Time Series Transformers

The reliable operation of modern power grids requires probabilistic load forecasts with well-calibrated uncertainty estimates. However, existing deep learning models produce overconfident point predictions that fail catastrophically under extreme weather distributional shifts. This study proposes a Bayesian Transformer (BT) framework that integrates three complementary uncertainty mechanisms into a PatchTST backbone: Monte Carlo Dropout for epistemic parameter uncertainty, variational feed-forward layers with log-uniform weight priors, and stochastic attention with learnable Gaussian noise perturbations on pre-softmax logits, representing, to the best of our knowledge, the first application of Bayesian attention to probabilistic load forecasting. A seven-level multi-quantile pinball-loss prediction head and post-training isotonic regression calibration produce sharp, near-nominally covered prediction intervals. Evaluation of five grid datasets (PJM, ERCOT, ENTSO-E Germany, France, and Great Britain) augmented with NOAA covariates across 24, 48, and 168-hour horizons demonstrates state-of-the-art performance. On the primary benchmark (PJM, H=24h), BT achieves a CRPS of 0.0289, improving 7.4% over Deep Ensembles and 29.9% over the deterministic LSTM, with 90.4% PICP at the 90% nominal level and the narrowest prediction intervals (4,960 MW) among all probabilistic baselines. During heat-wave and cold snap events, BT maintained 89.6% and 90.1% PICP respectively, versus 64.7% and 67.2% for the deterministic LSTM, confirming that Bayesian epistemic uncertainty naturally widens intervals for out-of-distribution inputs. Calibration remained stable across all horizons (89.8-90.4% PICP), while ablation confirmed that each component contributed a distinct value. The calibrated outputs directly support risk-based reserve sizing, stochastic unit commitment, and demand response activation.

Stock market prediction presents considerable challenges for investors, financial institutions, and policymakers operating in complex market environments characterized by noise, non-stationarity, and behavioral dynamics. Traditional forecasting methods, including fundamental analysis and technical indicators, often fail to capture the intricate patterns and cross-sectional dependencies inherent in financial markets. This paper presents an integrated framework combining a node transformer architecture with BERT-based sentiment analysis for stock price forecasting. The proposed model represents the stock market as a graph structure where individual stocks form nodes and edges capture relationships including sectoral affiliations, correlated price movements, and supply chain connections. A fine-tuned BERT model extracts sentiment information from social media posts and combines it with quantitative market features through attention-based fusion mechanisms. The node transformer processes historical market data while capturing both temporal evolution and cross-sectional dependencies among stocks. Experiments conducted on 20 S&P 500 stocks spanning January 1982 to March 2025 demonstrate that the integrated model achieves a mean absolute percentage error (MAPE) of 0.80% for one-day-ahead predictions, compared to 1.20% for ARIMA and 1.00% for LSTM. The inclusion of sentiment analysis reduces prediction error by 10% overall and 25% during earnings announcements, while the graph-based architecture contributes an additional 15% improvement by capturing inter-stock dependencies. Directional accuracy reaches 65% for one-day forecasts. Statistical validation through paired t-tests confirms the significance of these improvements (p < 0.05 for all comparisons). The model maintains lower error during high-volatility periods, achieving MAPE of 1.50% while baseline models range from 1.60% to 2.10%.

Early warning of intraoperative adverse events plays a vital role in reducing surgical risk and improving patient safety. While deep learning has shown promise in predicting the single adverse event, several key challenges remain: overlooking adverse event dependencies, underutilizing heterogeneous clinical data, and suffering from the class imbalance inherent in medical datasets. To address these issues, we construct the first Multi-label Adverse Events dataset (MuAE) for intraoperative adverse events prediction, covering six critical events. Next, we propose a novel Transformerbased multi-label learning framework (IAENet) that combines an improved Time-Aware Feature-wise Linear Modulation (TAFiLM) module for static covariates and dynamic variables robust fusion and complex temporal dependencies modeling. Furthermore, we introduce a Label-Constrained Reweighting Loss (LCRLoss) with co-occurrence regularization to effectively mitigate intra-event imbalance and enforce structured consistency among frequently co-occurring events. Extensive experiments demonstrate that IAENet consistently outperforms strong baselines on 5, 10, and 15-minute early warning tasks, achieving improvements of +5.05%, +2.82%, and +7.57% on average F1 score. These results highlight the potential of IAENet for supporting intelligent intraoperative decision-making in clinical practice.

