Study of Sensitivity to Weight Perturbation for Convolution Neural Network

Abstract

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.INDEX TERMS Convolutional neural network, sensitivity, weight perturbation.

Dynamic Neural Network Architectural and Topological Adaptation and Related Methods -- A Survey

“…network degradation induced by architecture modifications or quantization). We conjecture component-wise perturbation analysis [79] might lead to such guarantees as this technique has in similar scenarios not only been applied to study historical neural network architectures [80,81,82] but also yielded results for simple modern architectures recently [83].…”