Multi-scale hypergraph meets LLMs: Aligning large language models for time series analysis

Recently, there has been great success in leveraging pre-trained large language models (LLMs) for time series analysis. The core idea lies in effectively aligning the modality between natural language and time series. However, the multi-scale structures of natural language and time series have not been fully considered, resulting in insufficient utilization of LLMs capabilities. To this end, we propose MSH-LLM, a Multi-Scale Hypergraph method that aligns Large Language Models for time series analysis. Specifically, a hyperedging mechanism is designed to enhance the multi-scale semantic information of time series semantic space. Then, a cross-modality alignment (CMA) module is introduced to align the modality between natural language and time series at different scales. In addition, a mixture of prompts (MoP) mechanism is introduced to provide contextual information and enhance the ability of LLMs to understand the multi-scale temporal patterns of time series. Experimental results on 27 real-world datasets across 5 different applications demonstrate that MSH-LLM achieves the state-of-the-art results.

Interpretability in Deep Time Series Models Demands Semantic Alignment

Deep time series models continue to improve predictive performance, yet their deployment remains limited by their black-box nature. In response, existing interpretability approaches in the field keep focusing on explaining the internal model computations, without addressing whether they align or not with how a human would reason about the studied phenomenon. Instead, we state interpretability in deep time series models should pursue semantic alignment: predictions should be expressed in terms of variables that are meaningful to the end user, mediated by spatial and temporal mechanisms that admit user-dependent constraints. In this paper, we formalize this requirement and require that, once established, semantic alignment must be preserved under temporal evolution: a constraint with no analog in static settings. Provided with this definition, we outline a blueprint for semantically aligned deep time series models, identify properties that support trust, and discuss implications for model design.

Spectral Text Fusion: A Frequency-Aware Approach to Multimodal Time-Series Forecasting

Multimodal time series forecasting is crucial in real-world applications, where decisions depend on both numerical data and contextual signals. The core challenge is to effectively combine temporal numerical patterns with the context embedded in other modalities, such as text. While most existing methods align textual features with time-series patterns one step at a time, they neglect the multiscale temporal influences of contextual information such as time-series cycles and dynamic shifts. This mismatch between local alignment and global textual context can be addressed by spectral decomposition, which separates time series into frequency components capturing both short-term changes and long-term trends. In this paper, we propose SpecTF, a simple yet effective framework that integrates the effect of textual data on time series in the frequency domain. Our method extracts textual embeddings, projects them into the frequency domain, and fuses them with the time series' spectral components using a lightweight cross-attention mechanism. This adaptively reweights frequency bands based on textual relevance before mapping the results back to the temporal domain for predictions. Experimental results demonstrate that SpecTF significantly outperforms state-of-the-art models across diverse multi-modal time series datasets while utilizing considerably fewer parameters. Code is available at https://github.com/hiepnh137/SpecTF.

CAPS: Unifying Attention, Recurrence, and Alignment in Transformer-based Time Series Forecasting

This paper presents $\textbf{CAPS}$ (Clock-weighted Aggregation with Prefix-products and Softmax), a structured attention mechanism for time series forecasting that decouples three distinct temporal structures: global trends, local shocks, and seasonal patterns. Standard softmax attention entangles these through global normalization, while recent recurrent models sacrifice long-term, order-independent selection for order-dependent causal structure. CAPS combines SO(2) rotations for phase alignment with three additive gating paths -- Riemann softmax, prefix-product gates, and a Clock baseline -- within a single attention layer. We introduce the Clock mechanism, a learned temporal weighting that modulates these paths through a shared notion of temporal importance. Experiments on long- and short-term forecasting benchmarks surpass vanilla softmax and linear attention mechanisms and demonstrate competitive performance against seven strong baselines with linear complexity. Our code implementation is available at https://github.com/vireshpati/CAPS-Attention.

SEDformer: Event-Synchronous Spiking Transformers for Irregular Telemetry Time Series Forecasting

Telemetry streams from large-scale Internet-connected systems (e.g., IoT deployments and online platforms) naturally form an irregular multivariate time series (IMTS) whose accurate forecasting is operationally vital. A closer examination reveals a defining Sparsity-Event Duality (SED) property of IMTS, i.e., long stretches with sparse or no observations are punctuated by short, dense bursts where most semantic events (observations) occur. However, existing Graph- and Transformer-based forecasters ignore SED: pre-alignment to uniform grids with heavy padding violates sparsity by inflating sequences and forcing computation at non-informative steps, while relational recasting weakens event semantics by disrupting local temporal continuity. These limitations motivate a more faithful and natural modeling paradigm for IMTS that aligns with its SED property. We find that Spiking Neural Networks meet this requirement, as they communicate via sparse binary spikes and update in an event-driven manner, aligning naturally with the SED nature of IMTS. Therefore, we present SEDformer, an SED-enhanced Spiking Transformer for telemetry IMTS forecasting that couples: (1) a SED-based Spike Encoder converts raw observations into event synchronous spikes using an Event-Aligned LIF neuron, (2) an Event-Preserving Temporal Downsampling module compresses long gaps while retaining salient firings and (3) a stack of SED-based Spike Transformer blocks enable intra-series dependency modeling with a membrane-based linear attention driven by EA-LIF spiking features. Experiments on public telemetry IMTS datasets show that SEDformer attains state-of-the-art forecasting accuracy while reducing energy and memory usage, providing a natural and efficient path for modeling IMTS.

