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Tensor Flow
Tensors: n-dimensional arrays
A sequence of tensor operations
Deep learning process are flows of tensors
Vector: 1-D tensor
Matrix: 2-D tensor
Can represent also many machine learning algorithms
A simple ReLU network
a1 b1 c1
a0 b0 c0
w
a1=a0wa,a+b0wb,a+c0wc,a
b1=a0wa,b+b0wb,b+c0wc,b
c1=a0wa,c+b0wb,c+c0wc,c
Apply relu(…) on a1, b1, c1
Slower approach
Per-neuron operation
More efficient approach
Matrix operation
As matrix operations
a0
a1 b1 c1
a0 b0 c0
w
. =
=relu( )
b0 c0 a1 b1 c1
a1a1
=relu( )b1b1
=relu( )c1c1
wa,a
wb,a
wc,a
wa,b
wb,b
wc,b
wa,c
wb,c
wc,c
With TensorFlow
a1 b1 c1
a0 b0 c0
w
out = tf.nn.relu(y)
y = tf.matmul(x, w)
x w
a0 . =b0 c0
wa,a
wb,a
wc,a
wa,b
wb,b
wc,b
wa,c
wb,c
wc,c
a1 b1 c1
=relu( )a1a1
=relu( )b1b1
=relu( )c1c1
import tensorflow as tf
Define Tensors
xa,a
xb,a
xc,a
xa,b
xb,b
xc,b
xa,c
xb,c
xc,c
w
Variable(<initial-value>,
name=<optional-name>)
w = tf.Variable(tf.random_normal([3, 3]), name='w')
import tensorflow as tf
y = tf.matmul(x, w)
relu_out = tf.nn.relu(y)
Variable stores the state of current execution
Others are operations
TensorFlow
Code so far defines a data flow graph
MatMul
ReLU
Variable
x
w = tf.Variable(tf.random_normal([3, 3]), name='w')
import tensorflow as tf
y = tf.matmul(x, w)
relu_out = tf.nn.relu(y)
Each variable corresponds to a
node in the graph, not the result
Can be confusing at the beginning
TensorFlow
Code so far defines a data flow graph
Needs to specify how we
want to execute the graph MatMul
ReLU
Variable
x
Session
Manage resource for graph execution
w = tf.Variable(tf.random_normal([3, 3]), name='w')
sess = tf.Session()
y = tf.matmul(x, w)
relu_out = tf.nn.relu(y)
import tensorflow as tf
result = sess.run(relu_out)
Graph
Fetch
Retrieve content from a node
w = tf.Variable(tf.random_normal([3, 3]), name='w')
sess = tf.Session()
y = tf.matmul(x, w)
relu_out = tf.nn.relu(y)
import tensorflow as tf
print sess.run(relu_out)
MatMul
ReLU
Variable
x
Fetch
We have assembled the pipes
Fetch the liquid
Graph
sess = tf.Session()
y = tf.matmul(x, w)
relu_out = tf.nn.relu(y)
import tensorflow as tf
print sess.run(relu_out)
sess.run(tf.initialize_all_variables())
w = tf.Variable(tf.random_normal([3, 3]), name='w')
InitializeVariable
Variable is an empty node
MatMul
ReLU
Variable
x
Fetch
Fill in the content of a
Variable node
Graph
sess = tf.Session()
y = tf.matmul(x, w)
relu_out = tf.nn.relu(y)
import tensorflow as tf
print sess.run(relu_out)
sess.run(tf.initialize_all_variables())
w = tf.Variable(tf.random_normal([3, 3]), name='w')
x = tf.placeholder("float", [1, 3])
Placeholder
How about x?
