发表机构
Applied AI Institute（应用人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出MercerFlow，利用先验核的Mercer特征基作为潜在映射，在MLP中实现流匹配预测，以更低内存和时间成本达到或超越TSFlow的CRPS性能。
AI 中文摘要
近期研究表明，用于时间序列预测的概率流匹配受益于与数据匹配的先验分布。由此产生的先验引入了局部相关性，通常由序列架构（如循环神经网络（RNN）、结构化状态空间模型（S4）或Transformer）来吸收。然而，此类骨干网络在每轮训练中消耗大量GPU内存和时间。一种更廉价的替代方案是基于MLP的潜在空间流匹配：通过可逆映射将时间序列嵌入到单个潜在向量，并在该空间中学习流，从而使得表格型MLP可以将序列视为一组特征。在条件流匹配（CFM）预测中，先验与线性潜在映射选择之间的关系研究不足，但我们发现它强烈影响性能。固定变换（如傅里叶或离散余弦变换（DCT））仅对Ornstein-Uhlenbeck先验具有良好的条件性，而拟合数据的PCA映射虽强但依赖训练集，对训练-测试偏移敏感。因此，我们提出使用先验核的Mercer特征基：它能精确对角化中心化协方差，与训练数据解耦，并适应非平稳和周期性先验。在五个GluonTS基准（ETTh1、ETTh2、Weather、Electricity、Traffic）上，在与TSFlow共享协议下，所提出的MLP在CRPS上匹配或超越TSFlow，同时训练内存减少约4.7倍，每轮时间减少3.5至4.4倍。
英文摘要
Recent work has shown that probabilistic flow matching for time series forecasting benefits from a data-matched prior. The resulting prior introduces local correlations, which a sequential architecture usually absorbs: a recurrent neural network (RNN), a structured state-space model (S4), or a Transformer. However, such a backbone costs GPU memory and time per epoch. A cheaper alternative is MLP-based latent-space flow matching: embed the time series via an invertible map to a single latent vector and learn the flow there, so a tabular MLP can treat the series as a set of features. The relationship between the prior and the choice of linear latent map is understudied in conditional flow matching (CFM) forecasting, yet we found it strongly affects performance. Fixed transforms such as Fourier or discrete cosine (DCT) are only well-conditioned for Ornstein--Uhlenbeck priors, while a principal-component (PCA) map fit to the data is a strong but training-set-dependent reference sensitive to train--test shift. Instead, we propose to use the Mercer eigenbasis of the prior kernel: it diagonalises the centred covariance exactly, decouples from training data, and adapts to non-stationary and periodic priors. On five GluonTS benchmarks (ETTh1, ETTh2, Weather, Electricity, Traffic) under a shared protocol with TSFlow, the resulting MLP matches or beats it on CRPS at about $4.7\times$ less training memory and $3.5\times$--$4.4\times$ less time per epoch.
