Deep Learning

Keith Dillon
Spring 2019

drawing

Topic 7: Tensorflow

This topic:

  • Tensorflow

Reading:

  • Geron Chapter 9 (Up and Running with TensorFlow)
  • Geron Chapter 10 (Introduction to Artificial Neural Networks)

References

In [3]:
import tensorflow as tf
print(tf.VERSION)
1.13.1

Tensorflow

  • open source software library for numerical computation
  • Python & C API, many other languages but less supported
  • Underlying computations impemented in C++
  • Distributed & GPU (via CUDA) suppport $\rightarrow$ scalability
  • Mobile (Tensorflow ite), browser-based (Tensorflow.js) versions

Tensorflow API's

  • TF.Learn$^2$ API (tensorflow.con trib.learn),
    • compatible with Scikit-Learn.
    • can use it to train various types of neural networks in just a few lines of code
    • previously an independent project called Scikit Flow (or skflow).
  • TF-slim API (tensorflow.contrib.slim) to simplify building, training, and evaluating neural networks.
  • Several other high-level APIs built independently on top of TensorFlow
    • Keras
    • Pretty Tensor. Main Python API
    • much more flexibility (at the cost of higher complexity) to create all sorts of computations and neural network architectures
  • Includes highly efficient C++ implementations of many ML operations, particularly those needed to build neural networks.
  • A C++ API to define your own high-performance operations.

TensorBoard Visualization tool

  • Can browse through the computation graph,
  • view learning curves,
  • and more.

Computational Graph

A.k.a. Computation Graph

Break computation into a tree of elementary operations ("ops") and the flow of variables from input to outputs

drawing
  • Operations can take any number of inputs and produce any number of outputs
  • "+" operation takes two inputs and produces one output
  • Constants and variables are operations which take zero inputs and produce one output ("source ops")
  • inputs and outputs are multidimensional arrays called tensors (arrays of arrays of arrays of...)
    • Any number of dimensions
    • numpy ndarrays, e.g. [[[0,0],[0,0]],[[0,0],[0,0]],[[0,0],[0,0]]]

Computation graph for scalability

drawing

I. TF Basic operation

TensorFlow Graph

In [5]:
x = tf.Variable(3, name="x") 
y = tf.Variable(4, name="y") 
f = x*x*y + y + 2

Typing in the console/notebook like this sets a 'default graph', because TensorFlow supports multiple graphs (a faiirly unusual application, we won't need).

Note that the above code simply defines the default graph. It doesn't do anything.

TensorFlow Session object

  • Represents a connection between the client program (e.g. your Python script) and the C++ runtime.
  • Provides access to devices in the local machine, and remote devices using the distributed TensorFlow runtime.
  • Caches information about your tf.Graph so that you can efficiently run the same computation multiple times.
sess = tf.Session() sess.run(x.initializer) # equivalent to tf.get_default_session().run(x.initializer) sess.run(y.initializer) result = sess.run(f)

Process

  1. open a TensorFlow session
  2. use session to initialize the variables
  3. use session to evaluate f.
  4. close session to free up the resources
In [6]:
sess = tf.Session()
sess.run(x.initializer) # equivalent to tf.get_default_session().run(x.initializer)
sess.run(y.initializer)
result = sess.run(f)
print(result)
42
In [7]:
sess = tf.Session()
sess.run(x.initializer) # equivalent to tf.get_default_session().run(x.initializer)
sess.run(y.initializer)
result = sess.run(f)
print(result)
42
In [8]:
sess.close()

Python 'with' for cleanup

In [9]:
with tf.Session() as sess:
    x.initializer.run()
    y.initializer.run()
    result = f.eval() # equivalent to tf.get_default_session().run(f)
    
result
Out[9]:
42

Global Variables Initializer

creates a node in the graph that will initialize all variables when it is run

In [15]:
init = tf.global_variables_initializer()

InteractiveSession

  • Automatically sets itself as the default session
  • Only need to close it when done.
In [16]:
sess = tf.InteractiveSession()
init.run()
result = f.eval()
print(result)
42
In [17]:
sess.close()

