A Mechanistic Analysis of Transformers for Dynamical Systems

Transformers are increasingly adopted for modeling and forecasting time-series, yet their internal mechanisms remain poorly understood from a dynamical systems perspective. In contrast to classical autoregressive and state-space models, which benefit from well-established theoretical foundations, Transformer architectures are typically treated as black boxes. This gap becomes particularly relevant as attention-based models are considered for general-purpose or zero-shot forecasting across diverse dynamical regimes. In this work, we do not propose a new forecasting model, but instead investigate the representational capabilities and limitations of single-layer Transformers when applied to dynamical data. Building on a dynamical systems perspective we interpret causal self-attention as a linear, history-dependent recurrence and analyze how it processes temporal information. Through a series of linear and nonlinear case studies, we identify distinct operational regimes. For linear systems, we show that the convexity constraint imposed by softmax attention fundamentally restricts the class of dynamics that can be represented, leading to oversmoothing in oscillatory settings. For nonlinear systems under partial observability, attention instead acts as an adaptive delay-embedding mechanism, enabling effective state reconstruction when sufficient temporal context and latent dimensionality are available. These results help bridge empirical observations with classical dynamical systems theory, providing insight into when and why Transformers succeed or fail as models of dynamical systems.

DecoKAN: Interpretable Decomposition for Forecasting Cryptocurrency Market Dynamics

Accurate and interpretable forecasting of multivariate time series is crucial for understanding the complex dynamics of cryptocurrency markets in digital asset systems. Advanced deep learning methodologies, particularly Transformer-based and MLP-based architectures, have achieved competitive predictive performance in cryptocurrency forecasting tasks. However, cryptocurrency data is inherently composed of long-term socio-economic trends and local high-frequency speculative oscillations. Existing deep learning-based 'black-box' models fail to effectively decouple these composite dynamics or provide the interpretability needed for trustworthy financial decision-making. To overcome these limitations, we propose DecoKAN, an interpretable forecasting framework that integrates multi-level Discrete Wavelet Transform (DWT) for decoupling and hierarchical signal decomposition with Kolmogorov-Arnold Network (KAN) mixers for transparent and interpretable nonlinear modeling. The DWT component decomposes complex cryptocurrency time series into distinct frequency components, enabling frequency-specific analysis, while KAN mixers provide intrinsically interpretable spline-based mappings within each decomposed subseries. Furthermore, interpretability is enhanced through a symbolic analysis pipeline involving sparsification, pruning, and symbolization, which produces concise analytical expressions offering symbolic representations of the learned patterns. Extensive experiments demonstrate that DecoKAN achieves the lowest average Mean Squared Error on all tested real-world cryptocurrency datasets (BTC, ETH, XMR), consistently outperforming a comprehensive suite of competitive state-of-the-art baselines. These results validate DecoKAN's potential to bridge the gap between predictive accuracy and model transparency, advancing trustworthy decision support within complex cryptocurrency markets.

The Procrustean Bed of Time Series: The Optimization Bias of Point-wise Loss

Optimizing time series models via point-wise loss functions (e.g., MSE) relying on a flawed point-wise independent and identically distributed (i.i.d.) assumption that disregards the causal temporal structure, an issue with growing awareness yet lacking formal theoretical grounding. Focusing on the core independence issue under covariance stationarity, this paper aims to provide a first-principles analysis of the Expectation of Optimization Bias (EOB), formalizing it information-theoretically as the discrepancy between the true joint distribution and its flawed i.i.d. counterpart. Our analysis reveals a fundamental paradigm paradox: the more deterministic and structured the time series, the more severe the bias by point-wise loss function. We derive the first closed-form quantification for the non-deterministic EOB across linear and non-linear systems, and prove EOB is an intrinsic data property, governed exclusively by sequence length and our proposed Structural Signal-to-Noise Ratio (SSNR). This theoretical diagnosis motivates our principled debiasing program that eliminates the bias through sequence length reduction and structural orthogonalization. We present a concrete solution that simultaneously achieves both principles via DFT or DWT. Furthermore, a novel harmonized $\ell_p$ norm framework is proposed to rectify gradient pathologies of high-variance series. Extensive experiments validate EOB Theory's generality and the superior performance of debiasing program.

