NoisyLinear

Reference: Fortunato et al., "Noisy Networks for Exploration", ICLR, 2018 (arXiv:1706.10295).

$$y = (\mu^w + \sigma^w \odot \varepsilon^w)\,x + (\mu^b + \sigma^b \odot \varepsilon^b)$$

with factorised noise, so the layer draws in_features + out_features random numbers rather than their product.

Initialised as the paper's factorised case specifies: "each element $\mu_{i,j}$ was initialised by a sample from an independent uniform distribution $U[-1/\sqrt{p}, +1/\sqrt{p}]$ and each element $\sigma_{i,j}$ was initialised to a constant $\sigma_0/\sqrt{p}$", with $p$ the input width.

The noise is a buffer, not a per-call draw. Redrawing inside forward would make two calls on the same input two different networks, which breaks both the Monte-Carlo gradient the paper derives — one sample per optimisation step, its equation 13 — and any agent that needs a fixed policy for an episode. Call resample when a new sample is wanted. In eval() the noise is not used at all, so a deterministic policy is just the mean network.