Cycle Consistency Loss

• For two domains X, Y mapping $G:X\to Y$, $F:Y\to X$
• 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
• $L_{cyc}(G,F)={\mathbb{E}}_{x\sim p_{data}(x)}[||F(G(x))-x)|{|}_1]+{\mathbb{E}}_{x\sim p_{data}(y)}[||G(F(x))-x)|{|}_1]$
• ${\mathcal{L}}_{cyc}(G,F,X,Y)=\frac{1}{m}{\Sigma }_{i=1}^m[(F(G(x_i)-x_i)+(G(F(y_i))-y_i)]$