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
In [1]:
# As usual, a bit of setup
from __future__ import absolute_import, division, print_function
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
# 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 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))))
In [2]:
# Load the (preprocessed) CIFAR10 data.
data = get_CIFAR10_data()
for k, v in data.iteritems():
print('{}:'.format(k), v.shape)
In [3]:
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()
In [4]:
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))
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.
In [5]:
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('{} relative error: {:.2e}'.format(
name, rel_error(grad_num, grads[name])))
print()
In [6]:
# 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('Using dropout =', 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
print()
In [7]:
# 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'.format(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'.format(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()