XOR demonstration
Description for XOR demonstration notebook.
Notebook Contents
This notebook covers:
- Topic 1
- Topic 2
- Topic 3
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In [2]:
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
# XOR dataset
X = np.array([[0, 0], [0, 1], [1, 0], [1, 1]], dtype=np.float32)
y = np.array([[0], [1], [1], [0]], dtype=np.float32)
print("XOR Truth Table:")
print("Input\t\tOutput")
for i in range(len(X)):
print(f"{X[i]}\t{y[i][0]}")
print()
# Build the neural network model
model = tf.keras.Sequential([
tf.keras.layers.Dense(4, activation='relu', input_shape=(2,), name='hidden_layer'),
tf.keras.layers.Dense(1, activation='sigmoid', name='output_layer')
])
# Compile the model
model.compile(
optimizer=tf.keras.optimizers.Adam(learning_rate=0.1),
loss='binary_crossentropy',
metrics=['accuracy']
)
# Display model architecture
print("Model Architecture:")
model.summary()
print()
# Train the model
print("Training the network...")
history = model.fit(
X, y,
epochs=500,
verbose=0,
batch_size=4
)
# Print training progress
print(f"Final Loss: {history.history['loss'][-1]:.4f}")
print(f"Final Accuracy: {history.history['accuracy'][-1]:.4f}")
print()
# Make predictions
predictions = model.predict(X, verbose=0)
print("Results after training:")
print("Input\t\tExpected\tPredicted\tRounded")
for i in range(len(X)):
print(f"{X[i]}\t{y[i][0]}\t\t{predictions[i][0]:.4f}\t\t{round(predictions[i][0])}")
print()
# Visualize decision boundary
def plot_decision_boundary(model, X, y):
# Create a mesh grid
x_min, x_max = -0.5, 1.5
y_min, y_max = -0.5, 1.5
h = 0.01
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
# Predict for each point in the mesh
grid_points = np.c_[xx.ravel(), yy.ravel()]
Z = model.predict(grid_points, verbose=0)
Z = Z.reshape(xx.shape)
# Plot
plt.figure(figsize=(10, 8))
plt.contourf(xx, yy, Z, levels=20, cmap='RdBu', alpha=0.8)
plt.colorbar(label='Prediction')
# Plot the XOR points
colors = ['red' if label == 0 else 'blue' for label in y]
plt.scatter(X[:, 0], X[:, 1], c=colors, s=200, edgecolors='black', linewidths=2)
# Add labels to points
for i in range(len(X)):
plt.annotate(f'{int(y[i][0])}',
(X[i, 0], X[i, 1]),
fontsize=14,
ha='center',
va='center',
color='white',
weight='bold')
plt.xlabel('Input A', fontsize=12)
plt.ylabel('Input B', fontsize=12)
plt.title('XOR Problem - Decision Boundary', fontsize=14, weight='bold')
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig('xor_decision_boundary.png', dpi=150)
print("Decision boundary plot saved as 'xor_decision_boundary.png'")
# Plot training history
def plot_training_history(history):
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.plot(history.history['loss'])
plt.title('Model Loss Over Time')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.grid(True, alpha=0.3)
plt.subplot(1, 2, 2)
plt.plot(history.history['accuracy'])
plt.title('Model Accuracy Over Time')
plt.xlabel('Epoch')
plt.ylabel('Accuracy')
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig('xor_training_history.png', dpi=150)
print("Training history plot saved as 'xor_training_history.png'")
# Generate visualizations
plot_decision_boundary(model, X, y)
plot_training_history(history)
print("\nVisualization complete!")
# Optional: Show weights learned by the network
print("\nLearned Weights:")
for layer in model.layers:
weights = layer.get_weights()
print(f"\n{layer.name}:")
print(f" Weights shape: {weights[0].shape}")
print(f" Biases shape: {weights[1].shape}")
