Simple Neural Network in Python which learns AND gate

neural_network.py

import numpy as np


def sigmoid(x, derivative=False):
  return x*(1-x) if derivative else 1/(1+np.exp(-x))

class NeuralNetwork:
    def __init__(self, x, y):
        self.input      = x
        self.weights1   = np.random.rand(self.input.shape[1],4)
        self.weights2   = np.random.rand(4,1)
        self.y          = y
        self.output     = np.zeros(self.y.shape)

    def feedforward(self):
        self.layer1 = sigmoid(np.dot(self.input, self.weights1))
        self.output = sigmoid(np.dot(self.layer1, self.weights2))

    def backprop(self):
        # application of the chain rule to find derivative of the loss function with respect to weights2 and weights1
        d_weights2 = np.dot(self.layer1.T, (2*(self.y - self.output) * sigmoid(self.output, derivative=True)))
        d_weights1 = np.dot(self.input.T,  (np.dot(2*(self.y - self.output) * sigmoid(self.output, derivative=True), self.weights2.T) * sigmoid(self.layer1, derivative=True)))

        # update the weights with the derivative (slope) of the loss function
        self.weights1 += d_weights1
        self.weights2 += d_weights2

if __name__ == "__main__":
    X = np.array([[0,0],
                  [0,1],
                  [1,0],
                  [1,1]])
    y = np.array([[0],[0],[0],[1]])
    nn = NeuralNetwork(X,y)

    for i in range(1500):
        nn.feedforward()
        nn.backprop()

    print(nn.output)