Lecture 9
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@ -4,4 +4,4 @@ Lectures 1-2 use same handout.
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Lectures 3-6 use same handout.
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Lectures 7-12 use same handout.
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Lectures 7-11 use same handout.
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@ -1306,317 +1306,18 @@
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},
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{
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"cell_type": "code",
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"execution_count": 43,
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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||||
"ename": "NameError",
|
||||
"evalue": "name 'vertical_data' is not defined",
|
||||
"output_type": "error",
|
||||
"traceback": [
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m/tmp/ipykernel_169632/3189844108.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Create dataset\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvertical_data\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msamples\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclasses\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0;31m# Create model\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mdense1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mLayer_Dense\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# first dense layer, 2 inputs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mactivation1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mActivation_ReLU\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;31mNameError\u001b[0m: name 'vertical_data' is not defined"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
||||
File diff suppressed because one or more lines are too long
Binary file not shown.
@ -4,9 +4,10 @@
|
||||
|
||||
# %%
|
||||
# imports
|
||||
import matplotlib.pyplot as plt
|
||||
import numpy as np
|
||||
import nnfs
|
||||
from nnfs.datasets import spiral_data
|
||||
from nnfs.datasets import spiral_data, vertical_data
|
||||
nnfs.init()
|
||||
|
||||
# %%
|
||||
@ -192,4 +193,188 @@ if len(class_targets.shape) == 2:
|
||||
accuracy = np.mean(predictions == class_targets)
|
||||
print(f"Accuracy: {accuracy}")
|
||||
|
||||
# %% [markdown]
|
||||
# # The Need for Optimization
|
||||
|
||||
# %%
|
||||
#SIMPLER DATASET
|
||||
nnfs.init()
|
||||
X, y = vertical_data(samples=100, classes=3)
|
||||
plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap='brg')
|
||||
plt.show()
|
||||
|
||||
# %% [markdown]
|
||||
# # Test Strategy 1: Randomly Select Weights and Biases
|
||||
# For a large number of tests, randomly set weights and biases and look at accuracy.
|
||||
|
||||
# %%
|
||||
# Create dataset
|
||||
X, y = vertical_data(samples=100, classes=3)
|
||||
|
||||
# Create model
|
||||
dense1 = Layer_Dense(2, 3) # first dense layer, 2 inputs
|
||||
activation1 = Activation_ReLU()
|
||||
dense2 = Layer_Dense(3, 3) # second dense layer, 3 inputs, 3 outputs
|
||||
activation2 = Activation_Softmax()
|
||||
|
||||
# Create loss function
|
||||
loss_function = Loss_CategoricalCrossEntropy()
|
||||
|
||||
# Helper variables
|
||||
lowest_loss = 9999999 # some initial value
|
||||
best_dense1_weights = dense1.weights.copy()
|
||||
best_dense1_biases = dense1.biases.copy()
|
||||
best_dense2_weights = dense2.weights.copy()
|
||||
best_dense2_biases = dense2.biases.copy()
|
||||
|
||||
for iteration in range(10000):
|
||||
# Generate a new set of weights for iteration
|
||||
dense1.weights = 0.05 * np.random.randn(2, 3)
|
||||
dense1.biases = 0.05 * np.random.randn(1, 3)
|
||||
dense2.weights = 0.05 * np.random.randn(3, 3)
|
||||
dense2.biases = 0.05 * np.random.randn(1, 3)
|
||||
|
||||
# Perform a forward pass of the training data through this layer
|
||||
dense1.forward(X)
|
||||
activation1.forward(dense1.output)
|
||||
dense2.forward(activation1.output)
|
||||
activation2.forward(dense2.output)
|
||||
|
||||
# Perform a forward pass through activation function
|
||||
# it takes the output of second dense layer here and returns loss
|
||||
loss = loss_function.calculate(activation2.output, y)
|
||||
|
||||
# Calculate accuracy from output of activation2 and targets
|
||||
# calculate values along first axis
|
||||
predictions = np.argmax(activation2.output, axis=1)
|
||||
accuracy = np.mean(predictions == y)
|
||||
|
||||
# If loss is smaller - print and save weights and biases aside
|
||||
if loss < lowest_loss:
|
||||
print('New set of weights found, iteration:', iteration,'loss:', loss, 'acc:', accuracy)
|
||||
best_dense1_weights = dense1.weights.copy()
|
||||
best_dense1_biases = dense1.biases.copy()
|
||||
best_dense2_weights = dense2.weights.copy()
|
||||
best_dense2_biases = dense2.biases.copy()
|
||||
lowest_loss = loss
|
||||
|
||||
# %% [markdown]
|
||||
# # Test Strategy 2: Randomly Adjust Weights and Biases
|
||||
# For a large number of tests with a starting weight and bias, update the weights and biases by some small, random value. If the new accuracy is higher, keep the weights and biases. If the new accuracy is lower, revert back to the last weights and biases.
