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import numpy as np

# Sigmoid activation function
def sigmoid(x):
    return 1 / (1 + np.exp(-x))

# Derivative of sigmoid function
def sigmoid_derivative(x):
    return x * (1 - x)

# Parameters
alpha = 0.25  # Learning rate
input_pattern = np.array([0, 1])  # Input pattern
target_output = 1  # Target output
initial_weights = np.array([0.5, -0.3])  # Initial weights for simplicity

# Step 1: Feedforward pass
net_input = np.dot(initial_weights, input_pattern)  # net = w_1 * 0 + w_2 * 1 = w_2
output = sigmoid(net_input)  # Output of the neuron

# Step 2: Calculate error
error = target_output - output

# Step 3: Backpropagate error and update weights
delta = error * sigmoid_derivative(output)  # Gradient for weight update
weight_update = alpha * delta * input_pattern  # Compute weight changes

# Step 4: Update weights
new_weights = initial_weights + weight_update

# Output results
print(f"Initial Output: {output}")
print(f"Error: {error}")
print(f"Updated Weights: {new_weights}")