# Combating Mode Collapse in GAN Training: An Empirical Analysis using Hessian Eigenvalues

### Ricard Durall, Ricard Durall, Ricard Durall, Avraam Chatzimichailidis, Avraam Chatzimichailidis, Avraam Chatzimichailidis, Peter Labus, Peter Labus, Janis Keuper, Janis Keuper

#### Abstract

Generative adversarial networks (GANs) provide state-of-the-art results in image generation. However, despite being so powerful, they still remain very challenging to train. This is in particular caused by their highly non-convex optimization space leading to a number of instabilities. Among them, mode collapse stands out as one of the most daunting ones. This undesirable event occurs when the model can only fit a few modes of the data distribution, while ignoring the majority of them. In this work, we combat mode collapse using second-order gradient information. To do so, we analyse the loss surface through its Hessian eigenvalues, and show that mode collapse is related to the convergence towards sharp minima. In particular, we observe how the eigenvalues of the G are directly correlated with the occurrence of mode collapse. Finally, motivated by these findings, we design a new optimization algorithm called nudged-Adam (NuGAN) that uses spectral information to overcome mode collapse, leading to empirically more stable convergence properties.

Download#### Paper Citation

#### in Harvard Style

Durall R., Chatzimichailidis A., Labus P. and Keuper J. (2021). **Combating Mode Collapse in GAN Training: An Empirical Analysis using Hessian Eigenvalues**.In *Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP,* ISBN 978-989-758-488-6, pages 211-218. DOI: 10.5220/0010167902110218

#### in Bibtex Style

@conference{visapp21,

author={Ricard Durall and Avraam Chatzimichailidis and Peter Labus and Janis Keuper},

title={Combating Mode Collapse in GAN Training: An Empirical Analysis using Hessian Eigenvalues},

booktitle={Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP,},

year={2021},

pages={211-218},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010167902110218},

isbn={978-989-758-488-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP,

TI - Combating Mode Collapse in GAN Training: An Empirical Analysis using Hessian Eigenvalues

SN - 978-989-758-488-6

AU - Durall R.

AU - Chatzimichailidis A.

AU - Labus P.

AU - Keuper J.

PY - 2021

SP - 211

EP - 218

DO - 10.5220/0010167902110218