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

TL;DR

This paper introduces a Gradient-based Wang-Landau sampler for neural network output distribution estimation, improving sampling efficiency in high-dimensional input spaces by leveraging gradient-based proposals, with verified accuracy and novel insights.

Contribution

It proposes a novel gradient-based Wang-Landau algorithm that enhances sampling efficiency for neural network output distributions over input spaces.

Findings

GWL accurately estimates output distributions

CNN and ResNet map unrecognizable images to negative logits

Efficient exploration of input space subsets

Abstract

The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering insights toward a more comprehensive NN understanding. Exhaustive enumeration or traditional Monte Carlo methods for the entire input space can exhibit impractical sampling time, especially for high-dimensional inputs. To make such difficult sampling computationally feasible, in this paper, we propose a novel Gradient-based Wang-Landau (GWL) sampler. We first draw the connection between the output distribution of a NN and the density of states (DOS) of a physical system. Then, we renovate the classic sampler for the DOS problem, the Wang-Landau algorithm, by replacing its random proposals with gradient-based Monte Carlo proposals. This way, our GWL sampler investigates the under-explored subsets of the input space much more efficiently. Extensive experiments have verified the accuracy of the output distribution generated by GWL and also showcased several interesting findings - for example, in a binary image classification task, both CNN and ResNet mapped the majority of human unrecognizable images to very negative logit values.