Decorrelating the Future: Joint Frequency Domain Learning for Spatio-temporal Forecasting

• URL: http://arxiv.org/abs/2603.04418v1
• Date: Fri, 13 Feb 2026 20:42:49 GMT
• Title: Decorrelating the Future: Joint Frequency Domain Learning for Spatio-temporal Forecasting
• Abstract summary: We propose a frequency-enhanced training objective that extends supervision to the model-temporal spectrum.<n>FreST aligns predictions with ground truth in a unified spectral domain, effectively decorrelating complex dependencies across both space and time.
• Score: 2.502143380601666
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Standard direct forecasting models typically rely on point-wise objectives such as Mean Squared Error, which fail to capture the complex spatio-temporal dependencies inherent in graph-structured signals. While recent frequency-domain approaches such as FreDF mitigate temporal autocorrelation, they often overlook spatial and cross spatio-temporal interactions. To address this limitation, we propose FreST Loss, a frequency-enhanced spatio-temporal training objective that extends supervision to the joint spatio-temporal spectrum. By leveraging the Joint Fourier Transform (JFT), FreST Loss aligns model predictions with ground truth in a unified spectral domain, effectively decorrelating complex dependencies across both space and time. Theoretical analysis shows that this formulation reduces estimation bias associated with time-domain training objectives. Extensive experiments on six real-world datasets demonstrate that FreST Loss is model-agnostic and consistently improves state-of-the-art baselines by better capturing holistic spatio-temporal dynamics.