Accurate fault detection and localization in electrical distribution systems is crucial, especially with the increasing integration of distributed energy resources (DERs), which inject greater variability and complexity into grid operations. In this study, FaultXformer is proposed, a Transformer encoder-based architecture developed for automatic fault analysis using real-time current data obtained from phasor measurement unit (PMU). The approach utilizes time-series current data to initially extract rich temporal information in stage 1, which is crucial for identifying the fault type and precisely determining its location across multiple nodes. In Stage 2, these extracted features are processed to differentiate among distinct fault types and identify the respective fault location within the distribution system. Thus, this dual-stage transformer encoder pipeline enables high-fidelity representation learning, considerably boosting the performance of the work. The model was validated on a dataset generated from the IEEE 13-node test feeder, simulated with 20 separate fault locations and several DER integration scenarios, utilizing current measurements from four strategically located PMUs. To demonstrate robust performance evaluation, stratified 10-fold cross-validation is performed. FaultXformer achieved average accuracies of 98.76% in fault type classification and 98.92% in fault location identification across cross-validation, consistently surpassing conventional deep learning baselines convolutional neural network (CNN), recurrent neural network (RNN). long short-term memory (LSTM) by 1.70%, 34.95%, and 2.04% in classification accuracy and by 10.82%, 40.89%, and 6.27% in location accuracy, respectively. These results demonstrate the efficacy of the proposed model with significant DER penetration.

Multimodal time series forecasting has garnered significant attention for its potential to provide more accurate predictions than traditional single-modality models by leveraging rich information inherent in other modalities. However, due to fundamental challenges in modality alignment, existing methods often struggle to effectively incorporate multimodal data into predictions, particularly textual information that has a causal influence on time series fluctuations, such as emergency reports and policy announcements. In this paper, we reflect on the role of textual information in numerical forecasting and propose Time series transformers with Multimodal Mixture-of-Experts, TiMi, to unleash the causal reasoning capabilities of LLMs. Concretely, TiMi utilizes LLMs to generate inferences on future developments, which serve as guidance for time series forecasting. To seamlessly integrate both exogenous factors and time series into predictions, we introduce a Multimodal Mixture-of-Experts (MMoE) module as a lightweight plug-in to empower Transformer-based time series models for multimodal forecasting, eliminating the need for explicit representation-level alignment. Experimentally, our proposed TiMi demonstrates consistent state-of-the-art performance on sixteen real-world multimodal forecasting benchmarks, outperforming advanced baselines while offering both strong adaptability and interpretability.

Selecting the right deep learning model for power grid forecasting is challenging, as performance heavily depends on the data available to the operator. This paper presents a comprehensive benchmark of five modern neural architectures: two state space models (PowerMamba, S-Mamba), two Transformers (iTransformer, PatchTST), and a traditional LSTM. We evaluate these models on hourly electricity demand across six diverse US power grids for forecast windows between 24 and 168 hours. To ensure a fair comparison, we adapt each model with specialized temporal processing and a modular layer that cleanly integrates weather covariates. Our results reveal that there is no single best model for all situations. When forecasting using only historical load, PatchTST and the state space models provide the highest accuracy. However, when explicit weather data is added to the inputs, the rankings reverse: iTransformer improves its accuracy three times more efficiently than PatchTST. By controlling for model size, we confirm that this advantage stems from the architecture's inherent ability to mix information across different variables. Extending our evaluation to solar generation, wind power, and wholesale prices further demonstrates that model rankings depend on the forecast task: PatchTST excels on highly rhythmic signals like solar, while state space models are better suited for the chaotic fluctuations of wind and price. Ultimately, this benchmark provides grid operators with actionable guidelines for selecting the optimal forecasting architecture based on their specific data environments.

Accurate short-term power load forecasting is important to effectively manage, optimize, and ensure the robustness of modern power systems. This paper performs an empirical evaluation of a traditional statistical model and deep learning approaches for predicting short-term energy load. Four models, namely ARIMA, LSTM, BiLSTM, and Transformer, were leveraged on the PJM Hourly Energy Consumption data. The data processing involved interpolation, normalization, and a sliding-window sequence method. Each model's forecasting performance was evaluated for the 24-hour horizon using MAE, RMSE, and MAPE. Of the models tested, the Transformer model, which relies on self-attention algorithms, produced the best results with 3.8 percent of MAPE, with performance above any model in both accuracy and robustness. These findings underscore the growing potential of attention-based architectures in accurately capturing complex temporal patterns in power consumption data.

