Study of Sensitivity to Weight Perturbation for Convolution Neural Network

Exploring underlying properties of a neural network contributes to pursuing its internal behavior and functionality. For convolution neural networks (CNNs), a sensitivity measure to weight perturbation is introduced in this paper to reflect the extent of the network output variation, which could evaluate the effect of the weights on the network. The sensitivity is defined as the mathematical expectation of absolute output variation due to weight perturbation with respect to all possible inputs. Assuming that the conditional distribution of input obeys the normal, the sensitivity is iteratively computed layer to layer until the entire network. Without loss of generality, the paper proposes an approximate algorithm to compute a theoretical sensitivity, which is actually a function of mapping between the network's output variation and its weight perturbation. The experimental results demonstrate the coincidence of the computed theoretical sensitivity with the simulated actual output variation of the network. Thus a criterion can be established to evaluate the influence of weights on CNNs' output.