Cyclic image generation using chaotic dynamics

TL;DR

This paper extends the CycleGAN model to cyclically generate images among three categories, revealing that the process exhibits chaotic dynamics which influence the diversity and quality of generated images.

Contribution

It introduces a novel cyclic image generation method using chaotic dynamics, extending CycleGAN to multiple categories with analysis of the underlying chaotic behavior.

Findings

Generated images have high quality but reduced diversity.

The image sequences exhibit positive Lyapunov exponents indicating chaos.

The attractor's Lyapunov dimension aligns with the data manifold's intrinsic dimension.

Abstract

Successive image generation using cyclic transformations is demonstrated by extending the CycleGAN model to transform images among three different categories. Repeated application of the trained generators produces sequences of images that transition among the different categories. The generated image sequences occupy a more limited region of the image space compared with the original training dataset. Quantitative evaluation using precision and recall metrics indicates that the generated images have high quality but reduced diversity relative to the training dataset. Such successive generation processes are characterized as chaotic dynamics in terms of dynamical system theory. Positive Lyapunov exponents estimated from the generated trajectories confirm the presence of chaotic dynamics, with the Lyapunov dimension of the attractor found to be comparable to the intrinsic dimension of the training data manifold. The results suggest that chaotic dynamics in the image space defined by the deep generative model contribute to the diversity of the generated images, constituting a novel approach for multi-class image generation. This model can be interpreted as an extension of classical associative memory to perform hetero-association among image categories.