Is Flow Matching Just Trajectory Replay for Sequential Data?

Flow matching (FM) is increasingly used for time-series generation, but it is not well understood whether it learns a general dynamical structure or simply performs an effective "trajectory replay". We study this question by deriving the velocity field targeted by the empirical FM objective on sequential data, in the limit of perfect function approximation. For the Gaussian conditional paths commonly used in practice, we show that the implied sampler is an ODE whose dynamics constitutes a nonparametric, memory-augmented continuous-time dynamical system. The optimal field admits a closed-form expression as a similarity-weighted mixture of instantaneous velocities induced by past transitions, making the dataset dependence explicit and interpretable. This perspective positions neural FM models trained by stochastic optimization as parametric surrogates of an ideal nonparametric solution. Using the structure of the optimal field, we study sampling and approximation schemes that improve the efficiency and numerical robustness of ODE-based generation. On nonlinear dynamical system benchmarks, the resulting closed-form sampler yields strong probabilistic forecasts directly from historical transitions, without training.

DeXposure-FM: A Time-series, Graph Foundation Model for Credit Exposures and Stability on Decentralized Financial Networks

Credit exposure in Decentralized Finance (DeFi) is often implicit and token-mediated, creating a dense web of inter-protocol dependencies. Thus, a shock to one token may result in significant and uncontrolled contagion effects. As the DeFi ecosystem becomes increasingly linked with traditional financial infrastructure through instruments, such as stablecoins, the risk posed by this dynamic demands more powerful quantification tools. We introduce DeXposure-FM, the first time-series, graph foundation model for measuring and forecasting inter-protocol credit exposure on DeFi networks, to the best of our knowledge. Employing a graph-tabular encoder, with pre-trained weight initialization, and multiple task-specific heads, DeXposure-FM is trained on the DeXposure dataset that has 43.7 million data entries, across 4,300+ protocols on 602 blockchains, covering 24,300+ unique tokens. The training is operationalized for credit-exposure forecasting, predicting the joint dynamics of (1) protocol-level flows, and (2) the topology and weights of credit-exposure links. The DeXposure-FM is empirically validated on two machine learning benchmarks; it consistently outperforms the state-of-the-art approaches, including a graph foundation model and temporal graph neural networks. DeXposure-FM further produces financial economics tools that support macroprudential monitoring and scenario-based DeFi stress testing, by enabling protocol-level systemic-importance scores, sector-level spillover and concentration measures via a forecast-then-measure pipeline. Empirical verification fully supports our financial economics tools. The model and code have been publicly available. Model: https://huggingface.co/EVIEHub/DeXposure-FM. Code: https://github.com/EVIEHub/DeXposure-FM.

Revisiting the Generic Transformer: Deconstructing a Strong Baseline for Time Series Foundation Models

The recent surge in Time Series Foundation Models has rapidly advanced the field, yet the heterogeneous training setups across studies make it difficult to attribute improvements to architectural innovations versus data engineering. In this work, we investigate the potential of a standard patch Transformer, demonstrating that this generic architecture achieves state-of-the-art zero-shot forecasting performance using a straightforward training protocol. We conduct a comprehensive ablation study that covers model scaling, data composition, and training techniques to isolate the essential ingredients for high performance. Our findings identify the key drivers of performance, while confirming that the generic architecture itself demonstrates excellent scalability. By strictly controlling these variables, we provide comprehensive empirical results on model scaling across multiple dimensions. We release our open-source model and detailed findings to establish a transparent, reproducible baseline for future research.

