import random

import math

​

def relu(x):

    return x if x > 0 else 0.0

​

def relu_grad(x):

    return 1.0 if x > 0 else 0.0

​

def train_single_neuron(epochs=2000, lr=0.01, seed=42):

    random.seed(seed)

    # Generate simple 1D data: y = 2x + 1 + noise

    xs = [random.uniform(-2.0, 2.0) for _ in range(200)]

    ys = [2.0 * x + 1.0 + random.gauss(0, 0.1) for x in xs]

​

    # Parameters of a 1D neuron: w and b

    w = random.uniform(-1.0, 1.0)

    b = 0.0

​

    for epoch in range(epochs):

        dw = 0.0

        db = 0.0

        loss = 0.0

        for x, y in zip(xs, ys):

            z = w * x + b

            a = relu(z)

            # Mean squared error (per sample)

            diff = a - y

            loss += 0.5 * diff * diff