Attention Mechanisms in Dynamical Systems: A Case Study with Predator-Prey Models

Attention mechanisms are widely used in artificial intelligence to enhance performance and interpretability. In this paper, we investigate their utility in modeling classical dynamical systems -- specifically, a noisy predator-prey (Lotka-Volterra) system. We train a simple linear attention model on perturbed time-series data to reconstruct system trajectories. Remarkably, the learned attention weights align with the geometric structure of the Lyapunov function: high attention corresponds to flat regions (where perturbations have small effect), and low attention aligns with steep regions (where perturbations have large effect). We further demonstrate that attention-based weighting can serve as a proxy for sensitivity analysis, capturing key phase-space properties without explicit knowledge of the system equations. These results suggest a novel use of AI-derived attention for interpretable, data-driven analysis and control of nonlinear systems. For example our framework could support future work in biological modeling of circadian rhythms, and interpretable machine learning for dynamical environments.

Iterative Resolution of Prompt Ambiguities Using a Progressive Cutting-Search Approach

Generative AI systems have revolutionized human interaction by enabling natural language-based coding and problem solving. However, the inherent ambiguity of natural language often leads to imprecise instructions, forcing users to iteratively test, correct, and resubmit their prompts. We propose an iterative approach that systematically narrows down these ambiguities through a structured series of clarification questions and alternative solution proposals, illustrated with input/output examples as well. Once every uncertainty is resolved, a final, precise solution is generated. Evaluated on a diverse dataset spanning coding, data analysis, and creative writing, our method demonstrates superior accuracy, competitive resolution times, and higher user satisfaction compared to conventional one-shot solutions, which typically require multiple manual iterations to achieve a correct output.

Interval-Valued Time Series Classification Using $D_K$-Distance

In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting of univariate and multivariate interval-valued time series, overlooking another important aspect: classification. In this paper, we introduce a classification approach that treats intervals as unified entities, applicable to both univariate and multivariate interval-valued time series. Specifically, we first extend the point-valued time series imaging methods to interval-valued scenarios using the $D_K$-distance, enabling the imaging of interval-valued time series. Then, we employ suitable deep learning model for classification on the obtained imaging dataset, aiming to achieve classification for interval-valued time series. In theory, we derived a sharper excess risk bound for deep multiclassifiers based on offset Rademacher complexity. Finally, we validate the superiority of the proposed method through comparisons with various existing point-valued time series classification methods in both simulation studies and real data applications.

IISE PG&E Energy Analytics Challenge 2025: Hourly-Binned Regression Models Beat Transformers in Load Forecasting

Accurate electricity load forecasting is essential for grid stability, resource optimization, and renewable energy integration. While transformer-based deep learning models like TimeGPT have gained traction in time-series forecasting, their effectiveness in long-term electricity load prediction remains uncertain. This study evaluates forecasting models ranging from classical regression techniques to advanced deep learning architectures using data from the ESD 2025 competition. The dataset includes two years of historical electricity load data, alongside temperature and global horizontal irradiance (GHI) across five sites, with a one-day-ahead forecasting horizon. Since actual test set load values remain undisclosed, leveraging predicted values would accumulate errors, making this a long-term forecasting challenge. We employ (i) Principal Component Analysis (PCA) for dimensionality reduction and (ii) frame the task as a regression problem, using temperature and GHI as covariates to predict load for each hour, (iii) ultimately stacking 24 models to generate yearly forecasts. Our results reveal that deep learning models, including TimeGPT, fail to consistently outperform simpler statistical and machine learning approaches due to the limited availability of training data and exogenous variables. In contrast, XGBoost, with minimal feature engineering, delivers the lowest error rates across all test cases while maintaining computational efficiency. This highlights the limitations of deep learning in long-term electricity forecasting and reinforces the importance of model selection based on dataset characteristics rather than complexity. Our study provides insights into practical forecasting applications and contributes to the ongoing discussion on the trade-offs between traditional and modern forecasting methods.

Adaptive PCA-Based Outlier Detection for Multi-Feature Time Series in Space Missions

Analyzing multi-featured time series data is critical for space missions making efficient event detection, potentially onboard, essential for automatic analysis. However, limited onboard computational resources and data downlink constraints necessitate robust methods for identifying regions of interest in real time. This work presents an adaptive outlier detection algorithm based on the reconstruction error of Principal Component Analysis (PCA) for feature reduction, designed explicitly for space mission applications. The algorithm adapts dynamically to evolving data distributions by using Incremental PCA, enabling deployment without a predefined model for all possible conditions. A pre-scaling process normalizes each feature's magnitude while preserving relative variance within feature types. We demonstrate the algorithm's effectiveness in detecting space plasma events, such as distinct space environments, dayside and nightside transients phenomena, and transition layers through NASA's MMS mission observations. Additionally, we apply the method to NASA's THEMIS data, successfully identifying a dayside transient using onboard-available measurements.

