Abstract
Accurate demand forecasting is essential for retail operations as it directly impacts supply chain efficiency, inventory management, and financial performance. However, forecasting retail time series presents significant challenges due to their irregular patterns, hierarchical structures, and strong dependence on external factors such as promotions, pricing strategies, and socio-economic conditions. This study evaluates the effectiveness of Transformer-based architectures, specifically Vanilla Transformer, Informer, Autoformer, ETSformer, NSTransformer, and Reformer, for probabilistic time series forecasting in retail. A key focus is the integration of explanatory variables, such as calendar-related indicators, selling prices, and socio-economic factors, which play a crucial role in capturing demand fluctuations. This study assesses how incorporating these variables enhances forecast accuracy, addressing a research gap in the comprehensive evaluation of explanatory variables within multiple Transformer-based models. Empirical results, based on the M5 dataset, show that incorporating explanatory variables generally improves forecasting performance. Models leveraging these variables achieve up to 12.4% reduction in Normalized Root Mean Squared Error (NRMSE) and 2.9% improvement in Mean Absolute Scaled Error (MASE) compared to models that rely solely on past sales. Furthermore, probabilistic forecasting enhances decision making by quantifying uncertainty, providing more reliable demand predictions for risk management. These findings underscore the effectiveness of Transformer-based models in retail forecasting and emphasize the importance of integrating domain-specific explanatory variables to achieve more accurate, context-aware predictions in dynamic retail environments.

Abstract
This study investigates the integration of deep learning for single-modality and multimodal data within materials science. Traditional methods for materials discovery are often resource-intensive and slow, prompting the exploration of machine learning to streamline the prediction of material properties. While single-modality models have been effective, they often miss the complexities inherent in material data. The paper explores multimodal data integration—combining text, images, and tabular data—and demonstrates its potential to improve predictive accuracy. Utilizing the Alexandria dataset, the research introduces a custom methodology involving multimodal data creation, model tuning with AutoGluon framework, and evaluation through targeted fusion techniques. Results reveal that multimodal approaches enhance predictive accuracy and efficiency, particularly when text and image data are integrated. However, challenges remain in predicting complex features like band gaps. Future directions include incorporating new data types and refining specialized models to improve materials discovery and innovation.

Abstract
This study investigates the effectiveness of Transformer-based models for retail demand forecasting. We evaluated vanilla Transformer, Informer, Autoformer, PatchTST, and temporal fusion Transformer (TFT) against traditional baselines like AutoARIMA and AutoETS. Model performance was assessed using mean absolute scaled error (MASE) and weighted quantile loss (WQL). The M5 competition dataset, comprising 30,490 time series from 10 stores, served as the evaluation benchmark. The results demonstrate that Transformer-based models significantly outperform traditional baselines, with Transformer, Informer, and TFT leading the performance metrics. These models achieved MASE improvements of 26% to 29% and WQL reductions of up to 34% compared to the seasonal Na & iuml;ve method, particularly excelling in short-term forecasts. While Autoformer and PatchTST also surpassed traditional methods, their performance was slightly lower, indicating the potential for further tuning. Additionally, this study highlights a trade-off between model complexity and computational efficiency, with Transformer models, though computationally intensive, offering superior forecasting accuracy compared to the significantly slower traditional models like AutoARIMA. These findings underscore the potential of Transformer-based approaches for enhancing retail demand forecasting, provided the computational demands are managed effectively.

Abstract
Retailers depend on accurate sales forecasts to effectively plan operations and manage supply chains. These forecasts are needed across various levels of aggregation, making hierarchical forecasting methods essential for the retail industry. As competition intensifies, the use of promotions has become a widespread strategy, significantly impacting consumer purchasing behavior. This study seeks to improve forecast accuracy by incorporating promotional data into hierarchical forecasting models. Using a sales dataset from a major Portuguese retailer, base forecasts are generated for different hierarchical levels using ARIMA models and Multi-Layer Perceptron (MLP) neural networks. Reconciliation methods including bottom-up, top-down, and optimal reconciliation with OLS and WLS (struct) estimators are employed. The results show that MLPs outperform ARIMA models for forecast horizons longer than one day. While the addition of regressors enhances ARIMA's accuracy, it does not yield similar improvements for MLP. MLPs present a compelling balance of simplicity and efficiency, outperforming ARIMA in flexibility while offering faster training times and lower computational demands compared to more complex deep learning models, making them highly suitable for practical retail forecasting applications.

Abstract
Retailers depend on accurate forecasts of product sales at the Store x SKU level to efficiently manage their inventory. Consequently, there has been increasing interest in identifying more advanced statistical techniques that lead to accuracy improvements. However, the inclusion of multiple drivers affecting demand into commonly used ARIMA and ETS models is not straightforward, particularly when many explanatory variables are available. Moreover, regularization regression models that shrink the model's parameters allow for the inclusion of a lot of relevant information but do not intrinsically handle the dynamics of the demand. These problems have not been addressed by previous studies. Nevertheless, multiple simultaneous effects interacting are common in retailing. To be successful, any approach needs to be automatic, robust and efficiently scaleable. In this study, we design novel approaches to forecast retailer product sales taking into account the main drivers which affect SKU demand at store level. To address the variable selection challenge, the use of dimensionality reduction via principal components analysis (PCA) and shrinkage estimators was investigated. The empirical results, using a case study of supermarket sales in Portugal, show that both PCA and shrinkage are useful and result in gains in forecast accuracy in the order of 10% over benchmarks while offering insights on the impact of promotions. Focusing on the promotional periods, PCA-based models perform strongly, while shrinkage estimators over-shrink. For the non-promotional periods, shrinkage estimators significantly outperform the alternatives.