Simple GAN Generator

Implement the generator part of a simple GAN (Generative Adversarial Network).

The generator maps noise z to a fake sample through two layers:

1. Hidden: $h = \text{ReLU}(z \cdot W_1 + b_1)$
2. Output: $\text{fake} = \tanh(h \cdot W_2 + b_2)$

The tanh output ensures generated values are in [-1, 1].

Also compute the generator loss. Given a discriminator that outputs a score for the fake sample, the generator loss (non-saturating) is:

$$L_G = -\log(\sigma(D(\text{fake})))$$

where $\sigma$ is sigmoid and $D(\text{fake})$ is given as input.

Input:

• z: noise vector shape (batch, noise_dim)
• W1: shape (noise_dim, hidden_dim), b1: shape (hidden_dim,)
• W2: shape (hidden_dim, output_dim), b2: shape (output_dim,)
• disc_score: discriminator output for fake, shape (batch, 1)

Output: A dict with “fake” (shape (batch, output_dim)) and “loss” (scalar).