Tutorial: Binary Matcher with TensorFlow

--D. Thiebaut (talk) 15:26, 19 March 2017 (EDT)

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This page (which started as a Jupyter notebook) illustrates how to design a simple multi-layer Tensorflow Neural Net to recognize integers coded in binary and output them as a 1-hot vector. For example, if we assume that we have 5 bits, then there are 32 possible combinations. We associate with each 5-bit sequence a 1-hot vector. For example, 0,0,0,1,1, which is 3 in decimal, is associated with 0,0,0,1,0,0,0,0...,0, which has 31 0s and one 1. The only 1 is at Index 3. Similarly, if we have 1,1,1,1,1, which is 31 in decimal, then its associated 1-hot vector is 0,0,0,0,...0,0,1, another group of 31 0s and one last 1. Our binary input is coded in 5 bits, and we make it more interesting by adding 5 additional random bits. So the input is a vector of 10 bits, 5 random, and 5 representing a binary pattern associated with a 1-hot vector. The 1- hot vector is the output to be predicted by the network.

Source Files

This tutorial is in the form of a Jupyter Notebook, and made available here in various forms:

• pdf
• tgz-zipped archive containing the markdown and notebook

Preparing the Data

Let's prepare a set of data where we have 5 bits of input, plus 3 random bits, plus 32 outputs corresponding to 1-of for the integer coded in the 5 bits.

Preparing the Raw Data: 32 rows Binary and 1-Hot

We first create two arrays of 32 rows. The first array, called x32, contains the binary patterns for 0 to 31. The second array, called y32, contains the one-hot version of the equivalent entry in the x32 array. For example, [0,0,0,0,0] in x32 corresponds to [1,0,0,0,...,0] (one 1 followed by thirty one 0s) in y32. [1,1,1,1,1] in x32 corresponds to [0,0,0...,0,0,1] in y32.

from __future__ import print_function
import random
import numpy as np
import tensorflow as tf
# create the 32 binary values of 0 to 31
# as well as the 1-hot vector of 31 0s and one 1.
x32 = []
y32 = []
for i in range( 32 ):
 n5 = ("00000" + "{0:b}".format(i))[-5:]
 bits = [0]*32
 bits[i] = 1
 #print( n5,":", r3, "=", bits )
 nBits = [ int(n) for n in n5 ]

 #print( nBits, rBits, bits )
 #print( type(x), type(y), type(nBits), type(rBits), type( bits ))
 x32 = x32 + [nBits]
 y32 = y32 + [bits]

# print both collections to verify that we have the correct data.
# The x vectors will be fed to the neural net (NN) (along with some nois
y data), and
# we'll train the NN to generate the correct 1-hot vector.
print( "x = ", "\n".join( [str(k) for k in x32] ) )
print( "y = ", "\n".join( [str(k) for k in y32] ) )

Addition of Random Bits

Let's add some random bits (say 7) to the rows of x, and create a larger collection of rows, say 100.

x = []
y = []
noRandomBits = 5
for i in range( 100 ):
 # pick all the rows in a round-robin fashion.
 xrow = x32[i%32]
 yrow = y32[i%32]

 # generate a random int of 5 bits
 r5 = random.randint( 0, 31 )
 r5 = ("0"*noRandomBits + "{0:b}".format(r5))[-noRandomBits:]
 # create a list of integer bits for r5
 rBits = [ int(n) for n in r5 ]

 #create a new row of x and y values
 x.append( xrow + rBits )
 y.append( yrow )

# display x and y
for i in range( len( x ) ):
 print( "x[%2d] ="%i, ",".join( [str(k) for k in x[i] ] ), "y[%2d] ="%i, ",".join( [str(k) for k in y[i] ] ) )

Split Into Training and Testing

We'll split the 100 rows in 90 rows of training, and 10 rows for testing.

