用神经控制微分方程实现通用时间序列生成，支持任意采样网格。
Universal Time Series Generation with Neural Controlled Differential Equations
- 基于结构化线性微分方程构建连续时间生成模型
- 在不规则时间网格上表现优于固定网格模型
- 适合需要高表达力的概率预测任务
状态空间模型（SSMs）的序列通用性研究已提出高效且最大表达力的连续时间建模方法。现有工作集中于判别式场景，本文将其拓展至生成式时间序列建模，证明最大表达力的结构化线性控制微分方程（SLiCEs）是通用时间序列生成器，可逼近紧致潜空间上连续因果前推路径的分布律（在 $W_ ty$ 空间中）。基于此理论，我们提出生成型SLiCEs（G-SLiCEs），一种在路径空间上进行流匹配的连续时间生成模型。实验表明，更高表达力显著提升概率预测与下游任务性能，同时保留连续时间模型的优势：可推广至任意观测网格，尤其在不规则网格场景下表现优异。
原文摘要 · Abstract (English)
Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in $W_\infty$. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.
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