Xavier and He Weight Initialisation

Initialise weights too large and activations explode. Too small and they vanish. The fix is to scale the random weights by the layer's size:

• Xavier/Glorot (for tanh/sigmoid): normal with std $\sqrt{\dfrac{2}{\text{fan\_in} + \text{fan\_out}}}$
• He/Kaiming (for ReLU): normal with std $\sqrt{\dfrac{2}{\text{fan\_in}}}$

Implement init_weights(fan_in, fan_out, method, rng), returning a (fan_in, fan_out) array drawn with rng.normal(0, std, size=...), where method is "xavier" or "he". Raise ValueError for anything else.

Then implement activation_std_after(n_layers, width, method, activation, seed=0): push a batch of 256 standard-normal inputs through n_layers dense layers (no biases) initialised with init_weights (one np.random.default_rng(seed) for both inputs and weights), applying "relu" or "tanh" after each layer. Return the final activations' standard deviation.