Percent = 0.10
x_train = []
y_train = []
x_test = []
y_test = []
# pick 10 indexes in 0-31.
indexes = [5, 7, 10, 20, 21, 29, 3, 11, 12, 25]
for i in range( len( x ) ):
 if i in indexes:
 x_test.append( x[i] )
 y_test.append( y[i] )
 else:
 x_train.append( x[i] )
 y_train.append( y[i] )
# display train and set xs and ys
for i in range( len( x_train ) ):
 print( "x_train[%2d] ="%i, ",".join( [str(k) for k in x_train[i] ]
 ),
 "y_train[%2d] ="%i, ",".join( [str(k) for k in y_train[i] ] )
 )
print()
for i in range( len( x_test ) ):
 print( "x_test[%2d] ="%i, ",".join( [str(k) for k in x_test[i] ] ),
 "y_test[%2d] ="%i, ",".join( [str(k) for k in y_test[i] ] ) )

Package Xs and Ys as Numpy Arrays

We now make the train and test arrays into numpy arrays.

x_train_np = np.matrix( x_train ).astype( dtype=np.float32 )
y_train_np = np.matrix( y_train ).astype( dtype=np.float32 )
x_test_np = np.matrix( x_test ).astype( dtype=np.float32 )
y_test_np = np.matrix( y_test ).astype( dtype=np.float32 )
# get training size, number of features, and number of labels, using
# NN/ML vocabulary
train_size, num_features = x_train_np.shape
train_size, num_labels = y_train_np.shape

# Get the number of epochs for training.
test_size, num_eval_features = x_test_np.shape
test_size, num_eval_labels = y_test_np.shape
# Get the size of layer one.
if True:
 print( "tain size = ", train_size )
 print( "num features = ", num_features )
 print( "num labels = ", num_labels )
 print()
 print( "test size = ", test_size )
 print( "num eval features = ", num_eval_features )
 print( "num eval labels = ", num_eval_labels )

Definition of the Neural Network

Let's define the neural net. We assume it has just 1 layer.

Constants/Variables

We just have one, the learning rate with which the gradient optimizer will look for the optimal weights. It's a factor used when following the gradient of the function y = W.x + b, in order to look for the minimum of the difference between y and the target.

learning_Rate = 0.1

==Place-Holders It will have place holders for

• the X input
• the Y target. That's the vectors of Y values we generated above. The network will generate its own version of y, which we'll compare to the target. The closer the two are, the better.
• the drop-probability, which is defined as the "keep_probability", i.e. the probability a node from the

neural net will be kept in the computation. A value of 1.0 indicates that all the nodes are used in the processing of data through the network.

x = tf.placeholder("float", shape=[None, num_features])
target = tf.placeholder("float", shape=[None, num_labels])
keep_prob = tf.placeholder(tf.float32)

Variables

The variables contain tensors that TensorFlow will manipulate. Typically the Wi and bi coefficients of each layer. We'll assume just one later for right now, with num_features inputs (the width of the X vectors), and num_labels outputs (the width of the Y vectors). We initialize W0 and b0 with random values taken from a normal distribution.

W0 = tf.Variable( tf.random_normal( [num_features, num_labels ] ) )
b0 = tf.Variable( tf.random_normal( [num_labels] ) )
W1 = tf.Variable( tf.random_normal( [num_labels, num_labels * 2 ] ) )
b1 = tf.Variable( tf.random_normal( [num_labels * 2] ) )
W2 = tf.Variable( tf.random_normal( [num_labels * 2, num_labels ] ) )
b2 = tf.Variable( tf.random_normal( [num_labels] ) )

Model

The model simply defines what the output of the NN, y, is as a function of the input x. The softmax function transforms the output into probabilities between 0 and 1. This is what we need since we want the output of our network to match the 1-hot vector which is the format the y vectors are coded in.

#y0 = tf.nn.sigmoid( tf.matmul(x, W0) + b0 )
y0 = tf.nn.sigmoid( tf.matmul(x, W0) + b0 )
y1 = tf.nn.sigmoid( tf.matmul(y0, W1) + b1 )
y = tf.matmul( y1, W2) + b2
#y = tf.nn.softmax( tf.matmul( y0, W1) + b1 )

Training

We now define the cost operation, cost_op, i.e. measuring how "bad" the output of the network is compared to the correct output.

