analiza aiqbench
This research introduces a novel approach to probabilistic time series forecasting by utilizing the Mercer eigenbasis within a kernel-induced latent space. By replacing computationally expensive recurrent architectures with an MLP operating in this specific latent representation, the method achieves comparable or superior predictive accuracy while significantly reducing GPU memory usage and training time. The technique offers a more efficient alternative for handling local correlations in flow matching models without relying on fixed transforms that may suffer from train-test distribution shifts.
MercerFlow: Flow Matching in a Kernel-Induced Latent Space for Probabilistic Forecasting
arXiv:2610.06039v1 Announce Type: cross 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 $4.7\times$ less training memory and $3.5\times$--$4.4\times$ less time per epoch.
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 $4.7\times$ less training memory and $3.5\times$--$4.4\times$ less time per epoch.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.06039 [cs.LG]
(or arXiv:2610.06039v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.06039 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 315 cuvinte
Subiecte conexe
[AINews] Meta Muse Wonder & Wonder Full: MSL’s Claude 5.5-tier Frontier Model
Latent Space · 13 oct. 2026
[AINews] Reality Checks on AI News (Yegge shuts down Gas Town, Databricks’ +60% Astra cost)
Latent Space · 17 sept. 2026
Improving Function Space Flow Matching with Kernel Optimal Transport
arXiv · 30 sept. 2026
Generative Modeling of Discrete Data Using Geometric Latent Subspaces
arXiv · 28 sept. 2026