Learning to be Reproducible: Custom Loss Design for Robust Neural Networks

To enhance the reproducibility and reliability of deep learning models, we address a critical gap in current training methodologies: the lack of mechanisms that ensure consistent and robust performance across runs. Our empirical analysis reveals that even under controlled initialization and training conditions, the accuracy of the model can exhibit significant variability. To address this issue, we propose a Custom Loss Function (CLF) that reduces the sensitivity of training outcomes to stochastic factors such as weight initialization and data shuffling. By fine-tuning its parameters, CLF explicitly balances predictive accuracy with training stability, leading to more consistent and reliable model performance. Extensive experiments across diverse architectures for both image classification and time series forecasting demonstrate that our approach significantly improves training robustness without sacrificing predictive performance. These results establish CLF as an effective and efficient strategy for developing more stable, reliable and trustworthy neural networks.

On the Identifiability of Regime-Switching Models with Multi-Lag Dependencies

Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time series. We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs), encompassing Markov Switching Models (MSMs) and Switching Dynamical Systems (SDSs). For MSMs, we formulate the model as a temporally structured finite mixture and prove identifiability of both the number of regimes and the multi-lag transitions in a nonlinear-Gaussian setting. For SDSs, we establish identifiability of the latent variables up to permutation and scaling via temporal structure, which in turn yields conditions for identifiability of regime-dependent latent causal graphs (up to regime/node permutations). Our results hold in a fully unsupervised setting through architectural and noise assumptions that are directly enforceable via neural network design. We complement the theory with a flexible variational estimator that satisfies the assumptions and validate the results on synthetic benchmarks. Across real-world datasets from neuroscience, finance, and climate, identifiability leads to more trustworthy interpretability analysis, which is crucial for scientific discovery.

Efficient Deep Learning for Short-Term Solar Irradiance Time Series Forecasting: A Benchmark Study in Ho Chi Minh City

Reliable forecasting of Global Horizontal Irradiance (GHI) is essential for mitigating the variability of solar energy in power grids. This study presents a comprehensive benchmark of ten deep learning architectures for short-term (1-hour ahead) GHI time series forecasting in Ho Chi Minh City, leveraging high-resolution NSRDB satellite data (2011-2020) to compare established baselines (e.g. LSTM, TCN) against emerging state-of-the-art architectures, including Transformer, Informer, iTransformer, TSMixer, and Mamba. Experimental results identify the Transformer as the superior architecture, achieving the highest predictive accuracy with an R^2 of 0.9696. The study further utilizes SHAP analysis to contrast the temporal reasoning of these architectures, revealing that Transformers exhibit a strong "recency bias" focused on immediate atmospheric conditions, whereas Mamba explicitly leverages 24-hour periodic dependencies to inform predictions. Furthermore, we demonstrate that Knowledge Distillation can compress the high-performance Transformer by 23.5% while surprisingly reducing error (MAE: 23.78 W/m^2), offering a proven pathway for deploying sophisticated, low-latency forecasting on resource-constrained edge devices.

Deep Generative Models for Synthetic Financial Data: Applications to Portfolio and Risk Modeling

Synthetic financial data provides a practical solution to the privacy, accessibility, and reproducibility challenges that often constrain empirical research in quantitative finance. This paper investigates the use of deep generative models, specifically Time-series Generative Adversarial Networks (TimeGAN) and Variational Autoencoders (VAEs) to generate realistic synthetic financial return series for portfolio construction and risk modeling applications. Using historical daily returns from the S and P 500 as a benchmark, we generate synthetic datasets under comparable market conditions and evaluate them using statistical similarity metrics, temporal structure tests, and downstream financial tasks. The study shows that TimeGAN produces synthetic data with distributional shapes, volatility patterns, and autocorrelation behaviour that are close to those observed in real returns. When applied to mean--variance portfolio optimization, the resulting synthetic datasets lead to portfolio weights, Sharpe ratios, and risk levels that remain close to those obtained from real data. The VAE provides more stable training but tends to smooth extreme market movements, which affects risk estimation. Finally, the analysis supports the use of synthetic datasets as substitutes for real financial data in portfolio analysis and risk simulation, particularly when models are able to capture temporal dynamics. Synthetic data therefore provides a privacy-preserving, cost-effective, and reproducible tool for financial experimentation and model development.

