Cascade-KDE: Robust Time-Series Restoration under Out-of-Distribution Impulse Corruptions

Real-world time-series data in industrial sensing, healthcare, and energy systems is often corrupted by a mixture of Gaussian noise and occasional large-magnitude impulse outliers. For tasks that depend on local shape, such as ECG morphology analysis and battery degradation monitoring, the main requirement is not only low reconstruction error but also preservation of derivative peaks and task-critical features. We propose Cascade-KDE, a training-free restoration framework for corrupted time series. The method first estimates a two-dimensional temporal-amplitude density, then applies a Density-Truncated Robust Expectation to limit the influence of distant abnormal points, and finally refines the sequence through an exponential cascade with adaptive stopping. This design aims to improve robustness under out-of-distribution impulse corruptions while keeping the restored trajectory close to the original local structure. Across several benchmark datasets, the proposed method shows consistent gains over classical filters and representative learning-based baselines on curve fidelity, derivative preservation, downstream classification, and runtime efficiency. These results suggest that bounded density-based restoration is a practical option for feature-preserving preprocessing in noisy time-series pipelines.

AION: Next-Generation Tasks and Practical Harness for Time Series

Time series research is moving beyond fixed forecasting benchmarks toward realistic tasks that combine prediction, contextual reasoning, tool use, and structured decision support. Most benchmarks are built around clean data and short evaluation loops; agents alone may miss temporal constraints, evidence checks, or review before finalizing outputs. We first formalize next-generation time series tasks as three-component tuples consisting of a task file, a workspace, and a validation interface. We then present AION, a time series harness built from six component groups: agents, skills, rules, memory, evaluation, and protocols. In this harness, we use three design principles: temporal grounding, temporal knowledge-grounded reasoning, and reliability mechanisms such as post-experiment analysis and layered review. A Kaggle Store Sales case study shows that the harness produces more detailed process traces, more artifacts, and more review steps than the same base agent operating in OpenCode direct build mode. Taken together, these results argue for a paradigm shift from fixed tasks to realistic ones under real-world constraints.

Comparative Analysis of Liquid Neural Networks and LSTM for Sequential Pattern Recognition: Robustness, Efficiency, and Clinical Utility

Traditional Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) units operate on discrete time steps, often failing to capture the fluid temporal dynamics of real-world physical processes. Liquid Neural Networks (LNNs), specifically Closed-form Continuous-time (CfC) networks, address this by modeling the hidden state evolution as a continuous differential equation. In this paper, we conduct a comprehensive benchmarking study across four distinct sequential modalities: neuromorphic event-based data (N-MNIST), stroke-based drawing (QuickDraw), visual handwriting (IAM), and physiological time-series (PhysioNet Sepsis-3). Furthermore, we perform a rigorous stress test using temporal dropout to evaluate model robustness against missing data. Our findings reveal that LNNs consistently provide superior parameter efficiency and significantly higher robustness in natively temporal domains and clinical environments where data sparsity is prevalent. This extended preprint provides additional background on related datasets and the LNN theoretical lineage, supplemented with a detailed appendix documenting our full implementation and experimental settings.

Function-Valued Causal Influence in Nonlinear Time Series

Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true object learned by nonlinear autoregressive models: a state-dependent function whose effect varies across regimes, magnitudes, and contexts. We formalize function-valued causal influence for additive, contribution-decomposable architectures and show that scalar causal scores constitute a severe information bottleneck, conflating between-state variation with within-state residual noise. Using Neural Additive Vector Autoregression as a representative architecture, we introduce a practical framework based on Individual Conditional Expectation for estimating causal response functions directly from trained models. Through controlled synthetic experiments, we demonstrate that edges with indistinguishable scalar scores can exhibit qualitatively different functional behaviors, including monotonic, thresholded, saturating, and sign-changing effects. An applied case study on democratic development further shows that function-valued analysis reveals regime-specific and asymmetric causal structure systematically missed by score-centric approaches.

Optimal Time Window and Frequency Bandwidth Parameter Combination for Subject-Specific Motor Imagery EEG Classification

Motor-imagery (MI) EEG can be classified using supervised machine learning techniques such as Linear Discriminant Analysis applied to features extracted by Common Spatial Patterns. Performance of these models varies widely, possibly due to MI studies commonly utilising differing post-cue time windows and frequency bands to one another. This study aims to assess how the simultaneous optimisation of both these parameters impact MI classification performance. This is done by iteratively training and testing a series of subject-specific models on different combinations of frequency bandwidth and time window options across 109 subjects. This is followed by a statistical analysis using repeated measures ANOVA to uncover significant differences between different bandwidths and time windows in terms of accuracy across the patient cohort. The resulting visualisations and statistical tests show that there are, indeed, significant differences between both specific time windows and specific bandwidths in terms of accuracy. While the comparison of classification accuracies across 23 frequency bandwidths during five different time windows demonstrates an optimal temporal and spectral scale combination of (0, 4) s at the range of (4, 12) Hz across all subjects, the subjects demonstrate similar accuracies for other parameter combinations. These findings highlight the efficacy of personalised models to detect optimal temporal and spectral parameter combinations to best classify MI EEG signals that inherently vary across subjects.