Taskmaster Deconstructed: A Quantitative Look at Tension, Volatility, and Viewer Ratings

Taskmaster is a British television show that combines comedic performance with a formal scoring system. Despite the appearance of structured competition, it remains unclear whether scoring dynamics contribute meaningfully to audience engagement. We conducted a statistical analysis of 162 episodes across 18 series, using fifteen episode-level metrics to quantify rank volatility, point spread, lead changes, and winner dominance. None of these metrics showed a significant association with IMDb ratings, even after controlling for series effects. Long-term trends suggest that average points have increased over time, while volatility has slightly declined and rank spread has remained stable. These patterns indicate an attempt to enhance competitive visibility without altering the show's structural equilibrium. We also analyzed contestant rank trajectories and identified five recurring archetypes describing performance styles. These patterns suggest that viewer interest is shaped more by contestant behavior than by game mechanics.

Dynamics and Computational Principles of Echo State Networks: A Mathematical Perspective

Reservoir computing (RC) represents a class of state-space models (SSMs) characterized by a fixed state transition mechanism (the reservoir) and a flexible readout layer that maps from the state space. It is a paradigm of computational dynamical systems that harnesses the transient dynamics of high-dimensional state spaces for efficient processing of temporal data. Rooted in concepts from recurrent neural networks, RC achieves exceptional computational power by decoupling the training of the dynamic reservoir from the linear readout layer, thereby circumventing the complexities of gradient-based optimization. This work presents a systematic exploration of RC, addressing its foundational properties such as the echo state property, fading memory, and reservoir capacity through the lens of dynamical systems theory. We formalize the interplay between input signals and reservoir states, demonstrating the conditions under which reservoirs exhibit stability and expressive power. Further, we delve into the computational trade-offs and robustness characteristics of RC architectures, extending the discussion to their applications in signal processing, time-series prediction, and control systems. The analysis is complemented by theoretical insights into optimization, training methodologies, and scalability, highlighting open challenges and potential directions for advancing the theoretical underpinnings of RC.

Ethereum Price Prediction Employing Large Language Models for Short-term and Few-shot Forecasting

Cryptocurrencies have transformed financial markets with their innovative blockchain technology and volatile price movements, presenting both challenges and opportunities for predictive analytics. Ethereum, being one of the leading cryptocurrencies, has experienced significant market fluctuations, making its price prediction an attractive yet complex problem. This paper presents a comprehensive study on the effectiveness of Large Language Models (LLMs) in predicting Ethereum prices for short-term and few-shot forecasting scenarios. The main challenge in training models for time series analysis is the lack of data. We address this by leveraging a novel approach that adapts existing pre-trained LLMs on natural language or images from billions of tokens to the unique characteristics of Ethereum price time series data. Through thorough experimentation and comparison with traditional and contemporary models, our results demonstrate that selectively freezing certain layers of pre-trained LLMs achieves state-of-the-art performance in this domain. This approach consistently surpasses benchmarks across multiple metrics, including Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE), demonstrating its effectiveness and robustness. Our research not only contributes to the existing body of knowledge on LLMs but also provides practical insights in the cryptocurrency prediction domain. The adaptability of pre-trained LLMs to handle the nature of Ethereum prices suggests a promising direction for future research, potentially including the integration of sentiment analysis to further refine forecasting accuracy.

Quantum Observers: A NISQ Hardware Demonstration of Chaotic State Prediction Using Quantum Echo-state Networks

Recent advances in artificial intelligence have highlighted the remarkable capabilities of neural network (NN)-powered systems on classical computers. However, these systems face significant computational challenges that limit scalability and efficiency. Quantum computers hold the potential to overcome these limitations and increase processing power beyond classical systems. Despite this, integrating quantum computing with NNs remains largely unrealized due to challenges posed by noise, decoherence, and high error rates in current quantum hardware. Here, we propose a novel quantum echo-state network (QESN) design and implementation algorithm that can operate within the presence of noise on current IBM hardware. We apply classical control-theoretic response analysis to characterize the QESN, emphasizing its rich nonlinear dynamics and memory, as well as its ability to be fine-tuned with sparsity and re-uploading blocks. We validate our approach through a comprehensive demonstration of QESNs functioning as quantum observers, applied in both high-fidelity simulations and hardware experiments utilizing data from a prototypical chaotic Lorenz system. Our results show that the QESN can predict long time-series with persistent memory, running over 100 times longer than the median T}1 and T2 of the IBM Marrakesh QPU, achieving state-of-the-art time-series performance on superconducting hardware.

Adaptive Classification of Interval-Valued Time Series

In recent years, the modeling and analysis of interval-valued time series have garnered significant attention in the fields of econometrics and statistics. However, the existing literature primarily focuses on regression tasks while neglecting classification aspects. In this paper, we propose an adaptive approach for interval-valued time series classification. Specifically, we represent interval-valued time series using convex combinations of upper and lower bounds of intervals and transform these representations into images based on point-valued time series imaging methods. We utilize a fine-grained image classification neural network to classify these images, to achieve the goal of classifying the original interval-valued time series. This proposed method is applicable to both univariate and multivariate interval-valued time series. On the optimization front, we treat the convex combination coefficients as learnable parameters similar to the parameters of the neural network and provide an efficient estimation method based on the alternating direction method of multipliers (ADMM). On the theoretical front, under specific conditions, we establish a margin-based multiclass generalization bound for generic CNNs composed of basic blocks involving convolution, pooling, and fully connected layers. Through simulation studies and real data applications, we validate the effectiveness of the proposed method and compare its performance against a wide range of point-valued time series classification methods.