Preliminary: Conditional GANs

$$$$L_GAN == E_((x, c) ~ p_data(x, c)) + E_((z, c) ~ p_g(z, c)),

L_AC == E_((x, c) ~ p_data(x, c)) + _lambda_c * E_((z, c) ~ p_g(z,

c))

Gap of Log-Densities (GOLD)

$$$$log(p_data(x, c) - log(p_g(x, c) == underbrace_marginal(log(p_data(x)

/p_g(x))) + underbrace_conditional(log(p_data(c / x)/p_g(c /

x)))))

Gap of Log-Densities (GOLD)

$$$$d(x, c_x) = if(log(D_G(x)/(1 - D_G(x)) - log(D_C(c_x / x) """(if

x is a real sample of class c_x)"""))): (log(D_G(x)/(1 - D_G(x)

) + log(D_C(c_x / x) """(if x is a generated sample of class

c_x)""")))