Multivariate time series (MTS) classification has attracted increasing attention across various domains. Existing methods either decompose MTS into separate univariate series, ignoring inter-variable dependencies, or jointly model all variables, which may lead to over-smoothing and loss of semantic structure. These limitations become particularly pronounced when dealing with complex and heterogeneous variable types. To address these challenges, we propose SwinGroupNet (SGN), which explores a novel perspective for constructing variable interaction and temporal dependency. Specifically, SGN processes multi-scale time series using (1) Variable Group Embedding (VGE), which partitions variables into groups and performs independent group-wise embedding; (2) Multi-Scale Group Window Mixing (MGWM), which reconstructs variable interactions by modeling both intra-group and inter-group dependencies while extracting multi-scale temporal features; and (3) Periodic Window Shifting and Merging (PWSM), which exploits inherent periodic patterns to enable hierarchical temporal interaction and feature aggregation. Extensive experiments on diverse benchmark datasets from multiple domains demonstrate that SGN consistently achieves state-of-the-art performance, with an average improvement of 4.2% over existing methods. We release the source code at https://github.com/colison/SGN.

A foundation model for medical time series, pretrained on ethically approved clinical datasets, can substantially reduce annotation burdens, minimize the need for task-specific tuning, and promote reliable transferability across healthcare institutions, data modalities, and clinical tasks, especially in data-scarce or privacysensitive environments. However, existing generalist time series foundation models struggle to handle medical time series data due to their inherent challenges, including irregular intervals, heterogeneous sampling rates, and frequent missing values. To address these challenges, we introduce MIRA, a unified foundation model specifically designed for medical time series forecasting. MIRA incorporates a Continuous-Time Rotary Positional Encoding that enables fine-grained modeling of variable time intervals, a frequency-specific mixture-of-experts layer that routes computation across latent frequency regimes to further promote temporal specialization, and a Continuous Dynamics Extrapolation Block based on Neural ODE that models the continuous trajectory of latent states, enabling accurate forecasting at arbitrary target timestamps. Pretrained on a large-scale and diverse medical corpus comprising over 454 billion time points collect from publicly available datasets, MIRA achieves reductions in forecasting errors by an average of 8% and 6% in out-of-distribution and in-distribution scenarios, respectively, when compared to other zero-shot and fine-tuned baselines. We also introduce a comprehensive benchmark spanning multiple downstream clinical tasks, establishing a foundation for future research in medical time series modeling. Our code is available at Microsoft/MIRA.

Long-term time series forecasting (LTSF) aims to predict future trends based on historical data. While longer lookback windows theoretically offer more comprehensive insights, Transformer-based models often struggle with them. On one hand, longer windows introduce more noise and redundancy, hindering the model's learning process. On the other hand, Transformers suffer from attention dispersion and are prone to overfitting to noise, especially when processing long sequences. In this paper, we introduce the Maximum Effective Window (MEW) metric to assess a model's ability to effectively utilize the lookback window.

Foundation models for time series analysis (TSA) have attracted significant attention. However, challenges such as training data scarcity and imbalance continue to hinder their development. Inspired by complex dynamic system theories, we design a series-symbol data generation mechanism, enabling the unrestricted creation of high-quality time series data paired with corresponding symbolic expressions. To leverage series-symbol data pairs with strong correlations, we develop SymTime, a pre-trained foundation model for enhancing time series representation using symbolic information. SymTime demonstrates competitive performance across five major TSA tasks when fine-tunes with downstream tasks, rivaling foundation models pre-trained on real-world datasets. This approach underscores the potential of series-symbol data generation and pretraining mechanisms in overcoming data scarcity and enhancing task performance.

Unlike MLPs, Kolmogorov-Arnold Networks (KANs) expose explicit learnable edge functions on every connection, enabling mechanistic explanation in time-series forecasting. This paper introduces Temporal Functional Circuits, a framework that transforms KAN edge functions from latent visualizations into faithful, temporally grounded explanations. Built on a gated residual KAN that decomposes forecasts into a linear base and a sparsely activated KAN correction, the framework (i) maps each edge to input lags via output-aware attribution, (ii) ranks edges by learned activation range, and (iii) validates faithfulness through edge-level interventions including zeroing and spline removal. Removing the learned B-spline component while retaining the base SiLU term degrades forecasts, providing evidence that the spline shape itself carries predictive value beyond the base activation. On four synthetic regimes of increasing complexity, the learned gate opens progressively wider as signal complexity grows. On regime-switching signals, gated KAN achieves 59% lower MSE than linear-only models. Across eight benchmarks, the gated architecture is competitive with linear, attention, and MLP alternatives, while providing interpretable edge functions that MLP-based corrections cannot offer.

Time series forecasting models often exhibit inconsistent performance across datasets with varying statistical and structural properties. Despite the wide range of available forecasting techniques, it remains unclear whether model selection can be reliably guided by simple data characteristics. This paper investigates why rule-based model selection fails in time series forecasting by analyzing the relationship between data-regime descriptors and model performance. A descriptor-based framework is introduced to characterize time series using measurable properties, including trend strength, seasonality, noise level, and temporal dependence. Based on these descriptors, a rule-based selection mechanism is formulated to map data regimes to candidate forecasting models. The approach is evaluated on multiple real-world datasets across different domains and forecasting horizons. The results show that rule-based model selection achieves low accuracy, with correct model identification occurring in only a small fraction of cases. Significant discrepancies are observed between recommended and empirically optimal models, particularly in noisy and mixed regimes. Further analysis reveals that model performance is highly sensitive to both dataset characteristics and forecasting horizon, resulting in substantial ranking instability across scenarios. These findings explain why simple heuristic rules fail to generalize and demonstrate that forecasting performance cannot be reliably predicted using static, descriptor-based approaches. This study provides empirical evidence that model selection in time series forecasting is inherently context-dependent and highlights the need for more adaptive, data-driven strategies.

Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency: practitioners value understanding how a model transforms temporal features, not merely what it predicts. Transformer-based models achieve strong accuracy but their attention weights reveal only token-level relevance, not the functional transformations applied to each feature. This work proposes DECOMPKAN, a lightweight attention-free architecture that combines trend-residual decomposition, channel-wise patching, learned instance normalization, and B-spline Kolmogorov-Arnold Network (KAN) edge functions. Each KAN edge learns an explicit, inspectable 1D scalar function ϕ(x) over learned patch-embedding coordinates that can be directly visualized, offering a form of architectural transparency not directly available in attention-based or MLP-based architectures. On standard benchmarks, DECOMPKAN achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations among selected published baselines, and achieves best or tied-best MSE on 20 of 36 comparisons (25 of 36 MAE; ties counted for all tied models) under a controlled same-recipe evaluation across 9 datasets including the physiological PPG-DaLiA benchmark. The architecture shows particular strength on datasets with smooth temporal dynamics (Solar 17%, ECL 10%vs.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of taskagnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).