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.

Echo State Networks for Time Series Forecasting: Hyperparameter Sweep and Benchmarking

This paper investigates the forecasting performance of Echo State Networks (ESNs) for univariate time series forecasting using a subset of the M4 Forecasting Competition dataset. Focusing on monthly and quarterly time series with at most 20 years of historical data, we evaluate whether a fully automatic, purely feedback-driven ESN can serve as a competitive alternative to widely used statistical forecasting methods. The study adopts a rigorous two-stage evaluation approach: a Parameter dataset is used to conduct an extensive hyperparameter sweep covering leakage rate, spectral radius, reservoir size, and information criteria for regularization, resulting in over four million ESN model fits; a disjoint Forecast dataset is then used for out-of-sample accuracy assessment. Forecast accuracy is measured using MASE and sMAPE and benchmarked against simple benchmarks like drift and seasonal naive and statistical models like ARIMA, ETS, and TBATS. The hyperparameter analysis reveals consistent and interpretable patterns, with monthly series favoring moderately persistent reservoirs and quarterly series favoring more contractive dynamics. Across both frequencies, high leakage rates are preferred, while optimal spectral radii and reservoir sizes vary with temporal resolution. In the out-of-sample evaluation, the ESN performs on par with ARIMA and TBATS for monthly data and achieves the lowest mean MASE for quarterly data, while requiring lower computational cost than the more complex statistical models. Overall, the results demonstrate that ESNs offer a compelling balance between predictive accuracy, robustness, and computational efficiency, positioning them as a practical option for automated time series forecasting.

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.

TimeMar: Multi-Scale Autoregressive Modeling for Unconditional Time Series Generation

Generative modeling offers a promising solution to data scarcity and privacy challenges in time series analysis. However, the structural complexity of time series, characterized by multi-scale temporal patterns and heterogeneous components, remains insufficiently addressed. In this work, we propose a structure-disentangled multiscale generation framework for time series. Our approach encodes sequences into discrete tokens at multiple temporal resolutions and performs autoregressive generation in a coarse-to-fine manner, thereby preserving hierarchical dependencies. To tackle structural heterogeneity, we introduce a dual-path VQ-VAE that disentangles trend and seasonal components, enabling the learning of semantically consistent latent representations. Additionally, we present a guidance-based reconstruction strategy, where coarse seasonal signals are utilized as priors to guide the reconstruction of fine-grained seasonal patterns. Experiments on six datasets show that our approach produces higher-quality time series than existing methods. Notably, our model achieves strong performance with a significantly reduced parameter count and exhibits superior capability in generating high-quality long-term sequences. Our implementation is available at https://anonymous.4open.science/r/TimeMAR-BC5B.

LLM-Assisted Logic Rule Learning: Scaling Human Expertise for Time Series Anomaly Detection

Time series anomaly detection is critical for supply chain management to take proactive operations, but faces challenges: classical unsupervised anomaly detection based on exploiting data patterns often yields results misaligned with business requirements and domain knowledge, while manual expert analysis cannot scale to millions of products in the supply chain. We propose a framework that leverages large language models (LLMs) to systematically encode human expertise into interpretable, logic-based rules for detecting anomaly patterns in supply chain time series data. Our approach operates in three stages: 1) LLM-based labeling of training data instructed by domain knowledge, 2) automated generation and iterative improvements of symbolic rules through LLM-driven optimization, and 3) rule augmentation with business-relevant anomaly categories supported by LLMs to enhance interpretability. The experiment results showcase that our approach outperforms the unsupervised learning methods in both detection accuracy and interpretability. Furthermore, compared to direct LLM deployment for time series anomaly detection, our approach provides consistent, deterministic results with low computational latency and cost, making it ideal for production deployment. The proposed framework thus demonstrates how LLMs can bridge the gap between scalable automation and expert-driven decision-making in operational settings.

Bonnet: Ultra-fast whole-body bone segmentation from CT scans

This work proposes Bonnet, an ultra-fast sparse-volume pipeline for whole-body bone segmentation from CT scans. Accurate bone segmentation is important for surgical planning and anatomical analysis, but existing 3D voxel-based models such as nnU-Net and STU-Net require heavy computation and often take several minutes per scan, which limits time-critical use. The proposed Bonnet addresses this by integrating a series of novel framework components including HU-based bone thresholding, patch-wise inference with a sparse spconv-based U-Net, and multi-window fusion into a full-volume prediction. Trained on TotalSegmentator and evaluated without additional tuning on RibSeg, CT-Pelvic1K, and CT-Spine1K, Bonnet achieves high Dice across ribs, pelvis, and spine while running in only 2.69 seconds per scan on an RTX A6000. Compared to strong voxel baselines, Bonnet attains a similar accuracy but reduces inference time by roughly 25x on the same hardware and tiling setup. The toolkit and pre-trained models will be released at https://github.com/HINTLab/Bonnet.