MatMul
ReLU
Variable
x
Fetch
placeholder(<data type>,
shape=<optional-shape>,
name=<optional-name>)
Its content will be fed
Graph
import numpy as np
import tensorflow as tf
sess = tf.Session()
x = tf.placeholder("float", [1, 3])
w = tf.Variable(tf.random_normal([3, 3]), name='w')
y = tf.matmul(x, w)
relu_out = tf.nn.relu(y)
sess.run(tf.initialize_all_variables())
print sess.run(relu_out, feed_dict={x:np.array([[1.0, 2.0, 3.0]])})
Feed
MatMul
ReLU
Variable
x
FetchPump liquid into the pipe
Feed
Session management
Needs to release resource after use
sess.close()
Common usage
with tf.Session() as sess:
…
Interactive
sess = InteractiveSession()
Prediction
import numpy as np
import tensorflow as tf
with tf.Session() as sess:
x = tf.placeholder("float", [1, 3])
w = tf.Variable(tf.random_normal([3, 3]), name='w')
relu_out = tf.nn.relu(tf.matmul(x, w))
softmax = tf.nn.softmax(relu_out)
sess.run(tf.initialize_all_variables())
print sess.run(softmax, feed_dict={x:np.array([[1.0, 2.0, 3.0]])})
Softmax
Make predictions for n targets that sum to 1
Prediction Difference
import numpy as np
import tensorflow as tf
with tf.Session() as sess:
x = tf.placeholder("float", [1, 3])
w = tf.Variable(tf.random_normal([3, 3]), name='w')
relu_out = tf.nn.relu(tf.matmul(x, w))
softmax = tf.nn.softmax(relu_out)
sess.run(tf.initialize_all_variables())
answer = np.array([[0.0, 1.0, 0.0]])
print answer - sess.run(softmax, feed_dict={x:np.array([[1.0, 2.0, 3.0]])})
Learn parameters: Loss
Define loss function
Loss function for softmax
softmax_cross_entropy_with_logits(
logits, labels, name=<optional-name>)
labels = tf.placeholder("float", [1, 3])
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(
relu_out, labels, name='xentropy')
Learn parameters: Optimization
Gradient descent
class GradientDescentOptimizer
GradientDescentOptimizer(learning rate)
labels = tf.placeholder("float", [1, 3])
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(
relu_out, labels, name='xentropy')
optimizer = tf.train.GradientDescentOptimizer(0.1)
train_op = optimizer.minimize(cross_entropy)
sess.run(train_op,
feed_dict= {x:np.array([[1.0, 2.0, 3.0]]), labels:answer})
learning rate = 0.1
Iterative update
labels = tf.placeholder("float", [1, 3])
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(
relu_out, labels, name=‘xentropy')
optimizer = tf.train.GradientDescentOptimizer(0.1)
train_op = optimizer.minimize(cross_entropy)
for step in range(10):
sess.run(train_op,
feed_dict= {x:np.array([[1.0, 2.0, 3.0]]), labels:answer})
Gradient descent usually needs more than one step
Run multiple times
Add parameters for Softmax
…
softmax_w = tf.Variable(tf.random_normal([3, 3]))
logit = tf.matmul(relu_out, softmax_w)
softmax = tf.nn.softmax(logit)
…
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(
logit, labels, name=‘xentropy')
…
Do not want to use only non-negative input
Softmax layer
Add biases
…
w = tf.Variable(tf.random_normal([3, 3]))
b = tf.Variable(tf.zeros([1, 3]))
relu_out = tf.nn.relu(tf.matmul(x, w) + b)
softmax_w = tf.Variable(tf.random_normal([3, 3]))
softmax_b = tf.Variable(tf.zeros([1, 3]))
logit = tf.matmul(relu_out, softmax_w) + softmax_b
softmax = tf.nn.softmax(logit)
…
Biases initialized to zero
Make it deep
…
x = tf.placeholder("float", [1, 3])
relu_out = x
num_layers = 2
for layer in range(num_layers):
w = tf.Variable(tf.random_normal([3, 3]))
b = tf.Variable(tf.zeros([1, 3]))
relu_out = tf.nn.relu(tf.matmul(relu_out, w) + b)
…
Add layers
Visualize the graph
TensorBoard
writer = tf.train.SummaryWriter(
'/tmp/tf_logs', sess.graph_def)
tensorboard --logdir=/tmp/tf_logs
Improve naming, improve visualization
name_scope(name)
Help specify hierarchical names
…
for layer in range(num_layers):
with tf.name_scope('relu'):
w = tf.Variable(tf.random_normal([3, 3]))
b = tf.Variable(tf.zeros([1, 3]))
relu_out = tf.nn.relu(tf.matmul(relu_out, w) + b)
…
Will help visualizer to better
understand hierarchical relation
Move to outside the loop?
