The ubiquity of dynamic data in domains such as weather, healthcare, and energy underscores a growing need for effective interpretation and retrieval of time-series data. These data are inherently tied to domain-specific contexts, such as clinical notes or weather narratives, making cross-modal retrieval essential not only for downstream tasks but also for developing robust time-series foundation models by retrieval-augmented generation (RAG). Despite the increasing demand, time-series retrieval remains largely underexplored. Existing methods often lack semantic grounding, struggle to align heterogeneous modalities, and have limited capacity for handling multi-channel signals. To address this gap, we propose TRACE, a generic multimodal retriever that grounds time-series embeddings in aligned textual context. TRACE enables fine-grained channel-level alignment and employs hard negative mining to facilitate semantically meaningful retrieval. It supports flexible cross-modal retrieval modes, including Text-to-Timeseries and Timeseries-to-Text, effectively linking linguistic descriptions with complex temporal patterns. By retrieving semantically relevant pairs, TRACE enriches downstream models with informative context, leading to improved predictive accuracy and interpretability. Beyond a static retrieval engine, TRACE also serves as a powerful standalone encoder, with lightweight task-specific tuning that refines context-aware representations while maintaining strong cross-modal alignment. These representations achieve state-of-the-art performance on downstream forecasting and classification tasks. Extensive experiments across multiple domains highlight its dual utility, as both an effective encoder for downstream applications and a general-purpose retriever to enhance time-series models.

Diffusion models offer a physically grounded framework for probabilistic weather forecasting, but their typical reliance on slow, iterative solvers during inference makes them impractical for subseasonal-to-seasonal (S2S) applications where long lead-times and domain-driven calibration are essential. To address this, we introduce Swift, a single-step consistency model that, for the first time, enables autoregressive finetuning of a probability flow model with a continuous ranked probability score (CRPS) objective. This eliminates the need for multi-model ensembling or parameter perturbations. Results show that Swift produces skillful 6-hourly forecasts that remain stable for up to 75 days, running $39\times$ faster than state-of-the-art diffusion baselines while achieving forecast skill competitive with the numerical-based, operational IFS ENS. This marks a step toward efficient and reliable ensemble forecasting from medium-range to seasonal-scales.

Sea surface temperature (SST) prediction is a critical task in ocean science, supporting various applications, such as weather forecasting, fisheries management, and storm tracking. While existing data-driven methods have demonstrated significant success, they often neglect to leverage the rich domain knowledge accumulated over the past decades, limiting further advancements in prediction accuracy. The recent emergence of large language models (LLMs) has highlighted the potential of integrating domain knowledge for downstream tasks. However, the application of LLMs to SST prediction remains underexplored, primarily due to the challenge of integrating ocean domain knowledge and numerical data. To address this issue, we propose Ocean Knowledge Graph-enhanced LLM (OKG-LLM), a novel framework for global SST prediction. To the best of our knowledge, this work presents the first systematic effort to construct an Ocean Knowledge Graph (OKG) specifically designed to represent diverse ocean knowledge for SST prediction. We then develop a graph embedding network to learn the comprehensive semantic and structural knowledge within the OKG, capturing both the unique characteristics of individual sea regions and the complex correlations between them. Finally, we align and fuse the learned knowledge with fine-grained numerical SST data and leverage a pre-trained LLM to model SST patterns for accurate prediction. Extensive experiments on the real-world dataset demonstrate that OKG-LLM consistently outperforms state-of-the-art methods, showcasing its effectiveness, robustness, and potential to advance SST prediction. The codes are available in the online repository.

