SDE）建模其时间演化，其中流（漂移）和扩散项均由神经网络参数化。我们推导出一个合理的最大似然目标，并设计了一种无需模拟的高效训练方案。通过在具身与生成式人工智能任务上的实验，展示了该方法的通用性。据我们所知，这是首个证明基于SDE的连续时间建模在复杂场景中同样出色的成果，有望为高维、时间复杂的领域开启新的研究方向。
原文摘要 · Abstract (English)
Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets time-series data as \textit{discrete samples from an underlying continuous dynamical system}, and models its time evolution using Neural Stochastic Differential Equation (Neural SDE), where both the flow (drift) and diffusion terms are parameterized by neural networks. We derive a principled maximum likelihood objective and a \textit{simulation-free} scheme for efficient training of our Neural SDE model. We demonstrate the versatility of our approach through experiments on sequence modeling tasks across both embodied and generative AI. Notably, to the best of our knowledge, this is the first work to show that SDE-based continuous-time modeling also excels in such complex scenarios, and we hope that our work opens up new avenues for research of SDE models in high-dimensional and temporally intricate domains.
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