The recent advancements in time series analysis and forecasting have shown a significant shift towards more sophisticated and adaptive models. Researchers are increasingly focusing on developing methods that can handle the complexities and variability inherent in time series data. This includes the integration of deep learning techniques with traditional time series models to enhance predictive accuracy and robustness. Notably, there is a growing emphasis on the regularization of learnable embeddings to improve the transferability of models across different contexts. Additionally, the incorporation of predictive feedback mechanisms and multi-scale pattern extraction is proving to be effective in capturing long-term dependencies and adapting to data distribution shifts. Furthermore, the use of end-to-end model-based learning approaches is gaining traction for efficient analysis of high-dimensional data, such as in frequency selective surfaces. These developments collectively indicate a move towards more versatile and generalizable models that can be applied across a wide range of time series tasks, from forecasting to anomaly detection. Notably, the introduction of recursive residual decomposition for robust time series forecasting and the exploration of path-invariant embeddings for seismic source characterization are particularly innovative contributions that advance the field.