Please, write an addition to the following python code that will generate a 2d weight space contour plot: import matplotlib.pyplot as plt import numpy as np from sklearn.model_selection import train_test_split def sigmoid(sop): return 1.0/(1 + np.exp(-sop)) def error(predicted, target): return np.mean(np.power(predicted - target, 2)) def error_predicted_deriv(predicted, target): return 2 * (predicted - target) def activation_sop_deriv(sop): return sigmoid(sop) * (1.0 - sigmoid(sop)) def update_weights(weights, grads, learning_rate): return weights - learning_rate * grads # Generate data mean = np.array([-0.4, -0.8]) mean1 = np.array([0.4, 0.8]) cov = np.array([[0.84, 0], [0, 0.036]]) x1 = np.random.multivariate_normal(mean, cov, 50) x2 = np.random.multivariate_normal(mean1, cov, 50) data = np.concatenate((x1, x2)) # Generate desired output d = np.concatenate((np.zeros(50), np.ones(50))) # Split data into train and test sets X_train, X_test, d_train, d_test = train_test_split( data, d, test_size=0.2, random_state=0 ) # Assign labels to the data points labels = np.zeros(100) labels[:50] = -1 # class 1 labels[50:] = 1 # class 2 plt.scatter(data[labels==-1, 0], data[labels==-1, 1], c='r', label='Class 1') plt.scatter(data[labels==1, 0], data[labels==1, 1], c='b', label='Class 2') plt.legend() plt.show() # Initialize weights weights = np.random.rand(2) # Train the network max_iterations = 10 learning_rate = 1.5 MSE = [] train_pred = [] test_pred = [] for iteration in range(max_iterations): # Forward Pass sop = np.dot(X_train, weights) predicted = sigmoid(sop) err = error(predicted, d_train) # Backward Pass grad_predicted = error_predicted_deriv(predicted, d_train) grad_sop = activation_sop_deriv(sop) grad_weights = np.dot(X_train.T, grad_predicted * grad_sop) # Update weights weights = update_weights(weights, grad_weights, learning_rate) print("Updated weights:", weights) err = error(predicted, d_train) MSE.append(np.mean(err)) if iteration % 100 == 0: print(f"Iteration {iteration}: Error = {err}") log_MSE = np.log10(MSE) print("Final weights:", weights) plt.plot(range(10), log_MSE, label='Log MSE (dB)') plt.xlabel('Iteration') plt.ylabel('Log MSE (dB)') plt.legend() plt.show() .

1. Please, write an addition to the following python code that will generate a 2d weight space
contour plot:
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
def sigmoid(sop):
return 1.0/(1 + np.exp(-sop))
def error(predicted, target):
return np.mean(np.power(predicted - target, 2))
def error_predicted_deriv(predicted, target):
return 2 * (predicted - target)
def activation_sop_deriv(sop):
return sigmoid(sop) * (1.0 - sigmoid(sop))
def update_weights(weights, grads, learning_rate):
return weights - learning_rate * grads
# Generate data
mean = np.array([-0.4, -0.8])
mean1 = np.array([0.4, 0.8])
cov = np.array([[0.84, 0], [0, 0.036]])
x1 = np.random.multivariate_normal(mean, cov, 50)
x2 = np.random.multivariate_normal(mean1, cov, 50)
data = np.concatenate((x1, x2))
# Generate desired output
d = np.concatenate((np.zeros(50), np.ones(50)))

2. # Split data into train and test sets
X_train, X_test, d_train, d_test = train_test_split(
data, d, test_size=0.2, random_state=0
)
# Assign labels to the data points
labels = np.zeros(100)
labels[:50] = -1 # class 1
labels[50:] = 1 # class 2
plt.scatter(data[labels==-1, 0], data[labels==-1, 1], c='r', label='Class 1')
plt.scatter(data[labels==1, 0], data[labels==1, 1], c='b', label='Class 2')
plt.legend()
plt.show()
# Initialize weights
weights = np.random.rand(2)
# Train the network
max_iterations = 10
learning_rate = 1.5
MSE = []
train_pred = []
test_pred = []
for iteration in range(max_iterations):
# Forward Pass
sop = np.dot(X_train, weights)

3. predicted = sigmoid(sop)
err = error(predicted, d_train)
# Backward Pass
grad_predicted = error_predicted_deriv(predicted, d_train)
grad_sop = activation_sop_deriv(sop)
grad_weights = np.dot(X_train.T, grad_predicted * grad_sop)
# Update weights
weights = update_weights(weights, grad_weights, learning_rate)
print("Updated weights:", weights)
err = error(predicted, d_train)
MSE.append(np.mean(err))
if iteration % 100 == 0:
print(f"Iteration {iteration}: Error = {err}")
log_MSE = np.log10(MSE)
print("Final weights:", weights)
plt.plot(range(10), log_MSE, label='Log MSE (dB)')
plt.xlabel('Iteration')
plt.ylabel('Log MSE (dB)')
plt.legend()
plt.show()