Section 4a: From the variational bound to a trainable min-max game

Automated excerpt

Move the critic slider $w$: the blue curve shows $J(\theta, w)$ as a hill over $w$. Read aloud: "J of theta and w equals the expected value of $T_w(x)$ under $p_x$ minus the expected value of $f^*(T_w(x))$ under $p_\theta$. " In plain words: $J(\theta, w)$ is one single number measuring how well critic $w$ separates real data from fake data produced by generator $\theta$. For each critic, $$J(\theta, w) = \Big(0. 5\,T(a) + 0. 5\,T(b)\Big) - \Big(0. 8\,e^{T(a)-1} + 0. 2\,e^{T(b)-1}\Big)$$ Read aloud: "$J$ equals the real average of $T$ minus the model average of $e^{T-1}$.

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