II. Managing Graphs

Resetting graph

removes all nodes

In [18]:
tf.reset_default_graph()
In [4]:
# code to make this notebook's output stable across runs

def reset_graph(seed=42):
    tf.reset_default_graph()
    tf.set_random_seed(seed)
    np.random.seed(seed)

Adding nodes

Any node you create is automatically added to the default graph

In [20]:
x1 = tf.Variable(1)
x1.graph is tf.get_default_graph()
Out[20]:
True

Creating another graph (not as default)

In [21]:
graph = tf.Graph()
with graph.as_default():
    x2 = tf.Variable(2)

x2.graph is graph
Out[21]:
True
In [22]:
x2.graph is tf.get_default_graph()
Out[22]:
False

Evaluating Node Values

When you evaluate a node, TensorFlow automatically determines the set of nodes that it depends on and it evaluates these nodes first

In [23]:
w = tf.constant(3)
x = w + 2
y = x + 5
z = x * 3

with tf.Session() as sess:
    print(y.eval())  # 10
    print(z.eval())  # 15
10
15
w = tf.constant(3) x = w + 2 y = x + 5 z = x * 3
  • for y.eval(), TF computes x then y
  • For z.eval(), TF computes x then y then z
  • Note that this code recomputes w and x twice (one for each eval)

Evaluate multiple nodes at same time for efficiency

Tell TF to compute y and z in single evaluation of graph:

In [24]:
with tf.Session() as sess:
    y_val, z_val = sess.run([y, z])
    print(y_val)  # 10
    print(z_val)  # 15
10
15

III. Optimizing models with TF

Linear Regression with TensorFlow

  • $\mathbf X$ = data matrix (columns are features, rows are samples)
  • $\mathbf y$ = target vector of prices

We want a model (parametrized by $\boldsymbol\theta$) that estimates prices from features

$$ \mathbf X \boldsymbol\theta = \mathbf y$$

Exercise: draw a network that implements this computation

Hint: Compute one sample at a time

In [11]:
import numpy as np
from sklearn.datasets import fetch_california_housing
housing = fetch_california_housing()
Downloading Cal. housing from https://ndownloader.figshare.com/files/5976036 to /home/keith/scikit_learn_data

(appending a vector of ones to include a bias)

In [12]:
m, n = housing.data.shape
housing_data_plus_bias = np.c_[np.ones((m, 1)), housing.data] 

Plan A: Pseudoinverse solution

$$ \hat{\boldsymbol\theta} = (\mathbf X^T \mathbf X)^{-1} \mathbf X^T \mathbf y = \mathbf X^\dagger \mathbf y$$

As a computational graph, need nodes for:

  • the $\mathbf y$ input vector
  • the $\mathbf X^\dagger$ input matrix
  • the output product $\mathbf X^\dagger \mathbf y$
In [27]:
# make the graph for applying the pseudoinverse and evaluate it

reset_graph()
X = tf.constant(housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
XT = tf.transpose(X)
theta = tf.matmul(tf.matmul(tf.matrix_inverse(tf.matmul(XT, X)), XT), y)

with tf.Session() as sess:
    theta_value = theta.eval()
In [28]:
print(theta_value)
[[-3.62395554e+01]
 [ 4.38410223e-01]
 [ 9.56030935e-03]
 [-1.09072715e-01]
 [ 6.50818944e-01]
 [-3.61849015e-06]
 [-3.80502851e-03]
 [-4.14003015e-01]
 [-4.26401258e-01]]

Perform same operations in NumPy

In [13]:
X = housing_data_plus_bias
y = housing.target.reshape(-1, 1)
theta_numpy = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y) 

print(theta_numpy)
[[-3.69419202e+01]
 [ 4.36693293e-01]
 [ 9.43577803e-03]
 [-1.07322041e-01]
 [ 6.45065694e-01]
 [-3.97638942e-06]
 [-3.78654265e-03]
 [-4.21314378e-01]
 [-4.34513755e-01]]

Also...