Large-scale foundation models for scientific machine learning adapt to physical settings unseen during training, such as zero-shot transfer between turbulent scales. This phenomenon, in-context learning, challenges conventional understanding of learning and adaptation in physical systems. Here, we study in-context learning of dynamical systems in a minimal setting: we train a small two-layer, single-head transformer to forecast one dynamical system, and then evaluate its ability to forecast a different dynamical system without retraining. We discover an early tradeoff in training between in-distribution and out-of-distribution performance, which manifests as a secondary double descent phenomenon. We discover that attention-based models apply a transfer-operator forecasting strategy in-context. They (1) lift low-dimensional time series using delay embedding, to detect the system's higher-dimensional dynamical manifold, and (2) identify and forecast long-lived invariant sets that characterize the global flow on this manifold. Our results clarify the mechanism enabling large pretrained models to forecast unseen physical systems at test time without retraining, and they illustrate the unique ability of attention-based models to leverage global attractor information in service of short-term forecasts.

Normalization and scaling are fundamental preprocessing steps in time series modeling, yet their role in Transformer-based models remains underexplored from a theoretical perspective. In this work, we present the first formal analysis of how different normalization strategies, specifically instance-based and global scaling, impact the expressivity of Transformer-based architectures for time series representation learning. We propose a novel expressivity framework tailored to time series, which quantifies a model's ability to distinguish between similar and dissimilar inputs in the representation space. Using this framework, we derive theoretical bounds for two widely used normalization methods: Standard and Min-Max scaling. Our analysis reveals that the choice of normalization strategy can significantly influence the model's representational capacity, depending on the task and data characteristics. We complement our theory with empirical validation on classification and forecasting benchmarks using multiple Transformer-based models. Our results show that no single normalization method consistently outperforms others, and in some cases, omitting normalization entirely leads to superior performance. These findings highlight the critical role of preprocessing in time series learning and motivate the need for more principled normalization strategies tailored to specific tasks and datasets.

Modeling of longitudinal cohort data typically involves complex temporal dependencies between multiple variables. There, the transformer architecture, which has been highly successful in language and vision applications, allows us to account for the fact that the most recently observed time points in an individual's history may not always be the most important for the immediate future. This is achieved by assigning attention weights to observations of an individual based on a transformation of their values. One reason why these ideas have not yet been fully leveraged for longitudinal cohort data is that typically, large datasets are required. Therefore, we present a simplified transformer architecture that retains the core attention mechanism while reducing the number of parameters to be estimated, to be more suitable for small datasets with few time points. Guided by a statistical perspective on transformers, we use an autoregressive model as a starting point and incorporate attention as a kernel-based operation with temporal decay, where aggregation of multiple transformer heads, i.e. different candidate weighting schemes, is expressed as accumulating evidence on different types of underlying characteristics of individuals. This also enables a permutation-based statistical testing procedure for identifying contextual patterns. In a simulation study, the approach is shown to recover contextual dependencies even with a small number of individuals and time points. In an application to data from a resilience study, we identify temporal patterns in the dynamics of stress and mental health. This indicates that properly adapted transformers can not only achieve competitive predictive performance, but also uncover complex context dependencies in small data settings.

Electronic health records (EHR) are irregular, asynchronous multivariate time series. As time-series foundation models increasingly tokenize events rather than discretizing time, the input layout becomes a key design choice. Grids expose time$\times$variable structure but require imputation or missingness masks, risking error or sampling-policy shortcuts. Point-set tokenization avoids discretization but loses within-variable trajectories and time-local cross-variable context (Fig.1). We restore these priors in STructure-AwaRe (STAR) Set Transformer by adding parameter-efficient soft attention biases: a temporal locality penalty $-|Δt|/τ$ with learnable timescales and a variable-type affinity $B_{s_i,s_j}$ from a learned feature-compatibility matrix. We benchmark 10 depth-wise fusion schedules (Fig.2). On three ICU prediction tasks, STAR-Set achieves AUC/APR of 0.7158/0.0026 (CPR), 0.9164/0.2033 (mortality), and 0.8373/0.1258 (vasopressor use), outperforming regular-grid, event-time grid, and prior set baselines. Learned $τ$ and $B$ provide interpretable summaries of temporal context and variable interactions, offering a practical plug-in for context-informed time-series models.