How does downsampling affect needle electromyography signals? A generalisable workflow for understanding downsampling effects on high-frequency time series

Automated analysis of needle electromyography (nEMG) signals is emerging as a tool to support the detection of neuromuscular diseases (NMDs), yet the signals' high and heterogeneous sampling rates pose substantial computational challenges for feature-based machine-learning models, particularly for near real-time analysis. Downsampling offers a potential solution, but its impact on diagnostic signal content and classification performance remains insufficiently understood. This study presents a workflow for systematically evaluating information loss caused by downsampling in high-frequency time series. The workflow combines shape-based distortion metrics with classification outcomes from available feature-based machine learning models and feature space analysis to quantify how different downsampling algorithms and factors affect both waveform integrity and predictive performance. We use a three-class NMD classification task to experimentally evaluate the workflow. We demonstrate how the workflow identifies downsampling configurations that preserve diagnostic information while substantially reducing computational load. Analysis of shape-based distortion metrics showed that shape-aware downsampling algorithms outperform standard decimation, as they better preserve peak structure and overall signal morphology. The results provide practical guidance for selecting downsampling configurations that enable near real-time nEMG analysis and highlight a generalisable workflow that can be used to balance data reduction with model performance in other high-frequency time-series applications as well.

ParalESN: Enabling parallel information processing in Reservoir Computing

Reservoir Computing (RC) has established itself as an efficient paradigm for temporal processing. However, its scalability remains severely constrained by (i) the necessity of processing temporal data sequentially and (ii) the prohibitive memory footprint of high-dimensional reservoirs. In this work, we revisit RC through the lens of structured operators and state space modeling to address these limitations, introducing Parallel Echo State Network (ParalESN). ParalESN enables the construction of high-dimensional and efficient reservoirs based on diagonal linear recurrence in the complex space, enabling parallel processing of temporal data. We provide a theoretical analysis demonstrating that ParalESN preserves the Echo State Property and the universality guarantees of traditional Echo State Networks while admitting an equivalent representation of arbitrary linear reservoirs in the complex diagonal form. Empirically, ParalESN matches the predictive accuracy of traditional RC on time series benchmarks, while delivering substantial computational savings. On 1-D pixel-level classification tasks, ParalESN achieves competitive accuracy with fully trainable neural networks while reducing computational costs and energy consumption by orders of magnitude. Overall, ParalESN offers a promising, scalable, and principled pathway for integrating RC within the deep learning landscape.

Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Control

This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman variants-scalar-gated, per-mode gated, MLP-shaped spectral mapping, and low-rank Koopman operators which generalize and interpolate between strictly stable Koopman operators and unconstrained linear latent dynamics. Our formulation enables explicit control over the spectrum, stability, and rank of the linear transition operator while retaining compatibility with expressive nonlinear backbones such as Patchtst, Autoformer, and Informer. We evaluate the proposed operators in a large-scale benchmark that also includes LSTM, DLinear, and simple diagonal State-Space Models (SSMs), as well as lightweight transformer variants. Experiments across multiple horizons and patch lengths show that learnable Koopman models provide a favorable bias-variance trade-off, improved conditioning, and more interpretable latent dynamics. We provide a full spectral analysis, including eigenvalue trajectories, stability envelopes, and learned spectral distributions. Our results demonstrate that learnable Koopman operators are effective, stable, and theoretically principled components for deep forecasting.

Do Not Waste Your Rollouts: Recycling Search Experience for Efficient Test-Time Scaling

Test-Time Scaling enhances the reasoning capabilities of Large Language Models by allocating additional inference compute to broaden the exploration of the solution space. However, existing search strategies typically treat rollouts as disposable samples, where valuable intermediate insights are effectively discarded after each trial. This systemic memorylessness leads to massive computational redundancy, as models repeatedly re-derive discovered conclusions and revisit known dead ends across extensive attempts. To bridge this gap, we propose \textbf{Recycling Search Experience (RSE)}, a self-guided, training-free strategy that turns test-time search from a series of isolated trials into a cumulative process. By actively distilling raw trajectories into a shared experience bank, RSE enables positive recycling of intermediate conclusions to shortcut redundant derivations and negative recycling of failure patterns to prune encountered dead ends. Theoretically, we provide an analysis that formalizes the efficiency gains of RSE, validating its advantage over independent sampling in solving complex reasoning tasks. Empirically, extensive experiments on HMMT24, HMMT25, IMO-Bench, and HLE show that RSE consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art scaling efficiency.