Related papers

• FreKoo++: Learning Continuous Spectral Dynamics for Temporal Domain Generalization [28.679725417985008]
  Temporal Domain Generalization aims to learn from historical domains and generalize to unseen future distributions under concept drift.<n>We propose FreKoo++, a novel continuous spectral-dynamical framework that pioneers the unification of continuous Koopman modal dynamics with adaptive spectral disentanglement.<n>FreKoo++ achieves state-of-the-art performance under complex multi-scale drifts and irregular sampling.
  arXiv  Detail & Related papers  (2026-08-23T05:22:47Z)
• RouteTS: Frequency-Time Routing for Time Series Forecasting [2.872284417339312]
  RouteTS is a unified forecasting framework that partitions the frequency spectrum via routing and amplitude delegates to their mathematically optimal domains.<n>Extensive experiments demonstrate that RouteTS achieves competitive prediction accuracy across diverse real-world datasets.
  arXiv  Detail & Related papers  (2026-08-05T02:35:27Z)
• Learning Spatio-Temporal Foundation Models from Pure Synthetic Data [85.23980441738811]
  NeoST is a scalable synthetic-training corpus to real-world bias, a latent-space reasoning architecture that generates and iteratively refines multiple future trajectories, and latent-space objectives that emphasize structural dynamics and enable inference-time correction under distribution shifts.<n>Extensive experiments across diverse real-world benchmarks show that NeoST consistently outperforms existing STFMs in diverse real-worldtemporal systems.
  arXiv  Detail & Related papers  (2026-06-27T02:56:46Z)
• TimeAPN: Adaptive Amplitude-Phase Non-Stationarity Normalization for Time Series Forecasting [67.91113180885601]
  TimeAPN explicitly models and predicts non-stationary factors from both the time and frequency domains.<n>TimeAPN consistently improves long-term forecasting accuracy across multiple prediction horizons.<n>It outperforms state-of-the-art reversible normalization methods.
  arXiv  Detail & Related papers  (2026-03-18T07:21:24Z)
• MEMTS: Internalizing Domain Knowledge via Parameterized Memory for Retrieval-Free Domain Adaptation of Time Series Foundation Models [51.506429027626005]
  Memory for Time Series (MEMTS) is a lightweight and plug-and-play method for retrieval-free domain adaptation in time series forecasting.<n>Key component of MEMTS is a Knowledge Persistence Module (KPM), which internalizes domain-specific temporal dynamics.<n>This paradigm shift enables MEMTS to achieve accurate domain adaptation with constant-time inference and near-zero latency.
  arXiv  Detail & Related papers  (2026-02-14T14:00:06Z)
• Parallel Complex Diffusion for Scalable Time Series Generation [50.01609741902786]
  PaCoDi is a spectral-native architecture that decouples generative modeling in the frequency domain.<n>We show that PaCoDi outperforms existing baselines in both generation quality and inference speed.
  arXiv  Detail & Related papers  (2026-02-10T14:31:53Z)
• Time-Domain Linear Model-based Framework for Passive Acoustic Mapping of Cavitation Activity [4.219150964619931]
  Passive acoustic mapping enables the spatial mapping and temporal monitoring of cavitation activity.<n>Most conventional beamforming methods suffer from limited axial resolution due to the absence of a reference emission onset time.<n>We propose a linear playing model-based beam framework fully formulated in the time domain.
  arXiv  Detail & Related papers  (2025-11-25T17:48:04Z)
• Towards Non-Stationary Time Series Forecasting with Temporal Stabilization and Frequency Differencing [24.5925492214521]
  Time series often exhibit non-stationarity, including temporal distribution shifts and spectral variability.<n>We propose DTAF, a dual-branch framework that addresses non-stationarity in both the temporal and frequency domains.
  arXiv  Detail & Related papers  (2025-11-11T13:30:38Z)
• A Unified Frequency Domain Decomposition Framework for Interpretable and Robust Time Series Forecasting [81.73338008264115]
  Current approaches for time series forecasting, whether in the time or frequency domain, predominantly use deep learning models based on linear layers or transformers.<n>We propose FIRE, a unified frequency domain decomposition framework that provides a mathematical abstraction for diverse types of time series.<n>Fire consistently outperforms state-of-the-art models on long-term forecasting benchmarks.
  arXiv  Detail & Related papers  (2025-10-11T09:59:25Z)
• Frequency-Constrained Learning for Long-Term Forecasting [15.31488551912888]
  Real-world time series exhibit strong periodic structures arising from physical laws, human routines, or seasonal cycles.<n>Modern deep forecasting models often fail to capture these recurring patterns due to spectral bias and a lack of frequency-aware inductive priors.<n>We propose a simple yet effective method that enhances long-term forecasting by explicitly modeling periodicity.
  arXiv  Detail & Related papers  (2025-08-02T22:12:15Z)
• LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputation [55.800319453296886]
  Time series with missing or irregularly sampled data are a persistent challenge in machine learning.<n>We introduce a different Lombiable--Scargle layer that enables a reliable computation of the power spectrum of irregularly sampled data.
  arXiv  Detail & Related papers  (2025-06-20T14:48:42Z)
• Multivariate Long-term Time Series Forecasting with Fourier Neural Filter [42.60778405812048]
  We introduce FNF as the backbone and DBD as architecture to provide excellent learning capabilities and optimal learning pathways for spatial-temporal modeling.<n>We show that FNF unifies local time-domain and global frequency-domain information processing within a single backbone that extends naturally to spatial modeling.
  arXiv  Detail & Related papers  (2025-06-10T18:40:20Z)
• Cross Space and Time: A Spatio-Temporal Unitized Model for Traffic Flow Forecasting [16.782154479264126]
  Predicting backbone-temporal traffic flow presents challenges due to complex interactions between temporal factors. Existing approaches address these dimensions in isolation, neglecting their critical interdependencies. In this paper, we introduce Sanonymous-Temporal Unitized Unitized Cell (ASTUC), a unified framework designed to capture both spatial and temporal dependencies.
  arXiv  Detail & Related papers  (2024-11-14T07:34:31Z)
• Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling [68.8204255655161]
  We propose an artificial neural network with a mechanism to implicitly learn the phase spaces properties. Our approach is either as competitive as or better than most state-of-the-art strategies.
  arXiv  Detail & Related papers  (2020-06-19T21:04:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.