鲁棒是Robust的音译,也就是健壮和强壮的意思。它也是在异常和危险情况下系统生存的能力。比如说,计算机软件在输入错误、磁盘故障、网络过载或有意攻击情况下,能否不死机、不崩溃,就是该软件的鲁棒性。所谓“鲁棒性”,也是指控制系统在一定(结构,大小)的参数摄动下,维持其它某些性能的特性。根据对性能的不同定义,可分为稳定鲁棒性和性能鲁棒性。以闭环系统的鲁棒性作为目标设计得到的固定控制器称为鲁棒控制器。

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Advances in neural architecture search, as well as explainability and interpretability of connectionist architectures, have been reported in the recent literature. However, our understanding of how to design Bayesian Deep Learning (BDL) hyperparameters, specifically, the depth, width and ensemble size, for robust function mapping with uncertainty quantification, is still emerging. This paper attempts to further our understanding by mapping Bayesian connectionist representations to polynomials of different orders with varying noise types and ratios. We examine the noise-contaminated polynomials to search for the combination of hyperparameters that can extract the underlying polynomial signals while quantifying uncertainties based on the noise attributes. Specifically, we attempt to study the question that an appropriate neural architecture and ensemble configuration can be found to detect a signal of any n-th order polynomial contaminated with noise having different distributions and signal-to-noise (SNR) ratios and varying noise attributes. Our results suggest the possible existence of an optimal network depth as well as an optimal number of ensembles for prediction skills and uncertainty quantification, respectively. However, optimality is not discernible for width, even though the performance gain reduces with increasing width at high values of width. Our experiments and insights can be directional to understand theoretical properties of BDL representations and to design practical solutions.

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Advances in neural architecture search, as well as explainability and interpretability of connectionist architectures, have been reported in the recent literature. However, our understanding of how to design Bayesian Deep Learning (BDL) hyperparameters, specifically, the depth, width and ensemble size, for robust function mapping with uncertainty quantification, is still emerging. This paper attempts to further our understanding by mapping Bayesian connectionist representations to polynomials of different orders with varying noise types and ratios. We examine the noise-contaminated polynomials to search for the combination of hyperparameters that can extract the underlying polynomial signals while quantifying uncertainties based on the noise attributes. Specifically, we attempt to study the question that an appropriate neural architecture and ensemble configuration can be found to detect a signal of any n-th order polynomial contaminated with noise having different distributions and signal-to-noise (SNR) ratios and varying noise attributes. Our results suggest the possible existence of an optimal network depth as well as an optimal number of ensembles for prediction skills and uncertainty quantification, respectively. However, optimality is not discernible for width, even though the performance gain reduces with increasing width at high values of width. Our experiments and insights can be directional to understand theoretical properties of BDL representations and to design practical solutions.

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