Cross-Temporal Attention Fusion (CTAF) for Multimodal Physiological Signals in Self-Supervised Learning

We study multimodal affect modeling when EEG and peripheral physiology are asynchronous, which most fusion methods ignore or handle with costly warping. We propose Cross-Temporal Attention Fusion (CTAF), a self-supervised module that learns soft bidirectional alignments between modalities and builds a robust clip embedding using time-aware cross attention, a lightweight fusion gate, and alignment-regularized contrastive objectives with optional weak supervision. On the K-EmoCon dataset, under leave-one-out cross-validation evaluation, CTAF yields higher cosine margins for matched pairs and better cross-modal token retrieval within one second, and it is competitive with the baseline on three-bin accuracy and macro-F1 while using few labels. Our contributions are a time-aware fusion mechanism that directly models correspondence, an alignment-driven self-supervised objective tailored to EEG and physiology, and an evaluation protocol that measures alignment quality itself. Our approach accounts for the coupling between the central and autonomic nervous systems in psychophysiological time series. These results indicate that CTAF is a strong step toward label-efficient, generalizable EEG-peripheral fusion under temporal asynchrony.

T-LLM: Teaching Large Language Models to Forecast Time Series via Temporal Distillation

Time series forecasting plays a critical role in decision-making across many real-world applications. Unlike data in vision and language domains, time series data is inherently tied to the evolution of underlying processes and can only accumulate as real-world time progresses, limiting the effectiveness of scale-driven pretraining alone. This time-bound constraint poses a challenge for enabling large language models (LLMs) to acquire forecasting capability, as existing approaches primarily rely on representation-level alignment or inference-time temporal modules rather than explicitly teaching forecasting behavior to the LLM. We propose T-LLM, a temporal distillation framework that equips general-purpose LLMs with time series forecasting capability by transferring predictive behavior from a lightweight temporal teacher during training. The teacher combines trend modeling and frequency-domain analysis to provide structured temporal supervision, and is removed entirely at inference, leaving the LLM as the sole forecasting model. Experiments on benchmark datasets and infectious disease forecasting tasks demonstrate that T-LLM consistently outperforms existing LLM-based forecasting methods under full-shot, few-shot, and zero-shot settings, while enabling a simple and efficient deployment pipeline.

DREAMS: A Social Exchange Theory-Informed Modeling of Misinformation Engagement on Social Media

Social media engagement prediction is a central challenge in computational social science, particularly for understanding how users interact with misinformation. Existing approaches often treat engagement as a homogeneous time-series signal, overlooking the heterogeneous social mechanisms and platform designs that shape how misinformation spreads. In this work, we ask: ``Can neural architectures discover social exchange principles from behavioral data alone?'' We introduce \textsc{Dreams} (\underline{D}isentangled \underline{R}epresentations and \underline{E}pisodic \underline{A}daptive \underline{M}odeling for \underline{S}ocial media misinformation engagements), a social exchange theory-guided framework that models misinformation engagement as a dynamic process of social exchange. Rather than treating engagement as a static outcome, \textsc{Dreams} models it as a sequence-to-sequence adaptation problem, where each action reflects an evolving negotiation between user effort and social reward conditioned by platform context. It integrates adaptive mechanisms to learn how emotional and contextual signals propagate through time and across platforms. On a cross-platform dataset spanning $7$ platforms and 2.37M posts collected between 2021 and 2025, \textsc{Dreams} achieves state-of-the-art performance in predicting misinformation engagements, reaching a mean absolute percentage error of $19.25$\%. This is a $43.6$\% improvement over the strongest baseline. Beyond predictive gains, the model reveals consistent cross-platform patterns that align with social exchange principles, suggesting that integrating behavioral theory can enhance empirical modeling of online misinformation engagement. The source code is available at: https://github.com/ltian678/DREAMS.

Deep Time-series Forecasting Needs Kernelized Moment Balancing

Deep time-series forecasting can be formulated as a distribution balancing problem aimed at aligning the distribution of the forecasts and ground truths. According to Imbens' criterion, true distribution balance requires matching the first moments with respect to any balancing function. We demonstrate that existing objectives fail to meet this criterion, as they enforce moment matching only for one or two predefined balancing functions, thus failing to achieve full distribution balance. To address this limitation, we propose direct forecasting with kernelized moment balancing (KMB-DF). Unlike existing objectives, KMB-DF adaptively selects the most informative balancing functions from a reproducing kernel hilbert space (RKHS) to enforce sufficient distribution balancing. We derive a tractable and differentiable objective that enables efficient estimation from empirical samples and seamless integration into gradient-based training pipelines. Extensive experiments across multiple models and datasets show that KMB-DF consistently improves forecasting accuracy and achieves state-of-the-art performance. Code is available at https://anonymous.4open.science/r/KMB-DF-403C.

Changepoint Detection As Model Selection: A General Framework

This dissertation presents a general framework for changepoint detection based on L0 model selection. The core method, Iteratively Reweighted Fused Lasso (IRFL), improves upon the generalized lasso by adaptively reweighting penalties to enhance support recovery and minimize criteria such as the Bayesian Information Criterion (BIC). The approach allows for flexible modeling of seasonal patterns, linear and quadratic trends, and autoregressive dependence in the presence of changepoints. Simulation studies demonstrate that IRFL achieves accurate changepoint detection across a wide range of challenging scenarios, including those involving nuisance factors such as trends, seasonal patterns, and serially correlated errors. The framework is further extended to image data, where it enables edge-preserving denoising and segmentation, with applications spanning medical imaging and high-throughput plant phenotyping. Applications to real-world data demonstrate IRFL's utility. In particular, analysis of the Mauna Loa CO2 time series reveals changepoints that align with volcanic eruptions and ENSO events, yielding a more accurate trend decomposition than ordinary least squares. Overall, IRFL provides a robust, extensible tool for detecting structural change in complex data.