T-STAR: A Context-Aware Transformer Framework for Short-Term Probabilistic Demand Forecasting in Dock-Based Shared Micro-Mobility

Reliable short-term demand forecasting is essential for managing shared micro-mobility services and ensuring responsive, user-centered operations. This study introduces T-STAR (Two-stage Spatial and Temporal Adaptive contextual Representation), a novel transformer-based probabilistic framework designed to forecast station-level bike-sharing demand at a 15-minute resolution. T-STAR addresses key challenges in high-resolution forecasting by disentangling consistent demand patterns from short-term fluctuations through a hierarchical two-stage structure. The first stage captures coarse-grained hourly demand patterns, while the second stage improves prediction accuracy by incorporating high-frequency, localized inputs, including recent fluctuations and real-time demand variations in connected metro services, to account for temporal shifts in short-term demand. Time series transformer models are employed in both stages to generate probabilistic predictions. Extensive experiments using Washington D.C.'s Capital Bikeshare data demonstrate that T-STAR outperforms existing methods in both deterministic and probabilistic accuracy. The model exhibits strong spatial and temporal robustness across stations and time periods. A zero-shot forecasting experiment further highlights T-STAR's ability to transfer to previously unseen service areas without retraining. These results underscore the framework's potential to deliver granular, reliable, and uncertainty-aware short-term demand forecasts, which enable seamless integration to support multimodal trip planning for travelers and enhance real-time operations in shared micro-mobility services.

From Numbers to Prompts: A Cognitive Symbolic Transition Mechanism for Lightweight Time-Series Forecasting

Large language models have achieved remarkable success in time series prediction tasks, but their substantial computational and memory requirements limit deployment on lightweight platforms. In this paper, we propose the Symbolic Transition Mechanism (STM) a novel framework that bridges numeric time series data and language models through symbolic abstraction and prompt engineering. STM transforms continuous time series values into symbol tokens with quantization techniques based on human cognitive structures, and captures temporal dynamics through structured transformations of symbols, enabling fast engineering based predictions in which language models focus on critical parts of time series data. STM is a general purpose mechanisms that ensure the integrity of backbone language models, but they significantly improve their efficiency by inferring the dynamic and structured patterns inherent in time series data. We evaluated STM on various time series datasets, paired with four small language models (SLM) with limited computational environments. For all models, STM achieves error reductions of up to 69% in MAE and 90% in MSE compared to the default backbone SLM without STM. These results demonstrate the potential of STM as an efficient, adaptable layer for symbol-driven time series prediction using foundation models. The accuracy improvements were made at negligible resource costs, with maximum GPU memory of the base model increasing by approximately 0.06% and latency overhead increasing by only 0.64%.

Dualformer: Time-Frequency Dual Domain Learning for Long-term Time Series Forecasting

Transformer-based models, despite their promise for long-term time series forecasting (LTSF), suffer from an inherent low-pass filtering effect that limits their effectiveness. This issue arises due to undifferentiated propagation of frequency components across layers, causing a progressive attenuation of high-frequency information crucial for capturing fine-grained temporal variations. To address this limitation, we propose Dualformer, a principled dual-domain framework that rethinks frequency modeling from a layer-wise perspective. Dualformer introduces three key components: (1) a dual-branch architecture that concurrently models complementary temporal patterns in both time and frequency domains; (2) a hierarchical frequency sampling module that allocates distinct frequency bands to different layers, preserving high-frequency details in lower layers while modeling low-frequency trends in deeper layers; and (3) a periodicity-aware weighting mechanism that dynamically balances contributions from the dual branches based on the harmonic energy ratio of inputs, supported theoretically by a derived lower bound. This design enables structured frequency modeling and adaptive integration of time-frequency features, effectively preserving high-frequency information and enhancing generalization. Extensive experiments conducted on eight widely used benchmarks demonstrate Dualformer's robustness and superior performance, particularly on heterogeneous or weakly periodic data. Our code is publicly available at https://github.com/Akira-221/Dualformer.

Patch-Level Tokenization with CNN Encoders and Attention for Improved Transformer Time-Series Forecasting

Transformer-based models have shown strong performance in time-series forecasting by leveraging self-attention to model long-range temporal dependencies. However, their effectiveness depends critically on the quality and structure of input representations derived from raw multivariate time-series data, particularly as sequence length and data scale increase. This paper proposes a two-stage forecasting framework that explicitly separates local temporal representation learning from global dependency modelling. In the proposed approach, a convolutional neural network operates on fixed-length temporal patches to extract short-range temporal dynamics and non-linear feature interactions, producing compact patch-level token embeddings. Token-level self-attention is applied during representation learning to refine these embeddings, after which a Transformer encoder models inter-patch temporal dependencies to generate forecasts. The method is evaluated on a synthetic multivariate time-series dataset with controlled static and dynamic factors, using an extended sequence length and a larger number of samples. Experimental results demonstrate that the proposed framework consistently outperforms a convolutional baseline under increased temporal context and remains competitive with a strong patch-based Transformer model. These findings indicate that structured patch-level tokenization provides a scalable and effective representation for multivariate time-series forecasting, particularly when longer input sequences are considered.

