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.

翻译：通过将CycleGAN模型扩展至三个不同类别间的图像转换，本文展示了利用循环变换进行连续图像生成的方法。经训练生成器的反复应用可产生在不同类别间转换的图像序列。与原始训练数据集相比，生成的图像序列占据图像空间中更为有限的区域。使用精确率与召回率指标的定量评估表明，生成图像虽具有较高品质，但其多样性相对于训练数据集有所降低。此类连续生成过程在动力系统理论框架下可表征为混沌动力学。根据生成轨迹估算的正李雅普诺夫指数证实了混沌动力学的存在，且吸引子的李雅普诺夫维度与训练数据流形的本征维度相当。研究结果表明，由深度生成模型定义的图像空间中的混沌动力学有助于提升生成图像的多样性，这为多类别图像生成提供了一种新方法。该模型可解释为经典联想记忆的扩展，能够执行图像类别间的异质关联。