Cycle Consistency Loss is a type of loss used for generative adversarial networks that performs unpaired image-to-image translation. It was introduced with the CycleGAN architecture. For two domains $X$ and $Y$, we want to learn a mapping $G : X \rightarrow Y$ and $F: Y \rightarrow X$. We want to enforce the intuition that these mappings should be reverses of each other and that both mappings should be bijections. Cycle Consistency Loss encourages $F\left(G\left(x\right)\right) \approx x$ and $G\left(F\left(y\right)\right) \approx y$. It reduces the space of possible mapping functions by enforcing forward and backwards consistency: $$ \mathcal{L}\_{cyc}\left(G, F\right) = \mathbb{E}\_{x \sim p\_{data}\left(x\right)}\left[||F\left(G\left(x\right)\right) - x||\_{1}\right] + \mathbb{E}\_{y \sim p\_{data}\left(y\right)}\left[||G\left(F\left(y\right)\right) - y||\_{1}\right] $$
Hierarchical Style Disentanglement, or HiSD, aims to disentangle different styles in image-to-image translation models. It organizes the labels into a hierarchical structure, where independent tags, exclusive attributes, and disentangled styles are allocated from top to bottom. To make the styles identified to the tags and attributes, the authors carefully redesign the modules, phases, and objectives.