AdjointBackMap: Reconstructing effective decision hypersurfaces from CNN layers using adjoint operators

There are several methods in the exploration of Convolutional Neural Networks' (CNNs') inner workings. 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. Since the reconstructed hyperplane (each point on the hypersurface) resides in the input space, we can easily visualize it. Our results show that the reconstructed hyperplane, 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 process is largely conditioned on the input, and the corresponding reconstructed hypersurfaces are highly sensitive to adversarial noise, thus providing insights on why CNNs are susceptible to adversarial attack.