A Neural Network from Scratch (Intuition)

The building block

A neuron computes a weighted sum of its inputs, adds a bias, and passes the result through a non-linear activation. Stack neurons into layers and you can approximate complex functions.

import numpy as np
def relu(x): return np.maximum(0, x)
def forward(x, W1, b1, W2, b2):
    h = relu(x @ W1 + b1)
    return h @ W2 + b2

Learning = adjusting weights

Training compares the output to the target (a loss), then uses backpropagation to nudge every weight in the direction that reduces the loss. Repeat over many examples and the network learns. Frameworks automate the calculus — but this is the whole idea.