  There are several effective methods in explaining the inner workings of
convolutional neural networks (CNNs). However, in general, finding the inverse
of the function performed by CNNs as a whole is an ill-posed problem. In this
paper, we propose a method based on adjoint operators to reconstruct, given an
arbitrary unit in the CNN (except for the first convolutional layer), its
effective hypersurface in the input space that replicates that unit's decision
surface conditioned on a particular input image. Our results show that the
hypersurface reconstructed this way, when multiplied by the original input
image, would give nearly the exact output value of that unit. We find that the
CNN unit's decision surface is largely conditioned on the input, and this may
explain why adversarial inputs can effectively deceive CNNs.
