视频里 Andrej Karpathy上课的时候说,这次的作业meaty but educational,确实很meaty,作业一般是由.ipynb文件和.py文件组成,这次因为每个.ipynb文件涉及到的.py文件较多,且互相之间有交叉,所以每篇博客只贴出一个.ipynb或者一个.py文件.(因为之前的作业由于是一个.ipynb文件对应一个.py文件,所以就整合到一篇博客里)
还是那句话,有错误希望帮我指出来,多多指教,谢谢
Dropout.ipynb内容:
[TOC]
Dropout
Dropout [1] is a technique for regularizing neural networks by randomly setting some features to zero during the forward pass. In this exercise you will implement a dropout layer and modify your fully-connected network to optionally use dropout.
[1] Geoffrey E. Hinton et al, "Improving neural networks by preventing co-adaptation of feature detectors", arXiv 2012
# As usual, a bit of setup
import time
import numpy as np
import matplotlib.pyplot as plt
from cs231n.classifiers.fc_net import *
from cs231n.data_utils import get_CIFAR10_data
from cs231n.gradient_check import eval_numerical_gradient, eval_numerical_gradient_array
from cs231n.solver import Solver
%matplotlib inline
plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
# for auto-reloading external modules
# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython
%load_ext autoreload
%autoreload 2
def rel_error(x, y):
""" returns relative error """
return np.max(np.abs(x - y) / (np.maximum(1e-8, np.abs(x) + np.abs(y))))
# Load the (preprocessed) CIFAR10 data.
data = get_CIFAR10_data()
for k, v in data.iteritems():
print '%s: ' % k, v.shape
X_val: (1000, 3, 32, 32)
X_train: (49000, 3, 32, 32)
X_test: (1000, 3, 32, 32)
y_val: (1000,)
y_train: (49000,)
y_test: (1000,)
Dropout forward pass
In the file cs231n/layers.py, implement the forward pass for dropout. Since dropout behaves differently during training and testing, make sure to implement the operation for both modes.
Once you have done so, run the cell below to test your implementation.
x = np.random.randn(500, 500) + 10
for p in [0.3, 0.6, 0.75]:
out, _ = dropout_forward(x, {'mode': 'train', 'p': p})
out_test, _ = dropout_forward(x, {'mode': 'test', 'p': p})
print 'Running tests with p = ', p
print 'Mean of input: ', x.mean()
print 'Mean of train-time output: ', out.mean()
print 'Mean of test-time output: ', out_test.mean()
print 'Fraction of train-time output set to zero: ', (out == 0).mean()
print 'Fraction of test-time output set to zero: ', (out_test == 0).mean()
print
Running tests with p = 0.3
Mean of input: 10.0008904838
Mean of train-time output: 9.9965610718
Mean of test-time output: 10.0008904838
Fraction of train-time output set to zero: 0.70018
Fraction of test-time output set to zero: 0.0
Running tests with p = 0.6
Mean of input: 10.0008904838
Mean of train-time output: 10.0017849856
Mean of test-time output: 10.0008904838
Fraction of train-time output set to zero: 0.39994
Fraction of test-time output set to zero: 0.0
Running tests with p = 0.75
Mean of input: 10.0008904838
Mean of train-time output: 10.007736608
Mean of test-time output: 10.0008904838
Fraction of train-time output set to zero: 0.249488
Fraction of test-time output set to zero: 0.0
Dropout backward pass
In the file cs231n/layers.py, implement the backward pass for dropout. After doing so, run the following cell to numerically gradient-check your implementation.
x = np.random.randn(10, 10) + 10
dout = np.random.randn(*x.shape)
dropout_param = {'mode': 'train', 'p': 0.8, 'seed': 123}
out, cache = dropout_forward(x, dropout_param)
dx = dropout_backward(dout, cache)
dx_num = eval_numerical_gradient_array(lambda xx: dropout_forward(xx, dropout_param)[0], x, dout)
print 'dx relative error: ', rel_error(dx, dx_num)
dx relative error: 5.44560491149e-11
Fully-connected nets with Dropout
In the file cs231n/classifiers/fc_net.py, modify your implementation to use dropout. Specificially, if the constructor the the net receives a nonzero value for the dropout parameter, then the net should add dropout immediately after every ReLU nonlinearity. After doing so, run the following to numerically gradient-check your implementation.