Add name_scope for softmax
Before After
Add regularization to the loss
eg. L2 regularize on the Softmax layer parameters
…
l2reg = tf.reduce_sum(tf.square(softmax_w))
loss = cross_entropy + l2reg
train_op = optimizer.minimize(loss)
…
print sess.run(l2reg)
…
Add it to the loss
Automatic gradient calculation
Add a parallel path
Use activation as bias
Everything is a tensor
Residual learning
ILSVRC 2015 classification task winer
He et al. 2015
Visualize states
Add summaries
scalar_summary histogram_summary
merged_summaries = tf.merge_all_summaries()
results = sess.run([train_op, merged_summaries],
feed_dict=…)
writer.add_summary(results[1], step)
Save and load models
tf.train.Saver(…)
Default will associate with all variables
all_variables()
save(sess, save_path, …)
restore(sess, save_path, …)
Replace initialization
That’s why we need to run initialization
separately
Convolution
conv2d(input, filter, strides, padding,
use_cudnn_on_gpu=None, name=None)
LSTM
# Parameters of gates are concatenated into one multiply for efficiency.
c, h = array_ops.split(1, 2, state)
concat = linear([inputs, h], 4 * self._num_units,True)
# i = input_gate, j = new_input, f = forget_gate, o = output_gate
i, j, f, o = array_ops.split(1, 4, concat)
new_c = c * sigmoid(f + self._forget_bias) + sigmoid(i) * tanh(j)
new_h = tanh(new_c) * sigmoid(o)
BasicLSTMCell
Word2Vec with TensorFlow
# Look up embeddings for inputs.
embeddings = tf.Variable(
tf.random_uniform([vocabulary_size, embedding_size], -1.0, 1.0))
embed = tf.nn.embedding_lookup(embeddings, train_inputs)
# Construct the variables for the NCE loss
nce_weights = tf.Variable(
tf.truncated_normal([vocabulary_size, embedding_size],
stddev=1.0 / math.sqrt(embedding_size)))
nce_biases = tf.Variable(tf.zeros([vocabulary_size]))
# Compute the average NCE loss for the batch.
# tf.nce_loss automatically draws a new sample of the negative labels each
# time we evaluate the loss.
loss = tf.reduce_mean(
tf.nn.nce_loss(nce_weights, nce_biases, embed, train_labels,
num_sampled, vocabulary_size))
Reuse Pre-trained models
Image recognition
Inception-v3
military uniform (866): 0.647296
suit (794): 0.0477196
academic gown (896): 0.0232411
bow tie (817): 0.0157356
bolo tie (940): 0.0145024
Try it on your Android
github.com/tensorflow/tensorflow/tree/master/tensorflow/
examples/android
Uses a Google Inception model to classify camera
frames in real-time, displaying the top results in an
overlay on the camera image.
Tensorflow Android Camera Demo
github.com/nivwusquorum/tensorflow-deepq
Reinforcement Learning using Tensor Flow
github.com/asrivat1/DeepLearningVideoGames
Using Deep Q Networks to LearnVideo Game Strategies
github.com/woodrush/neural-art-tf
Neural art
github.com/sherjilozair/char-rnn-tensorflow
github.com/fchollet/keras
github.com/jazzsaxmafia/show_and_tell.tensorflow
github.com/jikexueyuanwiki/tensorflow-zh
Google Brain Residency Program
Learn to conduct deep learning research w/experts in our team
Fixed one-year employment with salary, benefits, ...
Interesting problems,TensorFlow, and access to
computational resources
Goal after one year is to have conducted several research
projects
New one year immersion program in deep learning research
Google Brain Residency Program
Who should apply?
People with BSc, MSc or PhD, ideally in CS,
mathematics or statistics
Completed coursework in calculus, linear
algebra, and probability, or equiv.
