Neural Network Is Taking 1000 Epochs Just To Solve XOR - neural-network

Question

My Neural Network takes 1000 epochs just to solve XOR and when I increase number of neurons loss increases and it doesnt work.
Also before when I was using np.random.rand it did'nt work with a learning rate less than 1.
import numpy as np
input = np.array([[0, 1] ,[1, 0], [1, 1], [0, 0]])
labels = np.array([[1], [1], [0], [0]])
np.random.seed(0)
class NN:
def __init__(self):
self.layers = []
def add(self, layer):
self.layers.append(layer)
def loss(self, layer):
self.loss = layer
def predict(self, input):
output = input
for layer in self.layers:
output = layer.forward(output)
return output
def train(self, input, labels):
prediction = self.predict(input)
loss = self.loss.forward(prediction, labels)
gradient = self.loss.back() * 0.1
for layer in self.layers[::-1]:
gradient = layer.back(gradient)
return loss
Dense Layer
class Dense:
def __init__(self, input_size, output_size):
self.weights = np.random.randn(input_size, output_size) - 0.5
self.bias = np.random.randn(1, output_size) - 0.5
def forward(self, input):
self.input = input
output = np.dot(input, self.weights) + self.bias
return output
def back(self, gradient):
gradientW = np.dot(self.input.T, gradient)
self.weights -= gradientW
self.bias -= np.mean(gradient)
return np.dot(gradient, self.weights.T)
Sigmoid
class Sigmoid:
def forward(self, input):
output = 1 / (1+np.exp(-input))
self.output = output
return output
def back(self, gradient):
output = self.output * (1 - self.output)
gradient *= output
return gradient
I am using Mean Squaresd Error
class MSE:
def forward(self, input, labels):
self.input = input
self.labels = labels
return np.mean((labels - input)**2)
def back(self):
output = 2 * (self.input - self.labels)
return output
Calling the Class
N = NN()
N.add(Dense(2, 10))
N.add(Sigmoid())
N.add(Dense(10, 1))
N.add(Sigmoid())
N.loss(MSE())
Training
for i in range(1000):
loss = (N.train(input, labels))
if i%99==0:
print(loss)
print(N.predict(input))
Edit: I Tried this and now it works with 100 epochs. I needed an additional layer to increase neurons why? I tried to train it on AND but it doesnt work.
N = NN()
N.add(Dense(2, 50))
N.add(Sigmoid())
N.add(Dense(50, 1000))
N.add(Sigmoid())
N.add(Dense(1000, 50))
N.add(Sigmoid())
N.add(Dense(50, 1))
N.add(Sigmoid())
N.loss(MSE())