#prediction = tf.reduce_sum( tf.mul( tf.nn.softmax( y ), target ), reduc
tion_indices=1 )
#accuracy = tf.reduce_mean ( prediction )
#cost_op = tf.reduce_mean( tf.sub( 1.0, tf.reduce_sum( tf.mul( y, target
 ), reduction_indices=1 ) ) )

#cost_op = tf.reduce_mean(
# tf.sub( 1.0, tf.reduce_sum( tf.mul( target, tf.nn.softmax
(y) ), reduction_indices=[1] ) )
# )
# The cost_op below yields an ccuracy on training data of 0.86% and an a
ccuracy on test data = 0.49%
# for 1000 epochs and a batch size of 10.
cost_op = tf.reduce_mean(
 tf.nn.softmax_cross_entropy_with_logits( labels = target, logits =
y ) )

And now the training operation, or train_op, which is given the cost_op

#train_op = tf.train.GradientDescentOptimizer( learning_rate = learning_Rate ).minimize( cost_op )
train_op = tf.train.AdagradOptimizer( learning_rate = learning_Rate ).minimize( cost_op )

Initialization Phase

We need to create an initialization operation, init_op, as well. It won't be executed yet, not until the session starts, but we have to do it first.

init_op = tf.initialize_all_variables()

Start the Session

We are now ready to start a session!

sess = tf.Session()
sess.run( init_op )

Training the NN

We now train the Neural Net for 1000 epoch. In each epoch we feed just one vector of x to the network.

batchSize = 5
prediction = tf.equal( tf.argmax( y, 1 ), tf.argmax( target, 1) )
accuracy = tf.reduce_mean ( tf.cast( prediction, tf.float32 ) )
for epoch in range( 10000 ):
   for i in range( 0, train_size, batchSize ):
   xx = x_train_np[ i:i+batchSize, : ]
   yy = y_train_np[ i:i+batchSize, : ]
   sess.run( train_op, feed_dict={x: xx, target: yy} )


if epoch%100 == 0:
   co, to = sess.run( [cost_op,train_op], feed_dict={x: x_train_np, target: y_train_np} )
   print( epoch, "cost =", co, end=" " )
   accuracyNum = sess.run( accuracy, feed_dict={x: x_train_np, target : y_train_np} )
   print( "Accuracy on training data = %1.2f%%" % (accuracyNum*100), end = " " )
   accuracyNum = sess.run( accuracy, feed_dict={ x: x_test_np, target : y_test_np} )
   print( "Accuracy on test data = %1.2f%%" % ( accuracyNum*100 ) )

if False:
   print( "y = ", sess.run( y, feed_dict={ x: x_train_np, target : y_train_np} ) )
   print( "softmax(y) = ", sess.run( tf.nn.softmax( y ), feed_dict={ x: x_train_np, target : y_train_np} ) )
   print( "tf.mul(tf.nn.softmax(y), target) = ",
   sess.run( tf.mul( tf.nn.softmax( y ), target ),
   feed_dict={ x: x_train_np, target : y_train_np} ) )

#
#prediction = tf.reduce_sum( tf.mul( tf.nn.softmax( y ), target ), reduction_indices=1 )
accuracyNum = sess.run( accuracy, feed_dict={x: x_train_np, target : y_train_np} )
print( "Final Accuracy on training data = %1.2f%%" % (100.0*accuracyNum) )
accuracyNum = sess.run( accuracy, feed_dict={ x: x_test_np, target : y_test_np} )
print( "Final Accuracy on test data = %1.2f%%" % (100.0*accuracyNum) )

Output

0 cost = 4.06461 Accuracy on training data = 7.78% Accuracy on test data = 0.00%
100 cost = 0.0568146 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
200 cost = 0.0249612 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
300 cost = 0.0156735 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
400 cost = 0.0113394 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
500 cost = 0.00885047 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
600 cost = 0.00724066 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
700 cost = 0.00611609 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
800 cost = 0.00528698 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
900 cost = 0.00465089 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1000 cost = 0.00414775 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1100 cost = 0.00374 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1200 cost = 0.00340309 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1300 cost = 0.00312006 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1400 cost = 0.00287907 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1500 cost = 0.00267149 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1600 cost = 0.00249079 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1700 cost = 0.00233219 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1800 cost = 0.00219193 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
1900 cost = 0.00206695 Accuracy on training data = 100.00% Accuracy on test data = 90.00%
2000 cost = 0.00195495 Accuracy on training data = 100.00% Accuracy on test data = 90.00%