N, D, H1, H2, C = 2, 15, 20, 30, 10
X = np.random.randn(N, D)
y = np.random.randint(C, size=(N,))
for dropout in [0, 0.25, 0.5]:
print 'Running check with dropout = ', dropout
model = FullyConnectedNet([H1, H2], input_dim=D, num_classes=C,
weight_scale=5e-2, dtype=np.float64,
dropout=dropout, seed=123)
loss, grads = model.loss(X, y)
print 'Initial loss: ', loss
for name in sorted(grads):
f = lambda _: model.loss(X, y)[0]
grad_num = eval_numerical_gradient(f, model.params[name], verbose=False, h=1e-5)
print '%s relative error: %.2e' % (name, rel_error(grad_num, grads[name]))
print
Running check with dropout = 0
Initial loss: 2.3051948274
W1 relative error: 2.53e-07
W2 relative error: 1.50e-05
W3 relative error: 2.75e-07
b1 relative error: 2.94e-06
b2 relative error: 5.05e-08
b3 relative error: 1.17e-10
Running check with dropout = 0.25
Initial loss: 2.31264683457
W1 relative error: 1.48e-08
W2 relative error: 2.34e-10
W3 relative error: 3.56e-08
b1 relative error: 1.53e-09
b2 relative error: 1.84e-10
b3 relative error: 8.70e-11
Running check with dropout = 0.5
Initial loss: 2.30243758771
W1 relative error: 4.55e-08
W2 relative error: 2.97e-08
W3 relative error: 4.34e-07
b1 relative error: 1.87e-08
b2 relative error: 5.05e-09
b3 relative error: 7.49e-11
Regularization experiment
As an experiment, we will train a pair of two-layer networks on 500 training examples: one will use no dropout, and one will use a dropout probability of 0.75. We will then visualize the training and validation accuracies of the two networks over time.
# Train two identical nets, one with dropout and one without
num_train = 500
small_data = {
'X_train': data['X_train'][:num_train],
'y_train': data['y_train'][:num_train],
'X_val': data['X_val'],
'y_val': data['y_val'],
}
solvers = {}
dropout_choices = [0, 0.75]
for dropout in dropout_choices:
model = FullyConnectedNet([500], dropout=dropout)
print dropout
solver = Solver(model, small_data,
num_epochs=25, batch_size=100,
update_rule='adam',
optim_config={
'learning_rate': 5e-4,
},
verbose=True, print_every=100)
solver.train()
solvers[dropout] = solver
0
(Iteration 1 / 125) loss: 8.596245
(Epoch 0 / 25) train acc: 0.224000; val_acc: 0.183000
(Epoch 1 / 25) train acc: 0.382000; val_acc: 0.219000
(Epoch 2 / 25) train acc: 0.484000; val_acc: 0.248000
(Epoch 3 / 25) train acc: 0.620000; val_acc: 0.274000
(Epoch 4 / 25) train acc: 0.654000; val_acc: 0.246000
(Epoch 5 / 25) train acc: 0.726000; val_acc: 0.280000
(Epoch 6 / 25) train acc: 0.788000; val_acc: 0.304000
(Epoch 7 / 25) train acc: 0.818000; val_acc: 0.264000
(Epoch 8 / 25) train acc: 0.846000; val_acc: 0.270000
(Epoch 9 / 25) train acc: 0.896000; val_acc: 0.288000
(Epoch 10 / 25) train acc: 0.926000; val_acc: 0.297000
(Epoch 11 / 25) train acc: 0.964000; val_acc: 0.276000
(Epoch 12 / 25) train acc: 0.950000; val_acc: 0.275000
(Epoch 13 / 25) train acc: 0.964000; val_acc: 0.299000
(Epoch 14 / 25) train acc: 0.952000; val_acc: 0.275000
(Epoch 15 / 25) train acc: 0.974000; val_acc: 0.291000
(Epoch 16 / 25) train acc: 0.984000; val_acc: 0.290000
(Epoch 17 / 25) train acc: 0.968000; val_acc: 0.286000
