码农场三言两语讲完了反向传播，一个公式也没有，果然是面向“懒惰工程师”的快餐教程。比较喜欢“不提神经元，我们不是巫婆”的观点。这次不需要自己写算法，直接上TensorFlow了。
任务 2: 随机梯度下降
使用梯度下降和随机梯度下降训练一个全连接网络。
安装TensorFlow
新MacBookPro都是A卡，不用想cuda了，只能CPU。忍不住要黑：
Mac OS X Python 3.5 下的安装方法：
easy_install --upgrade six export TF_BINARY_URL=https://storage.googleapis.com/tensorflow/mac/cpu/tensorflow-0.11.0-py3-none-any.whl pip3 install --upgrade $TF_BINARY_URL
不要像官网那样用sudo，那不是pip的正确使用方式。
测试TensorFlow
python3
Python 3.5.2 (default, Sep 15 2016, 07:38:42)
[GCC 4.2.1 Compatible Apple LLVM 7.3.0 (clang-703.0.31)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> import tensorflow as tf
>>> hello = tf.constant('Hello, TensorFlow!')
>>> sess = tf.Session()
>>> print(sess.run(hello))
b'Hello, TensorFlow!'
>>> a = tf.constant(10)
>>> b = tf.constant(32)
>>> print(sess.run(a + b))
42
TensorFlow入门
TensorFlow的工作流程像一张图，先创建图，并在图上定义一些常量、变量和类似于函数的东西。如果熟悉OpenGL的话，肯定会觉得这有点像shader编程，我们在TF里写了段程序。
graph = tf.Graph() with graph.as_default(): ...
然后在图上创建一个session，意思就是我要调用刚才写的程序了
with tf.Session(graph=graph) as session: ...
第一次任务是用梯度下降训练一个非正则化的多项式逻辑斯谛回归，整个训练代码谷歌都给出了，注释也很详尽：
# With gradient descent training, even this much data is prohibitive.
# Subset the training data for faster turnaround.
train_subset = 10000
graph = tf.Graph()
with graph.as_default():
# Input data.
# Load the training, validation and test data into constants that are
# attached to the graph.
tf_train_dataset = tf.constant(train_dataset[:train_subset, :])
tf_train_labels = tf.constant(train_labels[:train_subset])
tf_valid_dataset = tf.constant(valid_dataset)
tf_test_dataset = tf.constant(test_dataset)
# Variables.
# These are the parameters that we are going to be training. The weight
# matrix will be initialized using random values following a (truncated)
# normal distribution. The biases get initialized to zero.
weights = tf.Variable(
tf.truncated_normal([image_size * image_size, num_labels]))
biases = tf.Variable(tf.zeros([num_labels]))
# Training computation.
# We multiply the inputs with the weight matrix, and add biases. We compute
# the softmax and cross-entropy (it's one operation in TensorFlow, because
# it's very common, and it can be optimized). We take the average of this
# cross-entropy across all training examples: that's our loss.
logits = tf.matmul(tf_train_dataset, weights) + biases
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
# Optimizer.
# We are going to find the minimum of this loss using gradient descent.
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
# Predictions for the training, validation, and test data.
# These are not part of training, but merely here so that we can report
# accuracy figures as we train.
train_prediction = tf.nn.softmax(logits)
valid_prediction = tf.nn.softmax(
tf.matmul(tf_valid_dataset, weights) + biases)
test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)
num_steps = 801
def accuracy(predictions, labels):
return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))
/ predictions.shape[0])
with tf.Session(graph=graph) as session:
# This is a one-time operation which ensures the parameters get initialized as
# we described in the graph: random weights for the matrix, zeros for the
# biases.
tf.initialize_all_variables().run()
print('Initialized')
for step in range(num_steps):
# Run the computations. We tell .run() that we want to run the optimizer,
# and get the loss value and the training predictions returned as numpy
# arrays.
_, l, predictions = session.run([optimizer, loss, train_prediction])
if (step % 100 == 0):
print('Loss at step %d: %f' % (step, l))
print('Training accuracy: %.1f%%' % accuracy(
predictions, train_labels[:train_subset, :]))
# Calling .eval() on valid_prediction is basically like calling run(), but
# just to get that one numpy array. Note that it recomputes all its graph
# dependencies.
print('Validation accuracy: %.1f%%' % accuracy(
valid_prediction.eval(), valid_labels))
print('Test accuracy: %.1f%%' % accuracy(test_prediction.eval(), test_labels))
注意官方代码中的
tf.global_variables_initializer().run()
在tensorflow-0.11.0中会抛出：
Traceback (most recent call last): File "udacity-deep-learning/2_fullyconnected.py", line 142, in <module> tf.global_variables_initializer().run() AttributeError: module 'tensorflow' has no attribute 'global_variables_initializer'
需要修改为
tf.initialize_all_variables().run()
运行后得到：
Loss at step 800: 1.066299 Training accuracy: 79.6% Validation accuracy: 75.0% Test accuracy: 83.0%
注意到这里的训练规模是
# With gradient descent training, even this much data is prohibitive. # Subset the training data for faster turnaround. train_subset = 10000
因为梯度下降实在太慢了，改用随机梯度下降会快一些，相较于上一版代码，只不过在每一个迭代中随机选取了部分实例用于训练:
with tf.Session(graph=graph) as session:
tf.global_variables_initializer().run()
print("Initialized")
for step in range(num_steps):
