FreKoo++ is a continuous spectral-dynamical framework designed for Temporal Domain Generalization (TDG). It unifies continuous Koopman modal dynamics with adaptive spectral disentanglement, mapping source-domain parameters into a latent space and modeling their evolution as a superposition of learnable continuous modes. The method handles irregular timestamps, supports arbitrary horizon extrapolation, and introduces an adaptive soft spectral weighting mechanism that isolates persistent dynamics from transient noise, achieving state‑of‑the‑art performance on discrete and continuous TDG benchmarks.
By En Yu, Xiaoyu Yang, Wei Duan, Guangquan Zhang, Jie Lu
arXiv:2606. 04930v1 Announce Type: cross Abstract: Real-time data analysis requires the ability to accurately and adaptively address nonlinear dynamics in a nonstationary data stream while preserving computational efficiency.
By Naoki Chihara, Ren Fujiwara, Yasuko Matsubara, Yasushi Sakurai
AdaMamba introduces an adaptive frequency-gated Mamba architecture for long‑term time series forecasting. The model integrates an interaction learning module that captures cross‑variable dependencies and multi‑scale context, and an adaptive frequency‑gated state space module that generates context‑dependent frequency bases and unifies temporal forgetting into a single time‑frequency gate. Experiments on seven public benchmarks and four domain‑specific datasets show that AdaMamba consistently outperforms state‑of‑the‑art baselines while remaining computationally efficient.
By Xudong Jiang, Mingshan Loo, Wengen Li, Mingrui Zhang, Jihong Guan, Shuigeng Zhou
The paper introduces CoSPOT, an online time series forecasting framework that uses a frozen pre‑trained large language model (LLM) as the core forecaster. CoSPOT adapts to evolving data by applying compositional spectral prompts—frequency‑domain basis prompts weighted by their amplitudes—allowing the model to represent unseen patterns as new combinations of learned bases while updating few parameters. Experiments on real‑world datasets show CoSPOT’s effectiveness in extended online phases and cross‑dataset scenarios with significant distribution shifts.
By Seungyoon Choi, Hyunchul Kim, Jae-Gil Lee, Chanyoung Park
The paper introduces FreqDiff, a Frequency-aware Diffusion framework designed to improve Temporal Knowledge Graph extrapolation. It frames future object prediction as a query-slot denoising task and employs a dual-stream denoiser that combines temporal dependency modeling with a context-aware spectral calibration branch. The spectral branch generates history-conditioned filters from learnable bases to recalibrate denoising representations, while a frequency-domain regularizer aligns the denoised output with the true target in spectral space, achieving state-of-the-art results on four public TKG benchmarks.
By Yanglei Gan, Peng He, Run Lin, Peiyuan Jiang, Yifan Wang, Qiao Liu
arXiv:2604. 01577v3 Announce Type: replace-cross Abstract: We study out of distribution generalization in streaming tasks where models are trained on short sequences but must operate over much longer, unknown horizons under bounded memory.
By Shota Takashiro, Masanori Koyama, Takeru Miyato, Yusuke Iwasawa, Yutaka Matsuo, Kohei Hayashi
The paper introduces an in‑span adaptation technique for reduced‑order models, where the reduced subspace is continually updated using the model’s own predictions via an incremental singular‑value decomposition with a forgetting factor. This creates a trajectory‑informed spectral preconditioner that reweights and realigns the basis without changing the subspace, enabling the model to better absorb future out‑of‑span corrections. The authors demonstrate the method on a 3‑D spiral example and nonlinear PDEs such as viscous Burgers and Fisher–KPP, and relate the approach to in‑context learning in dynamical systems.
By Amirpasha Hedayat, Laura Balzano, Karthik Duraisamy
arXiv:2606. 07695v1 Announce Type: cross Abstract: Multi-Modality Spatio-Temporal Forecasting (MoSTF) extends traditional spatio-temporal forecasting by incorporating diverse traffic modalities.
By Yongchao Li, Yang Li, Zhuoxuan Li, Jun Chen, Chu Zhang, Jinde Cao, Leszek Rutkowski
arXiv:2607. 06607v1 Announce Type: cross Abstract: Accurate long-term forecasting in complex systems is frequently compromised by dataset-level distribution shifts, where diverse underlying behavioral modes and evolving system states drive the dynamic multivariate time-series.
By Lanhao Li, Bingshu Xie, Lijun Sun, Xin Xue, Haoyi Zhou, Jianxin Li
The paper introduces CoSPOT, an LLM-based framework for online time series forecasting that uses compositional spectral prompts to adapt to non‑stationary environments. By keeping the large language model frozen and updating only spectral basis prompts derived from frequency‑domain decompositions, CoSPOT efficiently handles long‑term adaptation and unseen patterns. Experiments on real‑world datasets show its effectiveness in extended online phases and cross‑dataset scenarios with significant distribution shifts.
arXiv:2607. 02937v1 Announce Type: new Abstract: Reduced-order models compress high-dimensional dynamics into low-dimensional representations that can be evaluated rapidly, but they lose accuracy when online dynamics drift beyond the training data.
By Amirpasha Hedayat, Laura Balzano, Karthik Duraisamy
The paper introduces STFO (Spatio-Temporal Field Operator), a method for continual spatio‑temporal forecasting that decouples forecasting representations from specific sensor layouts. By normalizing coordinate‑based aggregation onto a fixed latent grid and using a spectral descriptor to adapt to process drift, STFO can reuse learned spatial maps across varying sensor configurations. Experiments on PEMS‑Stream, CA‑Stream, and AIR‑Stream show that STFO‑Large improves average MAE by 8.4% over DOL on PEMS‑Stream and 4.7% on CA‑Stream.
By Lewei Xie, Haoyu Zhang, Jiajun Zhou, Yulong Chen, Guanxing Chen, Yu-An Huang, Hau-San Wong, Yifan Zhang, Zhi-An Huang