The Lab.

1import numpy as np
2
3class Neuron:
4    """A single neuron, vectorized. No frameworks."""
5
6    def __init__(self, n_inputs: int) -> None:
7        # Xavier initialization
8        self.w = np.random.randn(n_inputs) * np.sqrt(2.0 / n_inputs)
9        self.b = np.zeros(1)
10
11    def forward(self, X: np.ndarray) -> np.ndarray:
12        z = X @ self.w + self.b
13        self.a = 1.0 / (1.0 + np.exp(-z))
14        return self.a
15
16    def backward(self, X: np.ndarray, dL_da: np.ndarray, lr: float):
17        da_dz = self.a * (1.0 - self.a)
18        delta = dL_da * da_dz
19        self.w -= lr * (X.T @ delta) / X.shape[0]
20        self.b -= lr * np.mean(delta)
21        return np.outer(delta, self.w)