The previous part borrowed σ_z = √n · σ_W · σ_x and moved on. This one derives it from the definition of expectation: three rules of arithmetic, why the cross term vanishes, why it is variance and not standard deviation that adds — and why diagnosing a network means watching the variance rather than the mean or the maximum.
One-hot makes a as related to e as it is to q; structure only appears once 27 dimensions are squeezed into 2. The table grows 729 → 531,441 while the first layer shrinks 8,100 parameters → 600 — and a dot product is not a cosine.
Cat-versus-dog and predicting the next character are the same problem, differing only in that the class count goes from 2 to 27. The three parts that difference requires: one-hot, softmax, cross-entropy — and why cross-entropy is not a fancier squared error.
Wrapping Value into Neuron / Layer / MLP. Where the parameter count comes from, how sz's sliding window lines the dimensions up, and why a three-line loop is the entire forward pass.
Starting from handwritten digit recognition: what neurons, layers, weights, biases and activation functions each are, and why the whole network is only a function.