Complete and hand in this completed worksheet (including its outputs and any supporting code outside of the worksheet) with your assignment submission. For more details see the assignments page on the course website.
This exercise is analogous to the SVM exercise. You will:
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from __future__ import absolute_import, division, print_function
import random
import numpy as np
from cs231n.data_utils import load_CIFAR10
import matplotlib.pyplot as plt
import seaborn
%matplotlib inline
# set default size of plots
plt.rcParams['figure.figsize'] = (10.0, 8.0)
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
# for auto-reloading extenrnal modules
# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython
%load_ext autoreload
%autoreload 2
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def get_CIFAR10_data(num_training=49000, num_validation=1000,
num_test=1000, num_dev=500):
"""
Load the CIFAR-10 dataset from disk and perform preprocessing
to prepare it for the linear classifier. These are the same
steps as we used for the SVM, but condensed to a single function.
"""
# Load the raw CIFAR-10 data
cifar10_dir = '../data/cifar10'
X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)
# subsample the data
mask = range(num_training, num_training + num_validation)
X_val = X_train[mask]
y_val = y_train[mask]
mask = range(num_training)
X_train = X_train[mask]
y_train = y_train[mask]
mask = range(num_test)
X_test = X_test[mask]
y_test = y_test[mask]
mask = np.random.choice(num_training, num_dev, replace=False)
X_dev = X_train[mask]
y_dev = y_train[mask]
# Preprocessing: reshape the image data into rows
X_train = np.reshape(X_train, (X_train.shape[0], -1))
X_val = np.reshape(X_val, (X_val.shape[0], -1))
X_test = np.reshape(X_test, (X_test.shape[0], -1))
X_dev = np.reshape(X_dev, (X_dev.shape[0], -1))
# Normalize the data: subtract the mean image
mean_image = np.mean(X_train, axis = 0)
X_train -= mean_image
X_val -= mean_image
X_test -= mean_image
X_dev -= mean_image
# add bias dimension and transform into columns
X_train = np.hstack([X_train, np.ones((X_train.shape[0], 1))])
X_val = np.hstack([X_val, np.ones((X_val.shape[0], 1))])
X_test = np.hstack([X_test, np.ones((X_test.shape[0], 1))])
X_dev = np.hstack([X_dev, np.ones((X_dev.shape[0], 1))])
return (X_train, y_train, X_val, y_val, X_test,
y_test, X_dev, y_dev)
# Invoke the above function to get our data.
(X_train, y_train, X_val, y_val, X_test, y_test, X_dev, y_dev) = \
get_CIFAR10_data()
print('Train data shape:', X_train.shape)
print('Train labels shape:', y_train.shape)
print('Validation data shape:', X_val.shape)
print('Validation labels shape:', y_val.shape)
print('Test data shape:', X_test.shape)
print('Test labels shape:', y_test.shape)
print('dev data shape:', X_dev.shape)
print('dev labels shape:', y_dev.shape)
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# First implement the naive softmax loss function with nested loops.
# Open the file cs231n/classifiers/softmax.py and implement the
# softmax_loss_naive function.
from cs231n.classifiers.softmax import softmax_loss_naive
from cs231n.classifiers.softmax import softmax_loss_vectorized
import time
# Generate a random softmax weight matrix and use it to
# compute the loss.
W = np.random.randn(3073, 10) * 0.0001
loss, grad = softmax_loss_naive(W, X_dev, y_dev, 0.0)
# As a rough sanity check, our loss should be something
# close to -log(0.1).
print('loss: {:f}'.format(loss))
print('sanity check: {:f}'.format(-np.log(0.1)))
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# Complete the implementation of softmax_loss_naive and implement a
# (naive) version of the gradient that uses nested loops.
from cs231n.gradient_check import grad_check_sparse
softmax_loss = softmax_loss_naive # djn
# As we did for the SVM, use numeric gradient checking as a
# debugging tool. The numeric gradient should be close to the
# analytic gradient.
print('Gradient check WITHOUT regularization')
print('=====================================')
loss, grad = softmax_loss(W, X_dev, y_dev, 0.0)
f = lambda w: softmax_loss(w, X_dev, y_dev, 0.0)[0]
grad_numerical = grad_check_sparse(f, W, grad, 10)
print('')
# similar to SVM case, do another gradient check with regularization
print('Gradient check WITH regularization')
print('==================================')
loss, grad = softmax_loss(W, X_dev, y_dev, 1e2)
f = lambda w: softmax_loss(w, X_dev, y_dev, 1e2)[0]
grad_numerical = grad_check_sparse(f, W, grad, 10)
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# Now that we have a naive implementation of the softmax loss
# function and its gradient, implement a vectorized version in
# softmax_loss_vectorized. The two versions should compute the
# same results, but the vectorized version should be much faster.
tic = time.time()
loss_naive, grad_naive = softmax_loss_naive(W, X_dev, y_dev, 0.00001)
toc = time.time()
print('naive loss: {:e} computed in {:f}s'.format(
loss_naive, toc - tic))
tic = time.time()
loss_vectorized, grad_vectorized = softmax_loss_vectorized(
W, X_dev, y_dev, 0.00001)
toc = time.time()
print('vectorized loss: {:e} computed in {:f}s'.format(
loss_vectorized, toc - tic))