AdaNODEs: Test Time Adaptation for Time Series Forecasting Using Neural ODEs

Test time adaptation (TTA) has emerged as a promising solution to adapt pre-trained models to new, unseen data distributions using unlabeled target domain data. However, most TTA methods are designed for independent data, often overlooking the time series data and rarely addressing forecasting tasks. This paper presents AdaNODEs, an innovative source-free TTA method tailored explicitly for time series forecasting. By leveraging Neural Ordinary Differential Equations (NODEs), we propose a novel adaptation framework that accommodates the unique characteristics of distribution shifts in time series data. Moreover, we innovatively propose a new loss function to tackle TTA for forecasting tasks. AdaNODEs only requires updating limited model parameters, showing effectiveness in capturing temporal dependencies while avoiding significant memory usage. Extensive experiments with one- and high-dimensional data demonstrate that AdaNODEs offer relative improvements of 5.88\% and 28.4\% over the SOTA baselines, especially demonstrating robustness across higher severity distribution shifts.

Intermittent time series forecasting: local vs global models

Intermittent time series, characterised by the presence of a significant amount of zeros, constitute a large percentage of inventory items in supply chain. Probabilistic forecasts are needed to plan the inventory levels; the predictive distribution should cover non-negative values, have a mass in zero and a long upper tail. Intermittent time series are commonly forecast using local models, which are trained individually on each time series. In the last years global models, which are trained on a large collection of time series, have become popular for time series forecasting. Global models are often based on neural networks. However, they have not yet been exhaustively tested on intermittent time series. We carry out the first study comparing state-of-the-art local (iETS, TweedieGP) and global models (D-Linear, DeepAR, Transformers) on intermittent time series. For neural networks models we consider three different distribution heads suitable for intermittent time series: negative binomial, hurdle-shifted negative binomial and Tweedie. We use, for the first time, the last two distribution heads with neural networks. We perform experiments on five large datasets comprising more than 40'000 real-world time series. Among neural networks D-Linear provides best accuracy; it also consistently outperforms the local models. Moreover, it has also low computational requirements. Transformers-based architectures are instead much more computationally demanding and less accurate. Among the distribution heads, the Tweedie provides the best estimates of the highest quantiles, while the negative binomial offers overall the best performance.

vLinear: A Powerful Linear Model for Multivariate Time Series Forecasting

In this paper, we present \textbf{vLinear}, an effective yet efficient \textbf{linear}-based multivariate time series forecaster featuring two components: the \textbf{v}ecTrans module and the WFMLoss objective. Many state-of-the-art forecasters rely on self-attention or its variants to capture multivariate correlations, typically incurring $\mathcal{O}(N^2)$ computational complexity with respect to the number of variates $N$. To address this, we propose vecTrans, a lightweight module that utilizes a learnable vector to model multivariate correlations, reducing the complexity to $\mathcal{O}(N)$. Notably, vecTrans can be seamlessly integrated into Transformer-based forecasters, delivering up to 5$\times$ inference speedups and consistent performance gains. Furthermore, we introduce WFMLoss (Weighted Flow Matching Loss) as the objective. In contrast to typical \textbf{velocity-oriented} flow matching objectives, we demonstrate that a \textbf{final-series-oriented} formulation yields significantly superior forecasting accuracy. WFMLoss also incorporates path- and horizon-weighted strategies to focus learning on more reliable paths and horizons. Empirically, vLinear achieves state-of-the-art performance across 22 benchmarks and 124 forecasting settings. Moreover, WFMLoss serves as an effective plug-and-play objective, consistently improving existing forecasters. The code is available at https://anonymous.4open.science/r/vLinear.