In which we propose neural network architecture (dune neural network) for
recognizing general noisy image without adding any artificial noise in the
training data. By representing each free parameter of the network as an
uncertainty interval, and applying a linear transformation to each input
element, we show that the resulting architecture achieves decent noise
robustness when faced with input data with white noise. We apply simple dune
neural networks for MNIST dataset and demonstrate that even for very noisy
input images which are hard for human to recognize, our approach achieved
better test set accuracy than human without dataset augmentation. We also find
that our method is robust for many other examples with various background
patterns added.

通过将神经网络架构中的每个自由参数表示为不确定性间隔，并对每个输入元素应用线性变换，我们提出了一种神经网络结构（土丘神经网络），用于识别普通嘈杂图像而无需在训练数据中添加任何人造噪音。通过对 MNIST 数据集的简单土丘神经网络的应用，我们证明了即使对于人类难以识别的非常嘈杂的输入图像，我们的方法在测试集准确性方面也优于人类且不需要数据增强，而且我们发现我们的方法对于添加各种背景模式的其他示例也很稳健。