MercerFlow: Flow Matching in a Kernel-Induced Latent Space for Probabilistic Forecasting

arXiv:2610.06039v1 Announce Type: new Abstract: 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 4.7imes less training memory and 3.5imes--4.4imes less time per epoch.

Related

• DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecasting
• Improving Ensemble Filters with Flow Matching
• Causally-Constrained Probabilistic Forecasting for Time-Series Anomaly Detection

Source: arXiv cs.LG | 2026-10-06