Hopformer: Homogeneity-Pursuit Transformer for Time Series Forecasting

Multivariate time series forecasting is fundamental to numerous domains such as energy, finance, and environmental monitoring, where complex temporal dependencies and cross-variable interactions pose enduring challenges. Existing Transformer-based methods capture temporal correlations through attention mechanisms but suffer from quadratic computational cost, while state-space models like Mamba achieve efficient long-context modeling yet lack explicit temporal pattern recognition. Therefore we introduce UniMamba, a unified spatial-temporal forecasting framework that integrates efficient state-space dynamics with attention-based dependency learning. UniMamba employs a Mamba Variate-Channel Encoding Layer enhanced with FFT-Laplace Transform and TCN to capture global temporal dependencies, and a Spatial Temporal Attention Layer to jointly model inter-variate correlations and temporal evolution. A Feedforward Temporal Dynamics Layer further fuses continuous and discrete contexts for accurate forecasting. Comprehensive experiments on eight public benchmark datasets demonstrate that UniMamba consistently outperforms state-of-the-art forecasting models in both forecasting accuracy and computational efficiency, establishing a scalable and robust solution for long-sequence multivariate time-series prediction.

Long-term multivariate time series plays a significant role in many application areas such as power systems, trading, etc. However, their accurate prediction is quite difficult for conventional forecasting methods as they often exhibit high dimensionality and complex relationships. Recent works show that transformer-based approaches are quite effective for long-term forecasting thanks to their attention mechanism. However, in the presence of complex high-dimensional inputs, they show evidence of oversmoothing, limited capacity, and opacity. To this end, this paper introduces SETTer, a transformer-based model that addresses these challenges by incorporating novel techniques for decoupled self-attention and hybrid masking. The proposed techniques enable SETTer to effectively capture the dominant short- and long-term patterns across the temporal and channel dimensions. In addition, we enrich the model layers with simple explainable structures that indicate the discriminative pattern of SETTer. We show that with a single-layer transformer architecture, SETTer can effectively model long-term dependencies in the presence of varying data complexities. Extensive experiments on real-word benchmark datasets for long-term multivariate time series forecasting demonstrate that SETTer outperforms state-of-the-art models in 88% of the scenarios.

We introduce TiRex-2, a recurrent xLSTM-based time series foundation model that generalizes the univariate TiRex to multivariate forecasting with both past and future covariates. Real-world forecasting is inherently sequential: observations arrive continuously, variables evolve jointly, and a subset of covariates is known ahead of time. Existing Transformer-based time series foundation models capture cross-variate dependencies but incur quadratic complexity in context length and require full-history recomputation as new observations arrive. TiRex-2 addresses these limitations through a memory-centric recurrent design that operates at constant per-patch cost under streaming. The model combines a bidirectional time mixer with an asymmetric grouped-attention variate mixer, enabling the integration of future-known covariates while preserving strict causality over target variables. To our knowledge, this is the first time series foundation model that achieves this combination of properties. To support scalable multivariate pretraining, we propose a synthetic coupling pipeline that composes diverse multivariate samples on the fly from large univariate corpora. Empirically, TiRex-2 achieves state-of-the-art zero-shot performance on GIFT-Eval and fev-bench, remains stable when streamed to arbitrary context lengths, and maintains constant inference cost per patch. The model uses 38.4M active parameters in univariate mode, with an additional 44.1M parameters activated for multivariate forecasting.