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

Weitang Liu, Yi-Zhuang You, Ying Wai Li, Jingbo Shang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:22338-22351, 2023.

Abstract

The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering in- sights toward a more comprehensive NN under- standing. 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, Wang-Landau algorithm, by re-placing 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-liu23aw, title = {Gradient-based Wang-Landau Algorithm: A Novel Sampler for Output Distribution of Neural Networks over the Input Space}, author = {Liu, Weitang and You, Yi-Zhuang and Li, Ying Wai and Shang, Jingbo}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {22338--22351}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/liu23aw/liu23aw.pdf}, url = {https://proceedings.mlr.press/v202/liu23aw.html}, abstract = {The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering in- sights toward a more comprehensive NN under- standing. 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, Wang-Landau algorithm, by re-placing 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.} }
Endnote
%0 Conference Paper %T Gradient-based Wang-Landau Algorithm: A Novel Sampler for Output Distribution of Neural Networks over the Input Space %A Weitang Liu %A Yi-Zhuang You %A Ying Wai Li %A Jingbo Shang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-liu23aw %I PMLR %P 22338--22351 %U https://proceedings.mlr.press/v202/liu23aw.html %V 202 %X The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering in- sights toward a more comprehensive NN under- standing. 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, Wang-Landau algorithm, by re-placing 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.
APA
Liu, W., You, Y., Li, Y.W. & Shang, J.. (2023). Gradient-based Wang-Landau Algorithm: A Novel Sampler for Output Distribution of Neural Networks over the Input Space. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:22338-22351 Available from https://proceedings.mlr.press/v202/liu23aw.html.

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