# As we did for the SVM, we use the Frobenius norm to compare
# the two versions of the gradient.
grad_difference = np.linalg.norm(grad_naive - grad_vectorized,
ord='fro')
print('Loss difference:', np.abs(loss_naive - loss_vectorized))
print('Gradient difference:', grad_difference)
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## [djn] A practice run with softmax
from cs231n.classifiers import Softmax
softmax = Softmax()
tic = time.time()
loss_hist = softmax.train(X_train, y_train,
learning_rate=1e-7, reg=5e4,
num_iters=1500, verbose=True)
toc = time.time()
print('That took {:f}s'.format(toc - tic))
# A useful debugging strategy is to plot the loss as a function of
# iteration number:
plt.plot(loss_hist)
plt.xlabel('Iteration number')
plt.ylabel('Loss value')
plt.show()
# Write the Softmax.predict function and evaluate the performance
# on both the training and validation set
y_train_pred = softmax.predict(X_train)
print('training accuracy: {:f}'.format(
np.mean(y_train == y_train_pred)))
y_val_pred = softmax.predict(X_val)
print('validation accuracy: {:f}'.format(
np.mean(y_val == y_val_pred)))
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# Use the validation set to tune hyperparameters (regularization
# strength and learning rate). You should experiment with different
# ranges for the learning rates and regularization strengths;
# if you are careful you should be able to get a classification
# accuracy of over 0.35 on the validation set.
from cs231n.classifiers import Softmax
results = {}
best_val = -1
best_softmax = None
num_iters = 600
#learning_rates = [1e-7, 5e-7]
#regularization_strengths = [5e4, 1e8]
#learning_rates = 10 ** (0.5 * np.random.rand(10) - 6.5)
#regularization_strengths = 10 ** (0.8 * np.random.rand(10) + 2.5)
learning_rates =10 ** (np.random.rand(5) - 6.5)
regularization_strengths = 10 ** (2 * np.random.rand(5) + 3)
num_lr = len(learning_rates)
num_reg = len(regularization_strengths)
num_pts = num_lr * num_reg
####################################################################
# TODO: #
# Use the validation set to set the learning rate and #
# regularization strength. This should be identical to the #
# validation that you did for the SVM; save the best trained #
# softmax classifer in best_softmax. #
####################################################################
import itertools
n_iters = 800
combinations = itertools.product(learning_rates,
regularization_strengths)
count = 0
for lr, reg in combinations:
np.random.seed(4023) # Keep W initialization invariant
softmax = Softmax()
softmax.train(X_train, y_train, learning_rate=lr, reg=reg,
num_iters=n_iters)
y_train_pred = softmax.predict(X_train)
y_val_pred = softmax.predict(X_val)
train_accuracy = np.mean(y_train == y_train_pred)
val_accuracy = np.mean(y_val == y_val_pred)
results[(lr, reg)] = (train_accuracy, val_accuracy)
if val_accuracy > best_val:
best_val = val_accuracy
best_softmax = softmax
count += 1
print('[{}/{}] (lr={}, reg={}) val_acc={}'.format(
count, num_pts, lr, reg, val_accuracy))
####################################################################
# END OF YOUR CODE #
####################################################################
# Print out results.
# for lr, reg in sorted(results):
# train_accuracy, val_accuracy = results[(lr, reg)]
# print('lr {:e} reg {:e} '
# 'train accuracy: {:f} val accuracy: {:f}'.format(
# lr, reg, train_accuracy, val_accuracy))
print('best validation accuracy achieved during cross-validation:',
best_val)
# Visualize the cross-validation results
import math
x_scatter = [math.log10(x[0]) for x in results]
y_scatter = [math.log10(x[1]) for x in results]
# plot training accuracy
cm = plt.cm.viridis #[djn] colormap
marker_size = 100
colors = [results[x][0] for x in results]
plt.subplot(2, 1, 1)
plt.scatter(x_scatter, y_scatter, marker_size,
c=colors, cmap=cm)
plt.colorbar()
plt.xlabel('log learning rate')
plt.ylabel('log regularization strength')
plt.title('CIFAR-10 training accuracy')
# plot validation accuracy
colors = [results[x][1] for x in results]
# default size of markers is 20
plt.subplot(2, 1, 2)
plt.scatter(x_scatter, y_scatter, marker_size,
c=colors, cmap=cm)
plt.colorbar()
plt.xlabel('log learning rate')
plt.ylabel('log regularization strength')
plt.title('CIFAR-10 validation accuracy')
plt.show()
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# Evaluate the best softmax on test set
y_test_pred = best_softmax.predict(X_test)
test_accuracy = np.mean(y_test == y_test_pred)
print('softmax on raw pixels final test set accuracy:',
test_accuracy)
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# Visualize the learned weights for each class
w = best_softmax.W[:-1,:] # strip out the bias
w = w.reshape(32, 32, 3, 10)
w_min, w_max = np.min(w), np.max(w)
classes = ['plane', 'car', 'bird', 'cat', 'deer',
'dog', 'frog', 'horse', 'ship', 'truck']
for i in xrange(10):
plt.subplot(2, 5, i + 1)
# Rescale the weights to be between 0 and 255
wimg = 255.0 * (w[:, :, :, i].squeeze() - w_min) \
/ (w_max - w_min)
plt.imshow(wimg.astype('uint8'))
plt.axis('off')
plt.title(classes[i])
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