We explore the use of transformers for solving quadratic programs and how this capability benefits decision-making problems that involve covariance matrices. We first show that the linear attention mechanism can provably solve unconstrained QPs by tokenizing the matrix variables (e.g.~$A$ of the objective $\frac{1}{2}x^\top Ax+b^\top x$) row-by-row and emulating gradient descent iterations. Furthermore, by incorporating MLPs, a transformer block can solve (i) $\ell_1$-penalized QPs by emulating iterative soft-thresholding and (ii) $\ell_1$-constrained QPs when equipped with an additional feedback loop. Our theory motivates us to introduce Time2Decide: a generic method that enhances a time series foundation model (TSFM) by explicitly feeding the covariance matrix between the variates. We empirically find that Time2Decide uniformly outperforms the base TSFM model for the classical portfolio optimization problem that admits an $\ell_1$-constrained QP formulation. Remarkably, Time2Decide also outperforms the classical "Predict-then-Optimize (PtO)" procedure, where we first forecast the returns and then explicitly solve a constrained QP, in suitable settings. Our results demonstrate that transformers benefit from explicit use of second-order statistics, and this can enable them to effectively solve complex decision-making problems, like portfolio construction, in one forward pass.

Accurate and up-to-date forecasting of the power grid's carbon footprint is crucial for effective product carbon footprint (PCF) accounting and informed decarbonization decisions. However, the carbon intensity of the grid exhibits high non-stationarity, and existing methods often struggle to effectively leverage periodic and oscillatory patterns. Furthermore, these methods tend to perform poorly when confronted with irregular exogenous inputs, such as missing data or misalignment. To tackle these challenges, we propose FTimeXer, a frequency-aware time-series Transformer designed with a robust training scheme that accommodates exogenous factors. FTimeXer features an Fast Fourier Transform (FFT)-driven frequency branch combined with gated time-frequency fusion, allowing it to capture multi-scale periodicity effectively. It also employs stochastic exogenous masking in conjunction with consistency regularization, which helps reduce spurious correlations and enhance stability. Experiments conducted on three real-world datasets show consistent improvements over strong baselines. As a result, these enhancements lead to more reliable forecasts of grid carbon factors, which are essential for effective PCF accounting and informed decision-making regarding decarbonization.

Transformer-based models have shown strong performance in time-series forecasting by leveraging self-attention to model long-range temporal dependencies. However, their effectiveness depends critically on the quality and structure of input representations derived from raw multivariate time-series data, particularly as sequence length and data scale increase. This paper proposes a two-stage forecasting framework that explicitly separates local temporal representation learning from global dependency modelling. In the proposed approach, a convolutional neural network operates on fixed-length temporal patches to extract short-range temporal dynamics and non-linear feature interactions, producing compact patch-level token embeddings. Token-level self-attention is applied during representation learning to refine these embeddings, after which a Transformer encoder models inter-patch temporal dependencies to generate forecasts. The method is evaluated on a synthetic multivariate time-series dataset with controlled static and dynamic factors, using an extended sequence length and a larger number of samples. Experimental results demonstrate that the proposed framework consistently outperforms a convolutional baseline under increased temporal context and remains competitive with a strong patch-based Transformer model. These findings indicate that structured patch-level tokenization provides a scalable and effective representation for multivariate time-series forecasting, particularly when longer input sequences are considered.

This paper presents an Artificial Intelligence (AI) integrated approach to Brain-Computer Interface (BCI)-based wheelchair development, utilizing a motor imagery right-left-hand movement mechanism for control. The system is designed to simulate wheelchair navigation based on motor imagery right and left-hand movements using electroencephalogram (EEG) data. A pre-filtered dataset, obtained from an open-source EEG repository, was segmented into arrays of 19x200 to capture the onset of hand movements. The data was acquired at a sampling frequency of 200Hz. The system integrates a Tkinter-based interface for simulating wheelchair movements, offering users a functional and intuitive control system. We propose TFormerEEG, a Transformer-driven deep learning architecture, for motor imagery EEG classification. The model achieves a test accuracy of 93.04% compared with various machine learning baseline models, including XGBoost, EEGNet, and an EEG-Deformer model. The TFormerEEG achieved a mean accuracy of 91.18% through stratified cross-validation, showcasing the effectiveness of this model.

