GAN Losses

Compute the discriminator loss and the generator loss of a standard GAN.

A GAN trains two networks against each other. The discriminator D outputs the probability that an input is real. It wants D(real) near 1 and D(fake) near 0, so its loss is binary cross entropy on both batches:

d_loss = -mean(log D(real)) - mean(log(1 - D(fake)))

The generator wants its fakes to be called real. Minimising log(1 - D(fake)) gives almost no gradient early in training, when the discriminator easily rejects every fake. So in practice the generator uses the non-saturating loss:

g_loss = -mean(log D(fake))

You are given the discriminator outputs d_real and d_fake as probabilities. Return (d_loss, g_loss).

Function signature

def gan_losses(d_real, d_fake):

Example

Input

gan_losses(np.array([0.9]), np.array([0.1]))

Output

(0.21072103, 2.30258509)

Reasoning

The discriminator is doing well: -ln 0.9 - ln(1 - 0.1) = 0.1054 + 0.1054. The generator is doing badly: its fake got 0.1, so its loss is -ln 0.1 = 2.303. That large loss still gives a strong gradient, which is why the non-saturating form is used.

Constraints and notes

• d_real and d_fake are 1D arrays of probabilities and can have different lengths.
• Clip both into [1e-7, 1 - 1e-7] before taking logs.
• Return two plain floats.