AdjointBackMap: Reconstructing Effective Decision Hypersurfaces from CNN Layers Using Adjoint Operators
This work provides a method to understand the input-conditioned decision surfaces of CNN units, which could help explain the vulnerability of CNNs to adversarial attacks for researchers in interpretability and adversarial robustness.
This paper proposes a method using adjoint operators to reconstruct the effective decision hypersurface of any CNN unit (except the first layer) in the input space. The reconstructed hypersurface, when multiplied by the input image, yields nearly the exact output value of the unit, suggesting that CNN unit decisions are highly input-conditioned.
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.