# Pick an offset within the training data, which has been randomized.
# Note: we could use better randomization across epochs.
offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
# Generate a minibatch.
batch_data = train_dataset[offset:(offset + batch_size), :]
batch_labels = train_labels[offset:(offset + batch_size), :]
# Prepare a dictionary telling the session where to feed the minibatch.
# The key of the dictionary is the placeholder node of the graph to be fed,
# and the value is the numpy array to feed to it.
feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
_, l, predictions = session.run(
[optimizer, loss, train_prediction], feed_dict=feed_dict)
得到
Minibatch loss at step 3000: 1.182136 Minibatch accuracy: 75.0% Validation accuracy: 79.0% Test accuracy: 86.6%
训练了更多迭代，accuracy上升了不少，用时却减少了很多。
题目
请在上述代码的基础上将其改造为使用ReLU激活函数f(x)=max(0,x)：
1024个隐藏层节点的神经网络。
batch_size = 128
hidden_size = 1024
graph = tf.Graph()
with graph.as_default():
# Input data. For the training data, we use a placeholder that will be fed
# at run time with a training minibatch.
tf_train_dataset = tf.placeholder(tf.float32,
shape=(batch_size, image_size * image_size))
tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
tf_valid_dataset = tf.constant(valid_dataset)
tf_test_dataset = tf.constant(test_dataset)
# Variables.
W1 = tf.Variable(tf.truncated_normal([image_size * image_size, hidden_size]))
b1 = tf.Variable(tf.zeros([hidden_size]))
W2 = tf.Variable(tf.truncated_normal([hidden_size, num_labels]))
b2 = tf.Variable(tf.zeros([num_labels]))
# Training computation.
y1 = tf.nn.relu(tf.matmul(tf_train_dataset, W1) + b1)
logits = tf.matmul(y1, W2) + b2
loss = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits)
y1_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, W1) + b1)
valid_logits = tf.matmul(y1_valid, W2) + b2
valid_prediction = tf.nn.softmax(valid_logits)
y1_test = tf.nn.relu(tf.matmul(tf_test_dataset, W1) + b1)
test_logits = tf.matmul(y1_test, W2) + b2
test_prediction = tf.nn.softmax(test_logits)
# Let's run it:
num_steps = 3001
with tf.Session(graph=graph) as session:
tf.initialize_all_variables().run()
print("Initialized")
for step in range(num_steps):
# Pick an offset within the training data, which has been randomized.
# Note: we could use better randomization across epochs.
offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
# Generate a minibatch.
batch_data = train_dataset[offset:(offset + batch_size), :]
batch_labels = train_labels[offset:(offset + batch_size), :]
# Prepare a dictionary telling the session where to feed the minibatch.
# The key of the dictionary is the placeholder node of the graph to be fed,
# and the value is the numpy array to feed to it.
feed_dict = {tf_train_dataset: batch_data, tf_train_labels: batch_labels}
_, l, predictions = session.run(
[optimizer, loss, train_prediction], feed_dict=feed_dict)
if (step % 500 == 0):
print("Minibatch loss at step %d: %f" % (step, l))
print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
print("Validation accuracy: %.1f%%" % accuracy(
valid_prediction.eval(), valid_labels))
print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))
两者的主要区别是，
逻辑斯谛回归：
weights = tf.Variable(tf.truncated_normal([image_size * image_size, num_labels])) biases = tf.Variable(tf.zeros([num_labels])) logits = tf.matmul(tf_train_dataset, weights) + biases loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
神经网络：
# Variables. W1 = tf.Variable(tf.truncated_normal([image_size * image_size, hidden_size])) b1 = tf.Variable(tf.zeros([hidden_size])) W2 = tf.Variable(tf.truncated_normal([hidden_size, num_labels])) b2 = tf.Variable(tf.zeros([num_labels])) # Training computation. y1 = tf.nn.relu(tf.matmul(tf_train_dataset, W1) + b1) logits = tf.matmul(y1, W2) + b2 loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
于是一个线性模型就进化为非线性的神经网络。
这一步得到：
Minibatch loss at step 3000: 1.465061 Minibatch accuracy: 83.6% Validation accuracy: 81.4% Test accuracy: 88.6%
由于随机数的因素，最终结果可能会有少许波动，但总体还是优于逻辑斯谛回归的。
机器要跟得上