Motivated, hard working, and have a strong
interest in deep learning
Programming experience
Google Brain Residency Program
Program Application & Timeline
DEADLINE: January 15, 2016
Thanks for your attention!

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Google TensorFlow Tutorial

  • 1. Tensor Flow Tensors: n-dimensional arrays A sequence of tensor operations Deep learning process are flows of tensors Vector: 1-D tensor Matrix: 2-D tensor Can represent also many machine learning algorithms
  • 2. A simple ReLU network a1 b1 c1 a0 b0 c0 w a1=a0wa,a+b0wb,a+c0wc,a b1=a0wa,b+b0wb,b+c0wc,b c1=a0wa,c+b0wb,c+c0wc,c Apply relu(…) on a1, b1, c1 Slower approach Per-neuron operation More efficient approach Matrix operation
  • 3. As matrix operations a0 a1 b1 c1 a0 b0 c0 w . = =relu( ) b0 c0 a1 b1 c1 a1a1 =relu( )b1b1 =relu( )c1c1 wa,a wb,a wc,a wa,b wb,b wc,b wa,c wb,c wc,c
  • 4. With TensorFlow a1 b1 c1 a0 b0 c0 w out = tf.nn.relu(y) y = tf.matmul(x, w) x w a0 . =b0 c0 wa,a wb,a wc,a wa,b wb,b wc,b wa,c wb,c wc,c a1 b1 c1 =relu( )a1a1 =relu( )b1b1 =relu( )c1c1 import tensorflow as tf
  • 5. Define Tensors xa,a xb,a xc,a xa,b xb,b xc,b xa,c xb,c xc,c w Variable(<initial-value>, name=<optional-name>) w = tf.Variable(tf.random_normal([3, 3]), name='w') import tensorflow as tf y = tf.matmul(x, w) relu_out = tf.nn.relu(y) Variable stores the state of current execution Others are operations
  • 6. TensorFlow Code so far defines a data flow graph MatMul ReLU Variable x w = tf.Variable(tf.random_normal([3, 3]), name='w') import tensorflow as tf y = tf.matmul(x, w) relu_out = tf.nn.relu(y) Each variable corresponds to a node in the graph, not the result Can be confusing at the beginning
  • 7. TensorFlow Code so far defines a data flow graph Needs to specify how we want to execute the graph MatMul ReLU Variable x Session Manage resource for graph execution w = tf.Variable(tf.random_normal([3, 3]), name='w') sess = tf.Session() y = tf.matmul(x, w) relu_out = tf.nn.relu(y) import tensorflow as tf result = sess.run(relu_out)
  • 8. Graph Fetch Retrieve content from a node w = tf.Variable(tf.random_normal([3, 3]), name='w') sess = tf.Session() y = tf.matmul(x, w) relu_out = tf.nn.relu(y) import tensorflow as tf print sess.run(relu_out) MatMul ReLU Variable x Fetch We have assembled the pipes Fetch the liquid
  • 9. Graph sess = tf.Session() y = tf.matmul(x, w) relu_out = tf.nn.relu(y) import tensorflow as tf print sess.run(relu_out) sess.run(tf.initialize_all_variables()) w = tf.Variable(tf.random_normal([3, 3]), name='w') InitializeVariable Variable is an empty node MatMul ReLU Variable x Fetch Fill in the content of a Variable node
  • 10. Graph sess = tf.Session() y = tf.matmul(x, w) relu_out = tf.nn.relu(y) import tensorflow as tf print sess.run(relu_out) sess.run(tf.initialize_all_variables()) w = tf.Variable(tf.random_normal([3, 3]), name='w') x = tf.placeholder("float", [1, 3]) Placeholder How about x? MatMul ReLU Variable x Fetch placeholder(<data type>, shape=<optional-shape>, name=<optional-name>) Its content will be fed
  • 11. Graph import numpy as np import tensorflow as tf sess = tf.Session() x = tf.placeholder("float", [1, 3]) w = tf.Variable(tf.random_normal([3, 3]), name='w') y = tf.matmul(x, w) relu_out = tf.nn.relu(y) sess.run(tf.initialize_all_variables()) print sess.run(relu_out, feed_dict={x:np.array([[1.0, 2.0, 3.0]])}) Feed MatMul ReLU Variable x FetchPump liquid into the pipe Feed