Electronic health Records (EHRs) have become a cornerstone in modern-day healthcare. They are a crucial part for analyzing the progression of patient health; however, their complexity, characterized by long, multivariate sequences, sparsity, and missing values poses significant challenges in traditional deep learning modeling. While Transformer-based models have demonstrated success in modeling EHR data and predicting clinical outcomes, their quadratic computational complexity and limited context length hinder their efficiency and practical applications. On the other hand, State Space Models (SSMs) like Mamba present a promising alternative offering linear-time sequence modeling and improved efficiency for handling long sequences, but focus mostly on mixing sequence-level information rather than channel-level data. To overcome these challenges, we propose HyMaTE (A Hybrid Mamba and Transformer Model for EHR Representation Learning), a novel hybrid model tailored for representing longitudinal data, combining the strengths of SSMs with advanced attention mechanisms. By testing the model on predictive tasks on multiple clinical datasets, we demonstrate HyMaTE's ability to capture an effective, richer, and more nuanced unified representation of EHR data. Additionally, the interpretability of the outcomes achieved by self-attention illustrates the effectiveness of our model as a scalable and generalizable solution for real-world healthcare applications. Codes are available at: https://github.com/healthylaife/HyMaTE.

Standard attention mechanisms in transformers employ static token representations that remain unchanged across all pair-wise computations in each layer. This limits their representational alignment with the potentially diverse relational dynamics of each token-pair interaction. While they excel in domains with relatively homogeneous relationships, standard attention's static relational learning struggles to capture the diverse, heterogeneous inter-channel dependencies of multivariate time series (MTS) data--where different channel-pair interactions within a single system may be governed by entirely different physical laws or temporal dynamics. To better align the attention mechanism for such domain phenomena, we propose attention with dynamic relational priming (prime attention). Unlike standard attention where each token presents an identical representation across all of its pair-wise interactions, prime attention tailors each token dynamically (or per interaction) through learnable modulations to best capture the unique relational dynamics of each token pair, optimizing each pair-wise interaction for that specific relationship. This representational plasticity of prime attention enables effective extraction of relationship-specific information in MTS while maintaining the same asymptotic computational complexity as standard attention. Our results demonstrate that prime attention consistently outperforms standard attention across benchmarks, achieving up to 6.5% improvement in forecasting accuracy. In addition, we find that prime attention achieves comparable or superior performance using up to 40% less sequence length compared to standard attention, further demonstrating its superior relational modeling capabilities.

This paper introduces Fuzzy Attention Network-Based Transformer (FANTF), an approach for time series forecasting, classification, and anomaly detection. FANTF combines fuzzy logic concepts with transformer architectures through a novel fuzzy attention mechanism. The proposed mechanism is inspired by Type-2 fuzzy set theory. It uses a learnable Gaussian uncertainty perturbation to model uncertainty in attention relevance scores. This makes it possible for the model to accurately capture uncertainty in temporal relationships better than normal deterministic attention. Transformers capacity to record complex temporal patterns and multivariate connections is enhanced by FANTF. The approach is both architecture-agnostic and task-agnostic. The proposed fuzzy attention module can be used as a direct replacement for the standard attention layer. To evaluate its effectiveness, FANTF is integrated into five transformer backbones: Transformer, Informer, PatchTST, Crossformer, and iTransformer. The fuzzy attention mechanism produces softer and more diverse attention distributions. It provides uncertainty-aware interpretations through attention heatmap visualizations. Experimental evaluations on some real-life datasets reveal that FANTF enhances the forecasting performance, classification, and anomaly detection tasks over traditional transformer-based models. FANTF achieves statistically significant and competitive performance improvements over standard transformer-based baselines on most benchmark datasets (p < 0.05, Wilcoxon signed-rank test), observed under noisy and non-stationary time series conditions.

Time series forecasting (TSF) is important in real-world applications. Recently, Transformer-based methods have achieved strong performance by modeling token dependencies through attention mechanisms. However, existing methods are usually trained mainly with prediction error losses, which may cause models to exploit both critical and redundant token dependencies. Such redundant dependencies can introduce irrelevant information and weaken generalization. To address this issue, we propose a simple yet effective token dependency selection strategy. Specifically, by jointly introducing the attention entropy constraint and prediction error constraint, the model can identify fewer but more critical inter-token dependencies and perform forecasting based on them, thus avoiding the interference of redundant dependencies. The proposed method can be easily extended to various Transformer-based TSF models. Experiments on multiple TSF datasets demonstrate its effectiveness.