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本文首先从几何和物理的角度分析了网络带噪声训练后的鲁棒性，再据此提出了一种自适应的训练方法，并通过仿真实验，证实了该方法的有效性；文中还从数学的角度定量分析了前馈网络对于噪声模式的鲁棒性，给出了设计鲁棒性网络的一般性原则。
In this paper, the robustness of the network with noise training is analyzed from the perspective of geometry and physics. Then an adaptive training method is proposed and the validity of the method is verified through simulation experiments. This paper quantitatively analyzes the robustness of the feedforward network to the noise mode and gives the general principle of designing a robust network.