LISA: Laplacian In-context Spectral Analysis

We propose Laplacian In-context Spectral Analysis (LISA), a method for inference-time adaptation of Laplacian-based time-series models using only an observed prefix. LISA combines delay-coordinate embeddings and Laplacian spectral learning to produce diffusion-coordinate state representations, together with a frozen nonlinear decoder for one-step prediction. We introduce lightweight latent-space residual adapters based on either Gaussian-process regression or an attention-like Markov operator over context windows. Across forecasting and autoregressive rollout experiments, LISA improves over the frozen baseline and is often most beneficial under changing dynamics. This work links in-context adaptation to nonparametric spectral methods for dynamical systems.

LASS-ODE: Scaling ODE Computations to Connect Foundation Models with Dynamical Physical Systems

Foundation models have transformed language, vision, and time series data analysis, yet progress on dynamic predictions for physical systems remains limited. Given the complexity of physical constraints, two challenges stand out. $(i)$ Physics-computation scalability: physics-informed learning can enforce physical regularization, but its computation (e.g., ODE integration) does not scale to extensive systems. $(ii)$ Knowledge-sharing efficiency: the attention mechanism is primarily computed within each system, which limits the extraction of shared ODE structures across systems. We show that enforcing ODE consistency does not require expensive nonlinear integration: a token-wise locally linear ODE representation preserves physical fidelity while scaling to foundation-model regimes. Thus, we propose novel token representations that respect locally linear ODE evolution. Such linearity substantially accelerates integration while accurately approximating the local data manifold. Second, we introduce a simple yet effective inter-system attention that augments attention with a common structure hub (CSH) that stores shared tokens and aggregates knowledge across systems. The resulting model, termed LASS-ODE (\underline{LA}rge-\underline{S}cale \underline{S}mall \underline{ODE}), is pretrained on our $40$GB ODE trajectory collections to enable strong in-domain performance, zero-shot generalization across diverse ODE systems, and additional improvements through fine-tuning.

A compliant ankle-actuated compass walker with triggering timing control

Passive dynamic walkers are widely adopted as a mathematical model to represent biped walking. The stable locomotion of these models is limited to tilted surfaces, requiring gravitational energy. Various techniques, such as actuation through the ankle and hip joints, have been proposed to extend the applicability of these models to level ground and rough terrain with improved locomotion efficiency. However, most of these techniques rely on impulsive energy injection schemes and torsional springs, which are quite challenging to implement in a physical platform. Here, a new model is proposed, named triggering controlled ankle actuated compass gait (TC-AACG), which allows non-instantaneous compliant ankle pushoff. The proposed technique can be implemented in physical platforms via series elastic actuators (SEAs). Our systematic examination shows that the proposed approach extends the locomotion capabilities of a biped model compared to impulsive ankle pushoff approach. We provide extensive simulation analysis investigating the locomotion speed, mechanical cost of transport, and basin of attraction of the proposed model.

EEO-TFV: Escape-Explore Optimizer for Web-Scale Time-Series Forecasting and Vision Analysis

Transformer-based foundation models have achieved remarkable progress in tasks such as time-series forecasting and image segmentation. However, they frequently suffer from error accumulation in multivariate long-sequence prediction and exhibit vulnerability to out-of-distribution samples in image-related tasks. Furthermore, these challenges become particularly pronounced in large-scale Web data analysis tasks, which typically involve complex temporal patterns and multimodal features. This complexity substantially increases optimization difficulty, rendering models prone to stagnation at saddle points within high-dimensional parameter spaces. To address these issues, we propose a lightweight Transformer architecture in conjunction with a novel Escape-Explore Optimizer (EEO). The optimizer enhances both exploration and generalization while effectively avoiding sharp minima and saddle-point traps. Experimental results show that, in representative Web data scenarios, our method achieves performance on par with state-of-the-art models across 11 time-series benchmark datasets and the Synapse medical image segmentation task. Moreover, it demonstrates superior generalization and stability, thereby validating its potential as a versatile cross-task foundation model for Web-scale data mining and analysis.

