Transformers are widely used across data modalities, and yet the principles distilled from text models often transfer imperfectly to models trained to other modalities. In this paper, we analyze Transformers through the lens of rank structure. Our focus is on the time series setting, where the structural properties of the data differ remarkably from those of text or vision. We show that time-series embeddings, unlike text or vision, exhibit sharply decaying singular value spectra: small patch sizes and smooth continuous mappings concentrate the data into low-rank subspaces. From this, we prove that the associated $Q/K/V$ projections admit accurate low-rank approximations, and that attention layers become compressible in proportion to the decay of the embedding spectrum. We introduce the concept of flow-of-ranks, a phenomenon by which nonlinear mixing across depth inflates the rank, explaining why early layers are most amenable to compression and why ranks grow with depth. Guided by these theoretical and empirical results, we use these insights to compress Chronos, a large time series foundation model, achieving a reduction of $65\%$ in inference time and $81\%$ in memory, without loss of accuracy. Our findings provide principled guidance for allocating width, depth, and heads in time series foundation models, and for exploiting their inherent compressibility.

Accurate wave height prediction is critical for maritime safety and coastal resilience, yet conventional physics-based models and traditional machine learning methods face challenges in computational efficiency and nonlinear dynamics modeling. This study introduces Chronos, the first implementation of a large language model (LLM)-powered temporal architecture (Chronos) optimized for wave forecasting. Through advanced temporal pattern recognition applied to historical wave data from three strategically chosen marine zones in the Northwest Pacific basin, our framework achieves multimodal improvements: (1) 14.3% reduction in training time with 2.5x faster inference speed compared to PatchTST baselines, achieving 0.575 mean absolute scaled error (MASE) units; (2) superior short-term forecasting (1-24h) across comprehensive metrics; (3) sustained predictive leadership in extended-range forecasts (1-120h); and (4) demonstrated zero-shot capability maintaining median performance (rank 4/12) against specialized operational models. This LLM-enhanced temporal modeling paradigm establishes a new standard in wave prediction, offering both computationally efficient solutions and a transferable framework for complex geophysical systems modeling.

This study explores the potential of zero-shot time series forecasting, an innovative approach leveraging pre-trained foundation models, to forecast mortality rates without task-specific fine-tuning. We evaluate two state-of-the-art foundation models, TimesFM and CHRONOS, alongside traditional and machine learning-based methods across three forecasting horizons (5, 10, and 20 years) using data from 50 countries and 111 age groups. In our investigations, zero-shot models showed varying results: while CHRONOS delivered competitive shorter-term forecasts, outperforming traditional methods like ARIMA and the Lee-Carter model, TimesFM consistently underperformed. Fine-tuning CHRONOS on mortality data significantly improved long-term accuracy. A Random Forest model, trained on mortality data, achieved the best overall performance. These findings underscore the potential of zero-shot forecasting while highlighting the need for careful model selection and domain-specific adaptation.

Modeling car-following behavior is essential for traffic simulation, analyzing driving patterns, and understanding complex traffic flows with varying levels of autonomous vehicles. Traditional models like the Safe Distance Model and Intelligent Driver Model (IDM) require precise parameter calibration and often lack generality due to simplified assumptions about driver behavior. While machine learning and deep learning methods capture complex patterns, they require large labeled datasets. Foundation models provide a more efficient alternative. Pre-trained on vast, diverse time series datasets, they can be applied directly to various tasks without the need for extensive re-training. These models generalize well across domains, and with minimal fine-tuning, they can be adapted to specific tasks like car-following behavior prediction. In this paper, we apply Chronos, a state-of-the-art public time series foundation model, to analyze car-following behavior using the Open ACC dataset. Without fine-tuning, Chronos outperforms traditional models like IDM and Exponential smoothing with trend and seasonality (ETS), and achieves similar results to deep learning models such as DeepAR and TFT, with an RMSE of 0.60. After fine-tuning, Chronos reduces the error to an RMSE of 0.53, representing a 33.75% improvement over IDM and a 12-37% reduction compared to machine learning models like ETS and deep learning models including DeepAR, WaveNet, and TFT. This demonstrates the potential of foundation models to significantly advance transportation research, offering a scalable, adaptable, and highly accurate approach to predicting and simulating car-following behaviors.

While recent advancements in foundation models have significantly impacted machine learning, rigorous tests on the performance of time series foundation models (TSFMs) remain largely underexplored. This paper presents an empirical study evaluating the zero-shot, long-horizon forecasting abilities of several leading TSFMs over two synthetic datasets constituting noisy periodic time series. We assess model efficacy across different noise levels, underlying frequencies, and sampling rates. As benchmarks for comparison, we choose two statistical techniques: a Fourier transform (FFT)-based approach and a linear autoregressive (AR) model. Our findings demonstrate that while for time series with bounded periods and higher sampling rates, TSFMs can match or outperform the statistical approaches, their forecasting abilities deteriorate with longer periods, higher noise levels, lower sampling rates and more complex shapes of the time series.

Deep learning models have shown strong performance in load forecasting, but they generally require large amounts of data for model training before being applied to new scenarios, which limits their effectiveness in data-scarce scenarios. Inspired by the great success of pre-trained language models (LLMs) in natural language processing, this paper proposes a zero-shot load forecasting approach using an advanced LLM framework denoted as the Chronos model. By utilizing its extensive pre-trained knowledge, the Chronos model enables accurate load forecasting in data-scarce scenarios without the need for extensive data-specific training. Simulation results across five real-world datasets demonstrate that the Chronos model significantly outperforms nine popular baseline models for both deterministic and probabilistic load forecasting with various forecast horizons (e.g., 1 to 48 hours), even though the Chronos model is neither tailored nor fine-tuned to these specific load datasets. Notably, Chronos reduces root mean squared error (RMSE), continuous ranked probability score (CRPS), and quantile score (QS) by approximately 7.34%-84.30%, 19.63%-60.06%, and 22.83%-54.49%, respectively, compared to baseline models. These results highlight the superiority and flexibility of the Chronos model, positioning it as an effective solution in data-scarce scenarios.

Transformer architectures have shown promising results in time series processing. However, despite recent advances in subquadratic attention mechanisms or state-space models, processing very long sequences still imposes significant computational requirements. Token merging, which involves replacing multiple tokens with a single one calculated as their linear combination, has shown to considerably improve the throughput of vision transformer architectures while maintaining accuracy. In this work, we go beyond computer vision and perform the first investigations of token merging in time series analysis on both time series transformers and state-space models. To effectively scale token merging to long sequences, we introduce local merging, a domain-specific token merging algorithm that selectively combines tokens within a local neighborhood, adjusting the computational complexity from linear to quadratic based on the neighborhood size. Our comprehensive empirical evaluation demonstrates that token merging offers substantial computational benefits with minimal impact on accuracy across various models and datasets. On the recently proposed Chronos foundation model, we achieve accelerations up to 5400 % with only minor accuracy degradations.

We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.