He weight initialization

Background

Weight initialization sets the starting scale of a network's parameters. If weights are too large or too small, signals (and gradients) explode or vanish as they pass through layers. He initialization (Kaiming, 2015) is designed for ReLU networks: it draws weights from a zero-mean normal whose variance is $2/n_{\text{in}}$, which keeps the variance of activations roughly constant across layers.

Problem statement

Implement he_init(fan_in, fan_out, seed=42) that returns a weight matrix of shape (fan_in, fan_out) with entries drawn from:

$$W_{ij} \sim \mathcal{N}\!\left(0,\ \frac{2}{n_{\text{in}}}\right)$$

Use np.random.default_rng(seed) and scale standard normal samples by $\sqrt{2/n_{\text{in}}}$.

Input

• fan_in — int, number of input units $n_{\text{in}}$ (rows).
• fan_out — int, number of output units (columns).
• seed — int, RNG seed for reproducibility.

Output

An np.ndarray of shape (fan_in, fan_out), each entry $\sim \mathcal{N}(0, 2/n_{\text{in}})$.

Examples

Example 1

Input:  fan_in = 4, fan_out = 3, seed = 0
Output: array of shape (4, 3); empirical std approximately sqrt(2/4) = 0.707

Explanation: each weight is a standard normal sample multiplied by $\sqrt{2/4}=0.7071$, so the entries have mean $\approx 0$ and standard deviation $\approx 0.707$.

Constraints

• The scaling factor is $\sqrt{2/n_{\text{in}}}$ (the "2" is what distinguishes He from Xavier/Glorot, which uses 1 or $2/(n_{in}+n_{out})$).
• Use np.random.default_rng(seed) so results are reproducible.
• Return a real-valued array of shape (fan_in, fan_out).

Notes

• The factor 2 compensates for ReLU zeroing out half its inputs (halving the variance) — for tanh you would use Xavier's factor of 1 instead.
• Initializing all weights to the same constant breaks symmetry: every neuron in a layer would learn the same thing, so random init is essential.