Cyclic image generation using chaotic dynamics

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.