|
||||
|
||||
# %%
|
||||
# Create dataset
|
||||
X, y = vertical_data(samples=100, classes=3)
|
||||
|
||||
# Create model
|
||||
dense1 = Layer_Dense(2, 3) # first dense layer, 2 inputs
|
||||
activation1 = Activation_ReLU()
|
||||
dense2 = Layer_Dense(3, 3) # second dense layer, 3 inputs, 3 outputs
|
||||
activation2 = Activation_Softmax()
|
||||
|
||||
# Create loss function
|
||||
loss_function = Loss_CategoricalCrossEntropy()
|
||||
|
||||
# Helper variables
|
||||
lowest_loss = 9999999 # some initial value
|
||||
best_dense1_weights = dense1.weights.copy()
|
||||
best_dense1_biases = dense1.biases.copy()
|
||||
best_dense2_weights = dense2.weights.copy()
|
||||
best_dense2_biases = dense2.biases.copy()
|
||||
for iteration in range(10000):
|
||||
# Update weights with some small random values
|
||||
dense1.weights += 0.05 * np.random.randn(2, 3)
|
||||
dense1.biases += 0.05 * np.random.randn(1, 3)
|
||||
dense2.weights += 0.05 * np.random.randn(3, 3)
|
||||
dense2.biases += 0.05 * np.random.randn(1, 3)
|
||||
|
||||
# Perform a forward pass of our training data through this layer
|
||||
dense1.forward(X)
|
||||
activation1.forward(dense1.output)
|
||||
dense2.forward(activation1.output)
|
||||
activation2.forward(dense2.output)
|
||||
|
||||
# Perform a forward pass through activation function
|
||||
# it takes the output of second dense layer here and returns loss
|
||||
loss = loss_function.calculate(activation2.output, y)
|
||||
|
||||
# Calculate accuracy from output of activation2 and targets
|
||||
# calculate values along first axis
|
||||
predictions = np.argmax(activation2.output, axis=1)
|
||||
accuracy = np.mean(predictions == y)
|
||||
|
||||
# If loss is smaller - print and save weights and biases aside
|
||||
if loss < lowest_loss:
|
||||
print('New set of weights found, iteration:', iteration,'loss:', loss, 'acc:', accuracy)
|
||||
best_dense1_weights = dense1.weights.copy()
|
||||
best_dense1_biases = dense1.biases.copy()
|
||||
best_dense2_weights = dense2.weights.copy()
|
||||
best_dense2_biases = dense2.biases.copy()
|
||||
lowest_loss = loss
|
||||
# Revert weights and biases
|
||||
else:
|
||||
dense1.weights = best_dense1_weights.copy()
|
||||
dense1.biases = best_dense1_biases.copy()
|
||||
dense2.weights = best_dense2_weights.copy()
|
||||
dense2.biases = best_dense2_biases.copy()
|
||||
|
||||
# %% [markdown]
|
||||
# # Test Strategy 2 on Spiral Dataset
|
||||
|
||||
# %%
|
||||
# Create dataset
|
||||
X, y = spiral_data(samples=100, classes=3)
|
||||
|
||||
# Create model
|
||||
dense1 = Layer_Dense(2, 3) # first dense layer, 2 inputs
|
||||
activation1 = Activation_ReLU()
|
||||
dense2 = Layer_Dense(3, 3) # second dense layer, 3 inputs, 3 outputs
|
||||
activation2 = Activation_Softmax()
|
||||
|
||||
# Create loss function
|
||||
loss_function = Loss_CategoricalCrossEntropy()
|
||||
|
||||
# Helper variables
|
||||
lowest_loss = 9999999 # some initial value
|
||||
best_dense1_weights = dense1.weights.copy()
|
||||
best_dense1_biases = dense1.biases.copy()
|
||||
best_dense2_weights = dense2.weights.copy()
|
||||
best_dense2_biases = dense2.biases.copy()
|
||||
for iteration in range(10000):
|
||||
# Update weights with some small random values
|
||||
dense1.weights += 0.05 * np.random.randn(2, 3)
|
||||
dense1.biases += 0.05 * np.random.randn(1, 3)
|
||||
dense2.weights += 0.05 * np.random.randn(3, 3)
|
||||
dense2.biases += 0.05 * np.random.randn(1, 3)
|
||||
|
||||
# Perform a forward pass of our training data through this layer
|
||||
dense1.forward(X)
|
||||
activation1.forward(dense1.output)
|
||||
dense2.forward(activation1.output)
|
||||
activation2.forward(dense2.output)
|
||||
|
||||
# Perform a forward pass through activation function
|
||||
# it takes the output of second dense layer here and returns loss
|
||||
loss = loss_function.calculate(activation2.output, y)
|
||||
|
||||
# Calculate accuracy from output of activation2 and targets
|
||||
# calculate values along first axis
|
||||
predictions = np.argmax(activation2.output, axis=1)
|
||||
accuracy = np.mean(predictions == y)
|
||||
|
||||
# If loss is smaller - print and save weights and biases aside
|
||||
if loss < lowest_loss:
|
||||
print('New set of weights found, iteration:', iteration,'loss:', loss, 'acc:', accuracy)
|
||||
best_dense1_weights = dense1.weights.copy()
|
||||
best_dense1_biases = dense1.biases.copy()
|
||||
best_dense2_weights = dense2.weights.copy()
|
||||
best_dense2_biases = dense2.biases.copy()
|
||||
lowest_loss = loss
|
||||
# Revert weights and biases
|
||||
else:
|
||||
dense1.weights = best_dense1_weights.copy()
|
||||
dense1.biases = best_dense1_biases.copy()
|
||||
dense2.weights = best_dense2_weights.copy()
|
||||
dense2.biases = best_dense2_biases.copy()
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user