  • 12. Session management Needs to release resource after use sess.close() Common usage with tf.Session() as sess: … Interactive sess = InteractiveSession()
  • 13. Prediction import numpy as np import tensorflow as tf with tf.Session() as sess: x = tf.placeholder("float", [1, 3]) w = tf.Variable(tf.random_normal([3, 3]), name='w') relu_out = tf.nn.relu(tf.matmul(x, w)) softmax = tf.nn.softmax(relu_out) sess.run(tf.initialize_all_variables()) print sess.run(softmax, feed_dict={x:np.array([[1.0, 2.0, 3.0]])}) Softmax Make predictions for n targets that sum to 1
  • 14. Prediction Difference import numpy as np import tensorflow as tf with tf.Session() as sess: x = tf.placeholder("float", [1, 3]) w = tf.Variable(tf.random_normal([3, 3]), name='w') relu_out = tf.nn.relu(tf.matmul(x, w)) softmax = tf.nn.softmax(relu_out) sess.run(tf.initialize_all_variables()) answer = np.array([[0.0, 1.0, 0.0]]) print answer - sess.run(softmax, feed_dict={x:np.array([[1.0, 2.0, 3.0]])})
  • 15. Learn parameters: Loss Define loss function Loss function for softmax softmax_cross_entropy_with_logits( logits, labels, name=<optional-name>) labels = tf.placeholder("float", [1, 3]) cross_entropy = tf.nn.softmax_cross_entropy_with_logits( relu_out, labels, name='xentropy')
  • 16. Learn parameters: Optimization Gradient descent class GradientDescentOptimizer GradientDescentOptimizer(learning rate) labels = tf.placeholder("float", [1, 3]) cross_entropy = tf.nn.softmax_cross_entropy_with_logits( relu_out, labels, name='xentropy') optimizer = tf.train.GradientDescentOptimizer(0.1) train_op = optimizer.minimize(cross_entropy) sess.run(train_op, feed_dict= {x:np.array([[1.0, 2.0, 3.0]]), labels:answer}) learning rate = 0.1
  • 17. Iterative update labels = tf.placeholder("float", [1, 3]) cross_entropy = tf.nn.softmax_cross_entropy_with_logits( relu_out, labels, name=‘xentropy') optimizer = tf.train.GradientDescentOptimizer(0.1) train_op = optimizer.minimize(cross_entropy) for step in range(10): sess.run(train_op, feed_dict= {x:np.array([[1.0, 2.0, 3.0]]), labels:answer}) Gradient descent usually needs more than one step Run multiple times
  • 18. Add parameters for Softmax … softmax_w = tf.Variable(tf.random_normal([3, 3])) logit = tf.matmul(relu_out, softmax_w) softmax = tf.nn.softmax(logit) … cross_entropy = tf.nn.softmax_cross_entropy_with_logits( logit, labels, name=‘xentropy') … Do not want to use only non-negative input Softmax layer
  • 19. Add biases … w = tf.Variable(tf.random_normal([3, 3])) b = tf.Variable(tf.zeros([1, 3])) relu_out = tf.nn.relu(tf.matmul(x, w) + b) softmax_w = tf.Variable(tf.random_normal([3, 3])) softmax_b = tf.Variable(tf.zeros([1, 3])) logit = tf.matmul(relu_out, softmax_w) + softmax_b softmax = tf.nn.softmax(logit) … Biases initialized to zero
  • 20. Make it deep … x = tf.placeholder("float", [1, 3]) relu_out = x num_layers = 2 for layer in range(num_layers): w = tf.Variable(tf.random_normal([3, 3])) b = tf.Variable(tf.zeros([1, 3])) relu_out = tf.nn.relu(tf.matmul(relu_out, w) + b) … Add layers
  • 21. Visualize the graph TensorBoard writer = tf.train.SummaryWriter( '/tmp/tf_logs', sess.graph_def) tensorboard --logdir=/tmp/tf_logs
  • 22. Improve naming, improve visualization name_scope(name) Help specify hierarchical names … for layer in range(num_layers): with tf.name_scope('relu'): w = tf.Variable(tf.random_normal([3, 3])) b = tf.Variable(tf.zeros([1, 3])) relu_out = tf.nn.relu(tf.matmul(relu_out, w) + b) … Will help visualizer to better understand hierarchical relation Move to outside the loop?
