The majority of signal data captured in the real world uses numerous sensors with different resolutions. In practice, however, most deep learning architectures are fixed-resolution; they consider a single resolution at training time and inference time. This is convenient to implement but fails to fully take advantage of the diverse signal data that exists. In contrast, other deep learning architectures are adaptive-resolution; they directly allow various resolutions to be processed at training time and inference time. This benefits robustness and computational efficiency but introduces difficult design constraints that hinder mainstream use. In this work, we address the shortcomings of both fixed-resolution and adaptive-resolution methods by introducing Adaptive Resolution Residual Networks (ARRNs), which inherit the advantages of adaptive-resolution methods and the ease of use of fixed-resolution methods. We construct ARRNs from Laplacian residuals, which serve as generic adaptive-resolution adapters for fixed-resolution layers, and which allow casting high-resolution ARRNs into low-resolution ARRNs at inference time by simply omitting high-resolution Laplacian residuals, thus reducing computational cost on low-resolution signals without compromising performance. We complement this novel component with Laplacian dropout, which regularizes for robustness to a distribution of lower resolutions, and which also regularizes for errors that may be induced by approximate smoothing kernels in Laplacian residuals. We provide a solid grounding for the advantageous properties of ARRNs through a theoretical analysis based on neural operators, and empirically show that ARRNs embrace the challenge posed by diverse resolutions with greater flexibility, robustness, and computational efficiency.

Data mining, particularly the analysis of multivariate time series data, plays a crucial role in extracting insights from complex systems and supporting informed decision-making across diverse domains. However, assessing the similarity of multivariate time series data presents several challenges, including dealing with large datasets, addressing temporal misalignments, and the need for efficient and comprehensive analytical frameworks. To address all these challenges, we propose a novel integrated computational approach known as Multivariate Time series Alignment and Similarity Assessment (MTASA). MTASA is built upon a hybrid methodology designed to optimize time series alignment, complemented by a multiprocessing engine that enhances the utilization of computational resources. This integrated approach comprises four key components, each addressing essential aspects of time series similarity assessment, thereby offering a comprehensive framework for analysis. MTASA is implemented as an open-source Python library with a user-friendly interface, making it accessible to researchers and practitioners. To evaluate the effectiveness of MTASA, we conducted an empirical study focused on assessing agroecosystem similarity using real-world environmental data. The results from this study highlight MTASA's superiority, achieving approximately 1.5 times greater accuracy and twice the speed compared to existing state-of-the-art integrated frameworks for multivariate time series similarity assessment. It is hoped that MTASA will significantly enhance the efficiency and accessibility of multivariate time series analysis, benefitting researchers and practitioners across various domains. Its capabilities in handling large datasets, addressing temporal misalignments, and delivering accurate results make MTASA a valuable tool for deriving insights and aiding decision-making processes in complex systems.

Machine learning (ML) projects have become a leading tool in enormous domains of the computer industry. Their rule is far beyond computational aspects. Indeed, they are a focal point in designing analytical business decisions. The commercial usage of these models raises new challenges. The ML academic research often assumes that: The data in the database represents well the global data distribution.