In an effort to increase efficiency and safety, the automobile industry is undergoing a rapid transformation thanks to the integration of machine learning and artificial intelligence. In this study, computer vision an...
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Customer retention is essential in any industry. However, in the business sector, retaining existing customers has become even more critical due to intensified market competition. To proactively determine the likeliho...
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The spread of the Metaverse has created new moral and legal challenges, especially when it comes to protecting against fraud. This study explores the legal complexities surrounding Ethereum-specific metaverse transact...
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A variety of leaf diseases that can negatively impact crop output and quality present major problems to the development of potatoes. In this paper, a multi-model deep learning approach utilizing single convolutional n...
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data-driven models learned often struggle to generalize due to widespread subpopulation shifts, especially the presence of both spurious correlations and group imbalance (SC-GI). To learn models more powerful for defe...
The rapid advancement of blockchain has influenced numerous industries, playing a pivotal role. However, its drawbacks have gradually emerged. Different blockchains cannot interoperate, leading to "data islands.&...
Demands on the performance of database systems continue to increase. In state-of-the-art database systems, the storage engine is a major source of performance bottlenecks, and it is important to harness parallelism by...
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One of the largest health issues facing women worldwide is breast cancer, with a growing need for early and accurate diagnosis to improve the patient outcome. Traditional approaches like mammography and biopsy often c...
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Since its debut in 2016, ResNet has become arguably the most favorable architecture in deep neural network (DNN) design. It effectively addresses the gradient vanishing/exploding issue in DNN training, allowing engine...
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Since its debut in 2016, ResNet has become arguably the most favorable architecture in deep neural network (DNN) design. It effectively addresses the gradient vanishing/exploding issue in DNN training, allowing engineers to fully unleash DNN's potential in tackling challenging problems in various domains. Despite its practical success, an essential theoretical question remains largely open: how well/best can ResNet approximate functions? In this paper, we answer this question for several important function classes, including polynomials and smooth functions. In particular, we show that ResNet with constant width can approximate Lipschitz continuous function with a Lipschitz constant µ using O(c(d)(Ε/µ)-d/2) tunable weights, where c(d) is a constant depending on the input dimension d and ϵ > 0 is the target approximation error. Further, we extend such a result to Lebesgue-integrable functions with the upper bound characterized by the modulus of continuity. These results indicate a factor of d reduction in the number of tunable weights compared with the classical results for ReLU networks. Our results are also order-optimal in Ε, thus achieving optimal approximation rate, as they match a generalized lower bound derived in this paper. This work adds to the theoretical justifications for ResNet's stellar practical performance. Copyright 2024 by the author(s)
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