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The output distribution of a neural network (NN) over the entire input spacecaptures the complete input-output mapping relationship, offering insightstoward a more comprehensive NN understanding. Exhaustive enumeration ortraditional Monte Carlo methods for the entire input space can exhibitimpractical sampling time, especially for high-dimensional inputs. To make suchdifficult sampling computationally feasible, in this paper, we propose a novelGradient-based Wang-Landau (GWL) sampler. We first draw the connection betweenthe output distribution of a NN and the density of states (DOS) of a physicalsystem. Then, we renovate the classic sampler for the DOS problem, theWang-Landau algorithm, by replacing its random proposals with gradient-basedMonte Carlo proposals. This way, our GWL sampler investigates theunder-explored subsets of the input space much more efficiently. Extensiveexperiments have verified the accuracy of the output distribution generated byGWL and also showcased several interesting findings - for example, in a binaryimage classification task, both CNN and ResNet mapped the majority of humanunrecognizable images to very negative logit values.

Gradient-based Wang-Landau Algorithm: A Novel Sampler for Output Distribution of Neural Networks over the Input Space