DeepAI AI Chat
Log In Sign Up

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

by   Weitang Liu, et al.

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.


Learning Nonlinear State Space Models with Hamiltonian Sequential Monte Carlo Sampler

State space models (SSM) have been widely applied for the analysis and v...

Nested Sequential Monte Carlo Methods

We propose nested sequential Monte Carlo (NSMC), a methodology to sample...

A Neural Network MCMC sampler that maximizes Proposal Entropy

Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probabi...

Gradient-based Adaptive Importance Samplers

Importance sampling (IS) is a powerful Monte Carlo methodology for the a...

Capacity of the covariance perceptron

The classical perceptron is a simple neural network that performs a bina...

Lessons Learned and Improvements when Building Screen-Space Samplers with Blue-Noise Error Distribution

Recent work has shown that the error of Monte-Carlo rendering is visuall...

Neural Network-Based Approach to Phase Space Integration

Monte Carlo methods are widely used in particle physics to integrate and...