TemporalBench: A Benchmark for Evaluating LLM-Based Agents on Contextual and Event-Informed Time Series Tasks

It is unclear whether strong forecasting performance reflects genuine temporal understanding or the ability to reason under contextual and event-driven conditions. We introduce TemporalBench, a multi-domain benchmark designed to evaluate temporal reasoning behavior under progressively richer informational settings. TemporalBench adopts a four-tier task taxonomy that examines historical structure interpretation, context-free forecasting, contextual temporal reasoning, and event-conditioned prediction across four real-world domains: retail, healthcare, energy, and physical systems. By controlling access to future targets and contextual information, the benchmark enables a diagnostic analysis of whether models can correctly interpret temporal patterns, align them with external context, and adapt predictions when conditions change. Extensive baseline experiments show that strong numerical forecasting accuracy does not reliably translate into robust contextual or event-aware temporal reasoning; instead, existing agent frameworks exhibit fragmented strengths and systematic failure modes that remain largely hidden under forecasting-only benchmarks. The TemporalBench dataset is publicly available at https://huggingface.co/datasets/Melady/TemporalBench, and we additionally provide a public leaderboard at https://huggingface.co/spaces/Melady/TemporalBench_Leaderboard.

MuRAL-CPD: Active Learning for Multiresolution Change Point Detection

Change Point Detection (CPD) is a critical task in time series analysis, aiming to identify moments when the underlying data-generating process shifts. Traditional CPD methods often rely on unsupervised techniques, which lack adaptability to task-specific definitions of change and cannot benefit from user knowledge. To address these limitations, we propose MuRAL-CPD, a novel semi-supervised method that integrates active learning into a multiresolution CPD algorithm. MuRAL-CPD leverages a wavelet-based multiresolution decomposition to detect changes across multiple temporal scales and incorporates user feedback to iteratively optimize key hyperparameters. This interaction enables the model to align its notion of change with that of the user, improving both accuracy and interpretability. Our experimental results on several real-world datasets show the effectiveness of MuRAL-CPD against state-of-the-art methods, particularly in scenarios where minimal supervision is available.

DCD: Decomposition-based Causal Discovery from Autocorrelated and Non-Stationary Temporal Data

Multivariate time series in domains such as finance, climate science, and healthcare often exhibit long-term trends, seasonal patterns, and short-term fluctuations, complicating causal inference under non-stationarity and autocorrelation. Existing causal discovery methods typically operate on raw observations, making them vulnerable to spurious edges and misattributed temporal dependencies. We introduce a decomposition-based causal discovery framework that separates each time series into trend, seasonal, and residual components and performs component-specific causal analysis. Trend components are assessed using stationarity tests, seasonal components using kernel-based dependence measures, and residual components using constraint-based causal discovery. The resulting component-level graphs are integrated into a unified multi-scale causal structure. This approach isolates long- and short-range causal effects, reduces spurious associations, and improves interpretability. Across extensive synthetic benchmarks and real-world climate data, our framework more accurately recovers ground-truth causal structure than state-of-the-art baselines, particularly under strong non-stationarity and temporal autocorrelation.

Let Experts Feel Uncertainty: A Multi-Expert Label Distribution Approach to Probabilistic Time Series Forecasting

Time series forecasting in real-world applications requires both high predictive accuracy and interpretable uncertainty quantification. Traditional point prediction methods often fail to capture the inherent uncertainty in time series data, while existing probabilistic approaches struggle to balance computational efficiency with interpretability. We propose a novel Multi-Expert Learning Distributional Labels (LDL) framework that addresses these challenges through mixture-of-experts architectures with distributional learning capabilities. Our approach introduces two complementary methods: (1) Multi-Expert LDL, which employs multiple experts with different learned parameters to capture diverse temporal patterns, and (2) Pattern-Aware LDL-MoE, which explicitly decomposes time series into interpretable components (trend, seasonality, changepoints, volatility) through specialized sub-experts. Both frameworks extend traditional point prediction to distributional learning, enabling rich uncertainty quantification through Maximum Mean Discrepancy (MMD). We evaluate our methods on aggregated sales data derived from the M5 dataset, demonstrating superior performance compared to baseline approaches. The continuous Multi-Expert LDL achieves the best overall performance, while the Pattern-Aware LDL-MoE provides enhanced interpretability through component-wise analysis. Our frameworks successfully balance predictive accuracy with interpretability, making them suitable for real-world forecasting applications where both performance and actionable insights are crucial.

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.

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.