数字硬件上深度学习用于逆问题的局限性
Limitations of Deep Learning for Inverse Problems on Digital Hardware
AI总结：
本文分析了数字硬件（图灵机模型）对深度学习的内在限制，证明对于较小松弛参数，有限维逆问题不是Banach-Mazur可计算的，并给出了算法可获精度的下界。
摘要：
深度神经网络在过去几年取得了巨大成功。由于训练在数字硬件上进行，本文分析了当前硬件平台（建模为图灵机）上实际可计算的内容，这将导致深度学习的内在限制。为此，我们聚焦于逆问题类，特别是包含从测量中重建数据的任何任务。我们证明，对于较小的松弛参数，有限维逆问题不是 Banach-Mazur 可计算的。此外，我们的结果引入了算法可获得的精度的下界。
英文摘要：
Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines, which would lead to inherent restrictions of deep learning. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. We prove that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters. Even more, our results introduce a lower bound on the accuracy that can be obtained algorithmically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