(Epoch 18 / 25) train acc: 0.974000; val_acc: 0.297000
(Epoch 19 / 25) train acc: 0.972000; val_acc: 0.275000
(Epoch 20 / 25) train acc: 0.994000; val_acc: 0.296000
(Iteration 101 / 125) loss: 0.021468
(Epoch 21 / 25) train acc: 0.998000; val_acc: 0.298000
(Epoch 22 / 25) train acc: 0.994000; val_acc: 0.306000
(Epoch 23 / 25) train acc: 0.992000; val_acc: 0.303000
(Epoch 24 / 25) train acc: 0.994000; val_acc: 0.310000
(Epoch 25 / 25) train acc: 0.998000; val_acc: 0.303000
0.75
(Iteration 1 / 125) loss: 10.053350
(Epoch 0 / 25) train acc: 0.274000; val_acc: 0.230000
(Epoch 1 / 25) train acc: 0.352000; val_acc: 0.211000
(Epoch 2 / 25) train acc: 0.444000; val_acc: 0.269000
(Epoch 3 / 25) train acc: 0.566000; val_acc: 0.263000
(Epoch 4 / 25) train acc: 0.650000; val_acc: 0.257000
(Epoch 5 / 25) train acc: 0.680000; val_acc: 0.280000
(Epoch 6 / 25) train acc: 0.768000; val_acc: 0.310000
(Epoch 7 / 25) train acc: 0.774000; val_acc: 0.270000
(Epoch 8 / 25) train acc: 0.824000; val_acc: 0.274000
(Epoch 9 / 25) train acc: 0.894000; val_acc: 0.288000
(Epoch 10 / 25) train acc: 0.876000; val_acc: 0.282000
(Epoch 11 / 25) train acc: 0.924000; val_acc: 0.312000
(Epoch 12 / 25) train acc: 0.936000; val_acc: 0.309000
(Epoch 13 / 25) train acc: 0.894000; val_acc: 0.285000
(Epoch 14 / 25) train acc: 0.938000; val_acc: 0.281000
(Epoch 15 / 25) train acc: 0.948000; val_acc: 0.323000
(Epoch 16 / 25) train acc: 0.930000; val_acc: 0.303000
(Epoch 17 / 25) train acc: 0.944000; val_acc: 0.286000
(Epoch 18 / 25) train acc: 0.930000; val_acc: 0.316000
(Epoch 19 / 25) train acc: 0.984000; val_acc: 0.311000
(Epoch 20 / 25) train acc: 0.964000; val_acc: 0.310000
(Iteration 101 / 125) loss: 0.598348
(Epoch 21 / 25) train acc: 0.972000; val_acc: 0.332000
(Epoch 22 / 25) train acc: 0.990000; val_acc: 0.310000
(Epoch 23 / 25) train acc: 0.988000; val_acc: 0.300000
(Epoch 24 / 25) train acc: 0.978000; val_acc: 0.296000
(Epoch 25 / 25) train acc: 0.994000; val_acc: 0.310000
# Plot train and validation accuracies of the two models
train_accs = []
val_accs = []
for dropout in dropout_choices:
solver = solvers[dropout]
train_accs.append(solver.train_acc_history[-1])
val_accs.append(solver.val_acc_history[-1])
plt.subplot(3, 1, 1)
for dropout in dropout_choices:
plt.plot(solvers[dropout].train_acc_history, 'o', label='%.2f dropout' % dropout)
plt.title('Train accuracy')
plt.xlabel('Epoch')
plt.ylabel('Accuracy')
plt.legend(ncol=2, loc='lower right')
plt.subplot(3, 1, 2)
for dropout in dropout_choices:
plt.plot(solvers[dropout].val_acc_history, 'o', label='%.2f dropout' % dropout)
plt.title('Val accuracy')
plt.xlabel('Epoch')
plt.ylabel('Accuracy')
plt.legend(ncol=2, loc='lower right')
plt.gcf().set_size_inches(15, 15)
plt.show()
output11
Question
Explain what you see in this experiment. What does it suggest about dropout?
Answer
training accuracy is almost equal,both nearly 100%, but 0.75 drop out net's val accuracy is a little bit higher than none drop out net's.
this may suggest that drop out can regularize net, prevent overfit.
可以看到,两个网络的训练精度都达到了100%,但是运用了drop out的网络的val accuracy要比没用drop out 的网络要高那么一点.
可以看出来,drop out 起到了正则化向的作用,可以防止过拟合