SportsGPT: An LLM-driven Framework for Interpretable Sports Motion Assessment and Training Guidance

Existing intelligent sports analysis systems mainly focus on "scoring and visualization," often lacking automatic performance diagnosis and interpretable training guidance. Recent advances in Large Language Models (LLMs) and motion analysis techniques provide new opportunities to address the above limitations. In this paper, we propose SportsGPT, an LLM-driven framework for interpretable sports motion assessment and training guidance, which establishes a closed loop from motion time-series input to professional training guidance. First, given a set of high-quality target models, we introduce MotionDTW, a two-stage time series alignment algorithm designed for accurate keyframe extraction from skeleton-based motion sequences. Subsequently, we design a Knowledge-based Interpretable Sports Motion Assessment Model (KISMAM) to obtain a set of interpretable assessment metrics (e.g., insufficient extension) by contrasting the keyframes with the target models. Finally, we propose SportsRAG, a RAG-based training guidance model built upon Qwen3. Leveraging a 6B-token knowledge base, it prompts the LLM to generate professional training guidance by retrieving domain-specific QA pairs. Experimental results demonstrate that MotionDTW significantly outperforms traditional methods with lower temporal error and higher IoU scores. Furthermore, ablation studies validate the KISMAM and SportsRAG, confirming that SportsGPT surpasses general LLMs in diagnostic accuracy and professionalism.

Electric Vehicle Charging Load Forecasting: An Experimental Comparison of Machine Learning Methods

With the growing popularity of electric vehicles as a means of addressing climate change, concerns have emerged regarding their impact on electric grid management. As a result, predicting EV charging demand has become a timely and important research problem. While substantial research has addressed energy load forecasting in transportation, relatively few studies systematically compare multiple forecasting methods across different temporal horizons and spatial aggregation levels in diverse urban settings. This work investigates the effectiveness of five time series forecasting models, ranging from traditional statistical approaches to machine learning and deep learning methods. Forecasting performance is evaluated for short-, mid-, and long-term horizons (on the order of minutes, hours, and days, respectively), and across spatial scales ranging from individual charging stations to regional and city-level aggregations. The analysis is conducted on four publicly available real-world datasets, with results reported independently for each dataset. To the best of our knowledge, this is the first work to systematically evaluate EV charging demand forecasting across such a wide range of temporal horizons and spatial aggregation levels using multiple real-world datasets.

MotionTeller: Multi-modal Integration of Wearable Time-Series with LLMs for Health and Behavioral Understanding

As wearable sensing becomes increasingly pervasive, a key challenge remains: how can we generate natural language summaries from raw physiological signals such as actigraphy - minute-level movement data collected via accelerometers? In this work, we introduce MotionTeller, a generative framework that natively integrates minute-level wearable activity data with large language models (LLMs). MotionTeller combines a pretrained actigraphy encoder with a lightweight projection module that maps behavioral embeddings into the token space of a frozen decoder-only LLM, enabling free-text, autoregressive generation of daily behavioral summaries. We construct a novel dataset of 54383 (actigraphy, text) pairs derived from real-world NHANES recordings, and train the model using cross-entropy loss with supervision only on the language tokens. MotionTeller achieves high semantic fidelity (BERTScore-F1 = 0.924) and lexical accuracy (ROUGE-1 = 0.722), outperforming prompt-based baselines by 7 percent in ROUGE-1. The average training loss converges to 0.38 by epoch 15, indicating stable optimization. Qualitative analysis confirms that MotionTeller captures circadian structure and behavioral transitions, while PCA plots reveal enhanced cluster alignment in embedding space post-training. Together, these results position MotionTeller as a scalable, interpretable system for transforming wearable sensor data into fluent, human-centered descriptions, introducing new pathways for behavioral monitoring, clinical review, and personalized health interventions.