TimeClaw: A Time-Series AI Agent with Exploratory Execution Learning

Time series analysis underpins forecasting, monitoring, and decision making in domains such as finance and weather, where solving a task often requires both numerical accuracy and contextual reasoning. Recent progress has moved from specialized neural predictors to approaches built on LLMs and foundation models that can reason over time series inputs and use external tools. However, most such systems remain execution-centric: they focus on solving the current instance but learn little from exploratory execution. This is especially limiting in verifiable numeric settings, where multiple candidate executions and tool-use procedures may all be task-valid yet differ sharply in quantitative quality, and where early success can trigger tool-prior collapse that suppresses further exploration. To address this limitation, we present TimeClaw, an exploratory execution learning framework that turns exploratory execution into reusable hierarchical distilled experience through a four-stage loop: Explore, Compare, Distill, and Reinject. TimeClaw combines metric-supervised exploratory execution learning, task-aware tool dropout, and hierarchical distilled experience for inference-time reinjection, while keeping the base model frozen and avoiding online test-time adaptation. In an MTBench-aligned evaluation with 17 tasks that span finance and weather prediction and reasoning tasks, TimeClaw delivers consistent gains over the baselines. These results suggest that, for scientific systems, the bottleneck is not only execution-time capability, but how exploratory experience is compared, distilled, and reused.

Quantifying the Pre-training Dividend: Generative versus Latent Self-Supervised Learning for Time Series Foundation Models

The success of self-supervised learning (SSL) in vision and NLP has motivated its rapid adoption for time series. However, research has focused primarily on Generative paradigms and forecasting tasks, leaving the broader utility of learned representations unquantified. We establish a controlled framework to evaluate the "pre-training dividend": the value added by SSL across diverse temporal tasks. We systematically compare Generative paradigms against Latent Alignment architectures, introducing adaptations of LeJEPA and DINO for time series. These adaptations utilize Discrete Wavelet Transform (DWT) augmentations to enforce invariance to local fluctuations. Our analysis reveals that the pre-training dividend is highly asymmetric: SSL yields gains of up to 375% for anomaly detection and classification, yet remains marginal for forecasting. We demonstrate that representational utility is non-universal, governed by a precision-invariance trade-off where the specific signal resolution required by the task must align with the objective. Finally, we show that representation quality is largely independent of data origin and saturates at moderate architectural depths, suggesting a path to scaling via massive synthetic generation. Our code is available at: https://github.com/noammajor/Models

The Newsworthiness of Brazilian Distress: A Peak Analysis on Time Series of International Media Attention to Disasters in Brazil

Media coverage influences disaster response, yet the drivers of international media attention to local events remain unevenly understood. Brazil offers a compelling case: some of its natural and technological disasters occasionally hit the international headlines. However, systematic analyses of what makes these events be discussed abroad are still missing. Addressing this gap requires representative, validated and country-specific news datasets. This paper presents a peak analysis of 2k news about Brazilian fires and landslides in German newspapers from 2000 to 2024. Using time series segmentation to detect news event peaks, we examine the extent to which they can be temporally aligned with observations in national and global disaster databases.

Capabilities of Auto-encoders and Principal Component Analysis of the Reduction of Microstructural Images; Application on the Acceleration of Phase-Field Simulations

In this work, a data-driven framework based on Phase-Field simulations data is proposed to highlight the capabilities of neural networks to ensure accurate low dimensionality reduction of simulated microstructural images and to provide time-series analysis. The dataset was indeed constructed from high-fidelity Phase-Field simulations. Analyses demonstrated that the association of auto-encoder neural networks and principal component analyses leads to ensure efficient and significant dimensionality reduction: 1/196 of reduction ratio with more than 80% of accuracy. These findings give insight to apply analyses on data from the latent dimension. Application of Long Short Term Memory (LSTM) neural networks showed the possibility of making next frame predictions; that makes possible the acceleration of Phase-Field simulation without the need of high computing resources. We discussed the application of such a framework on various areas of research. Different methods are proposed from the conducted analyses, in order to ensure dimensionality reduction, including auto-encoders, principal component analysis and Artificial Neural Networks, and time-series analysis, including LSTM and Gated Recurrent Unit (GRU).

Compact Latent Manifold Translation: A Parameter-Efficient Foundation Model for Cross-Modal and Cross-Frequency Physiological Signal Synthesis

The analysis of physiological time series, such as electrocardiograms (ECG) and photoplethysmograms (PPG), is persistently hindered by modality and frequency gaps stemming from heterogeneous recording devices. Existing foundation models typically rely on continuous latent spaces, which frequently suffer from severe modality entanglement, lack high-fidelity cross-frequency generative capacity, and impose high computational costs that prohibit edge-device deployment. In this paper, we propose Compact Latent Manifold Translation (CLMT), a highly parameter-efficient (0.09B) unified framework that bridges these gaps through a novel two-stage discrete translation paradigm. First, we introduce a Universal Tokenizer utilizing Hierarchical Residual Vector Quantization (RVQ) to decouple heterogeneous signals into isolated, well-structured discrete latent manifolds, effectively preventing inter-modality interference. Second, a Context-Prompted Latent Translator maps these discrete tokens across modalities by integrating static physiological priors, reframing complex signal synthesis as a pure latent sequence translation task. Extensive evaluations demonstrate that our 0.09B model significantly outperforms massive baselines. In cross-modal PPG-to-ECG synthesis, it resolves temporal phase drift and dramatically improves the clinical R-peak detection F1-score from 0.37 (baseline) to 0.83. Furthermore, in extreme cross-frequency super-resolution (25Hz to 100Hz), it successfully recovers high-frequency diagnostic landmarks, achieving an unprecedented Pearson correlation of 0.9956. By learning a universal discrete language for biological signals with a fraction of the computational footprint, our approach sets a new trajectory for edge-deployable, multi-modal medical foundation models.