  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.
