# Cycle Consistency Loss - For two domains X, Y mapping $G: X \rightarrow Y$, $F: Y \rightarrow X$ - trying to enforce the intuition that these mappings should be reverses of each other and that both mappings should be bijections - Encourages $F(G(x)) \approx x \text{ and } G(F(y)) \approx y$ - reduces the space of possible mapping functions by enforcing forward and backwards consistency - $L_{cyc}(G,F) = \mathbb{E}_{x \sim p_{data}(x)}[||F(G(x))-x)||_{1}] + \mathbb{E}_{x \sim p_{data}(y)}[||G(F(x))-x)||_{1}]$ - $\mathcal{L}_{cyc}(G, F, X, Y) = \frac{1}{m}\Sigma_{i=1}^{m}[(F(G(x_{i})-x_{i})+ (G(F(y_{i}))-y_{i})]$