Marine heatwaves (MHWs), an extreme climate phenomenon, pose significant challenges to marine ecosystems and industries, with their frequency and intensity increasing due to climate change. This study introduces an integrated deep learning approach to forecast short-to-long-term MHWs on a global scale. The approach combines graph representation for modeling spatial properties in climate data, imbalanced regression to handle skewed data distributions, and temporal diffusion to enhance forecast accuracy across various lead times. To the best of our knowledge, this is the first study that synthesizes three spatiotemporal anomaly methodologies to predict MHWs. Additionally, we introduce a method for constructing graphs that avoids isolated nodes and provide a new publicly available sea surface temperature anomaly graph dataset. We examine the trade-offs in the selection of loss functions and evaluation metrics for MHWs. We analyze spatial patterns in global MHW predictability by focusing on historical hotspots, and our approach demonstrates better performance compared to traditional numerical models in regions such as the middle south Pacific, equatorial Atlantic near Africa, south Atlantic, and high-latitude Indian Ocean. We highlight the potential of temporal diffusion to replace the conventional sliding window approach for long-term forecasts, achieving improved prediction up to six months in advance. These insights not only establish benchmarks for machine learning applications in MHW forecasting but also enhance understanding of general climate forecasting methodologies.

Projecting intermediate representations onto the vocabulary is an increasingly popular interpretation tool for transformer-based LLMs, also known as the logit lens. We propose a quantitative extension to this approach and define spectral filters on intermediate representations based on partitioning the singular vectors of the vocabulary embedding and unembedding matrices into bands. We find that the signals exchanged in the tail end of the spectrum are responsible for attention sinking (Xiao et al. 2023), of which we provide an explanation. We find that the loss of pretrained models can be kept low despite suppressing sizable parts of the embedding spectrum in a layer-dependent way, as long as attention sinking is preserved. Finally, we discover that the representation of tokens that draw attention from many tokens have large projections on the tail end of the spectrum.

Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel smoothing for directional data. We generalize the classical mean shift algorithm to directional data, which allows us to identify local modes of the directional kernel density estimator (KDE). The statistical convergence rates of the directional KDE and its derivatives are derived, and the problem of mode estimation is examined. We also prove the ascending property of our directional mean shift algorithm and investigate a general problem of gradient ascent on the unit hypersphere. To demonstrate the applicability of our proposed algorithm, we evaluate it as a mode clustering method on both simulated and real-world datasets.

We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting model generalization at each scale, we also introduce a novel, projection based penalty operator across multiple dimension, using permutation operators for incorporating proximity and ordering information. The paper presents a detailed analysis of approximation properties in the reconstruction Reproducing Kernel Hilbert Spaces (RKHS) with emphasis on optimality and consistency of predictions and behavior of error functionals associated with the produced sparse representations. Results show the performance of the approach as a data reduction and modeling strategy on both synthetic (univariate and multivariate) and real datasets (time series). The sparse model for the test datasets, generated by the presented approach, is also shown to efficiently reconstruct the underlying process and preserve generalizability.

Paper proposes a hierarchical learning strategy for generation of sparse representations which capture the information content in large datasets and act as a model. The hierarchy arises from the approximation spaces considered at successively finer data dependent scales. Paper presents a detailed analysis of stability, convergence and behavior of error functionals associated with the approximations and well chosen set of applications. Results show the performance of the approach as a data reduction mechanism on both synthetic (univariate and multivariate) and real datasets (geo-spatial, computer vision and numerical model outcomes). The sparse model generated is shown to efficiently reconstruct data and minimize error in prediction.

Spatio-temporal data are ubiquitous in the agricultural, ecological, and environmental sciences, and their study is important for understanding and predicting a wide variety of processes. One of the difficulties with modeling spatial processes that change in time is the complexity of the dependence structures that must describe how such a process varies, and the presence of high-dimensional complex data sets and large prediction domains. It is particularly challenging to specify parameterizations for nonlinear dynamic spatio-temporal models (DSTMs) that are simultaneously useful scientifically and efficient computationally. Statisticians have developed deep hierarchical models that can accommodate process complexity as well as the uncertainties in the predictions and inference. However, these models can be expensive and are typically application specific. On the other hand, the machine learning community has developed alternative "deep learning" approaches for nonlinear spatio-temporal modeling. These models are flexible yet are typically not implemented in a probabilistic framework. The two paradigms have many things in common and suggest hybrid approaches that can benefit from elements of each framework. This overview paper presents a brief introduction to the deep hierarchical DSTM (DH-DSTM) framework, and deep models in machine learning, culminating with the deep neural DSTM (DN-DSTM). Recent approaches that combine elements from DH-DSTMs and echo state network DN-DSTMs are presented as illustrations.