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.

OATS: Online Data Augmentation for Time Series Foundation Models

Time Series Foundation Models (TSFMs) are a powerful paradigm for time series analysis and are often enhanced by synthetic data augmentation to improve the training data quality. Existing augmentation methods, however, typically rely on heuristics and static paradigms. Motivated by dynamic data optimization, which shows that the contribution of samples varies across training stages, we propose OATS (Online Data Augmentation for Time Series Foundation Models), a principled strategy that generates synthetic data tailored to different training steps. OATS leverages valuable training samples as principled guiding signals and dynamically generates high-quality synthetic data conditioned on them. We further design a diffusion-based framework to produce realistic time series and introduce an explore-exploit mechanism to balance efficiency and effectiveness. Experiments on TSFMs demonstrate that OATS consistently outperforms regular training and yields substantial performance gains over static data augmentation baselines across six validation datasets and two TSFM architectures. The code is available at the link https://github.com/microsoft/TimeCraft.

AWGformer: Adaptive Wavelet-Guided Transformer for Multi-Resolution Time Series Forecasting

Time series forecasting requires capturing patterns across multiple temporal scales while maintaining computational efficiency. This paper introduces AWGformer, a novel architecture that integrates adaptive wavelet decomposition with cross-scale attention mechanisms for enhanced multi-variate time series prediction. Our approach comprises: (1) an Adaptive Wavelet Decomposition Module (AWDM) that dynamically selects optimal wavelet bases and decomposition levels based on signal characteristics; (2) a Cross-Scale Feature Fusion (CSFF) mechanism that captures interactions between different frequency bands through learnable coupling matrices; (3) a Frequency-Aware Multi-Head Attention (FAMA) module that weights attention heads according to their frequency selectivity; (4) a Hierarchical Prediction Network (HPN) that generates forecasts at multiple resolutions before reconstruction. Extensive experiments on benchmark datasets demonstrate that AWGformer achieves significant average improvements over state-of-the-art methods, with particular effectiveness on multi-scale and non-stationary time series. Theoretical analysis provides convergence guarantees and establishes the connection between our wavelet-guided attention and classical signal processing principles.

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.

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.

TS-Debate: Multimodal Collaborative Debate for Zero-Shot Time Series Reasoning

Recent progress at the intersection of large language models (LLMs) and time series (TS) analysis has revealed both promise and fragility. While LLMs can reason over temporal structure given carefully engineered context, they often struggle with numeric fidelity, modality interference, and principled cross-modal integration. We present TS-Debate, a modality-specialized, collaborative multi-agent debate framework for zero-shot time series reasoning. TS-Debate assigns dedicated expert agents to textual context, visual patterns, and numerical signals, preceded by explicit domain knowledge elicitation, and coordinates their interaction via a structured debate protocol. Reviewer agents evaluate agent claims using a verification-conflict-calibration mechanism, supported by lightweight code execution and numerical lookup for programmatic verification. This architecture preserves modality fidelity, exposes conflicting evidence, and mitigates numeric hallucinations without task-specific fine-tuning. Across 20 tasks spanning three public benchmarks, TS-Debate achieves consistent and significant performance improvements over strong baselines, including standard multimodal debate in which all agents observe all inputs.

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.

Tabular Foundation Models Can Do Survival Analysis

While tabular foundation models have achieved remarkable success in classification and regression, adapting them to model time-to-event outcomes for survival analysis is non-trivial due to right-censoring, where data observations may end before the event occurs. We develop a classification-based framework that reformulates both static and dynamic survival analysis as a series of binary classification problems by discretizing event times. Censored observations are naturally handled as examples with missing labels at certain time points. This classification formulation enables existing tabular foundation models to perform survival analysis through in-context learning without explicit training. We prove that under standard censoring assumptions, minimizing our binary classification loss recovers the true survival probabilities as the training set size increases. We demonstrate through evaluation across $53$ real-world datasets that off-the-shelf tabular foundation models with this classification formulation outperform classical and deep learning baselines on average over multiple survival metrics.

DA-SPS: A Dual-stage Network based on Singular Spectrum Analysis, Patching-strategy and Spearman-correlation for Multivariate Time-series Prediction

Multivariate time-series forecasting, as a typical problem in the field of time series prediction, has a wide range of applications in weather forecasting, traffic flow prediction, and other scenarios. However, existing works do not effectively consider the impact of extraneous variables on the prediction of the target variable. On the other hand, they fail to fully extract complex sequence information based on various time patterns of the sequences. To address these drawbacks, we propose a DA-SPS model, which adopts different modules for feature extraction based on the information characteristics of different variables. DA-SPS mainly consists of two stages: the target variable processing stage (TVPS) and the extraneous variables processing stage (EVPS). In TVPS, the model first uses Singular Spectrum Analysis (SSA) to process the target variable sequence and then uses Long Short-Term Memory (LSTM) and P-Conv-LSTM which deploys a patching strategy to extract features from trend and seasonality components, respectively. In EVPS, the model filters extraneous variables that have a strong correlation with the target variate by using Spearman correlation analysis and further analyses them using the L-Attention module which consists of LSTM and attention mechanism. Finally, the results obtained by TVPS and EVPS are combined through weighted summation and linear mapping to produce the final prediction. The results on four public datasets demonstrate that the DA-SPS model outperforms existing state-of-the-art methods. Additionally, its performance in real-world scenarios is further validated using a private dataset collected by ourselves, which contains the test items' information on laptop motherboards.

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.