  • 23. Add name_scope for softmax Before After
  • 24. Add regularization to the loss eg. L2 regularize on the Softmax layer parameters … l2reg = tf.reduce_sum(tf.square(softmax_w)) loss = cross_entropy + l2reg train_op = optimizer.minimize(loss) … print sess.run(l2reg) … Add it to the loss Automatic gradient calculation
  • 26. Use activation as bias Everything is a tensor
  • 27. Residual learning ILSVRC 2015 classification task winer He et al. 2015
  • 28. Visualize states Add summaries scalar_summary histogram_summary merged_summaries = tf.merge_all_summaries() results = sess.run([train_op, merged_summaries], feed_dict=…) writer.add_summary(results[1], step)
  • 29. Save and load models tf.train.Saver(…) Default will associate with all variables all_variables() save(sess, save_path, …) restore(sess, save_path, …) Replace initialization That’s why we need to run initialization separately
  • 30. Convolution conv2d(input, filter, strides, padding, use_cudnn_on_gpu=None, name=None)
  • 31. LSTM # Parameters of gates are concatenated into one multiply for efficiency. c, h = array_ops.split(1, 2, state) concat = linear([inputs, h], 4 * self._num_units,True) # i = input_gate, j = new_input, f = forget_gate, o = output_gate i, j, f, o = array_ops.split(1, 4, concat) new_c = c * sigmoid(f + self._forget_bias) + sigmoid(i) * tanh(j) new_h = tanh(new_c) * sigmoid(o) BasicLSTMCell
  • 32. Word2Vec with TensorFlow # Look up embeddings for inputs. embeddings = tf.Variable( tf.random_uniform([vocabulary_size, embedding_size], -1.0, 1.0)) embed = tf.nn.embedding_lookup(embeddings, train_inputs) # Construct the variables for the NCE loss nce_weights = tf.Variable( tf.truncated_normal([vocabulary_size, embedding_size], stddev=1.0 / math.sqrt(embedding_size))) nce_biases = tf.Variable(tf.zeros([vocabulary_size])) # Compute the average NCE loss for the batch. # tf.nce_loss automatically draws a new sample of the negative labels each # time we evaluate the loss. loss = tf.reduce_mean( tf.nn.nce_loss(nce_weights, nce_biases, embed, train_labels, num_sampled, vocabulary_size))
  • 33. Reuse Pre-trained models Image recognition Inception-v3 military uniform (866): 0.647296 suit (794): 0.0477196 academic gown (896): 0.0232411 bow tie (817): 0.0157356 bolo tie (940): 0.0145024
  • 34. Try it on your Android github.com/tensorflow/tensorflow/tree/master/tensorflow/ examples/android Uses a Google Inception model to classify camera frames in real-time, displaying the top results in an overlay on the camera image. Tensorflow Android Camera Demo
  • 36. github.com/asrivat1/DeepLearningVideoGames Using Deep Q Networks to LearnVideo Game Strategies
  • 42. Google Brain Residency Program Learn to conduct deep learning research w/experts in our team Fixed one-year employment with salary, benefits, ... Interesting problems,TensorFlow, and access to computational resources Goal after one year is to have conducted several research projects New one year immersion program in deep learning research
  • 43. Google Brain Residency Program Who should apply? People with BSc, MSc or PhD, ideally in CS, mathematics or statistics Completed coursework in calculus, linear algebra, and probability, or equiv. Motivated, hard working, and have a strong interest in deep learning Programming experience
  • 44. Google Brain Residency Program Program Application & Timeline DEADLINE: January 15, 2016 Thanks for your attention!