  • note there's a numpy.linalg.pinv function too

  • And a sklearn linear regression model, which will handle bias for you

Plan B: Gradient Descent Solution (gradient by hand)

Rather implementing the inverse function as a graph, we will implement the forward function for computing the MSE

$$ MSE = \frac{1}{N}\Vert \mathbf X \boldsymbol\theta - \mathbf y\Vert^2$$

We can use the gradient of this function wrt $\boldsymbol\theta$ to find the minimizer $\boldsymbol\theta^*$, via gradient descent.

Graph nodes:

  1. the $\mathbf y$ input vector constant
  2. the $\mathbf X$ input matrix constant
  3. $\boldsymbol\theta$ input variable vector
  4. $\mathbf X \boldsymbol\theta = \mathbf y_{pred}$ calculation
  5. $\mathbf y - \mathbf y_{pred} = error$ calculation
  6. $\frac{1}{N}\Vert error \Vert^2 = mse$ calculation
In [14]:
# First normalize the data

from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
scaled_housing_data = scaler.fit_transform(housing.data)
scaled_housing_data_plus_bias = np.c_[np.ones((m, 1)), scaled_housing_data]
In [31]:
# now make the graph

reset_graph()

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")


# initialize to uniform random #s
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta") 

y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")
In [32]:
# manually compute gradient 
gradients = 2/m * tf.matmul(tf.transpose(X), error)

# implement as additional node which changes theta
learning_rate = 0.01
training_op = tf.assign(theta, theta - learning_rate * gradients)
In [33]:
# initialize and run graph

n_epochs = 1000

init = tf.global_variables_initializer()

with tf.Session() as sess:
    sess.run(init)

    for epoch in range(n_epochs):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())
        sess.run(training_op)
    
    best_theta = theta.eval()
Epoch 0 MSE = 9.16154
Epoch 100 MSE = 0.71450025
Epoch 200 MSE = 0.56670487
Epoch 300 MSE = 0.55557173
Epoch 400 MSE = 0.5488112
Epoch 500 MSE = 0.54363626
Epoch 600 MSE = 0.5396291
Epoch 700 MSE = 0.5365092
Epoch 800 MSE = 0.5340677
Epoch 900 MSE = 0.5321473
In [34]:
print(best_theta)
[[ 2.0685525 ]
 [ 0.8874028 ]
 [ 0.14401656]
 [-0.3477089 ]
 [ 0.36178377]
 [ 0.00393811]
 [-0.04269556]
 [-0.6614528 ]
 [-0.63752776]]
In [35]:
# numpy pseudoinverse with scaled data

theta_numpy = np.linalg.pinv(scaled_housing_data_plus_bias).dot(housing.target.reshape(-1, 1))
print(theta_numpy)
[[ 2.06855817]
 [ 0.8296193 ]
 [ 0.11875165]
 [-0.26552688]
 [ 0.30569623]
 [-0.004503  ]
 [-0.03932627]
 [-0.89988565]
 [-0.870541  ]]

Plan C: Using Autodiff

Rather than specify the gradient ourselves, we tell TF to compute it for a node and choice of variable(s)

https://www.tensorflow.org/api_docs/python/tf/gradients

drawing
In [15]:
# first remake the graph to remove old gradient node

reset_graph()

n_epochs = 1000
learning_rate = 0.01

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")
In [16]:
# gradient time

gradients = tf.gradients(mse, [theta])[0]
In [17]:
# now proceed as before

training_op = tf.assign(theta, theta - learning_rate * gradients)
init = tf.global_variables_initializer()

with tf.Session() as sess:
    sess.run(init)
    for epoch in range(n_epochs):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())
        sess.run(training_op)
    
    best_theta = theta.eval()
Epoch 0 MSE = 9.161543
Epoch 100 MSE = 0.7145006
Epoch 200 MSE = 0.56670463
Epoch 300 MSE = 0.5555716
Epoch 400 MSE = 0.5488117
Epoch 500 MSE = 0.5436362
Epoch 600 MSE = 0.5396292
Epoch 700 MSE = 0.53650916
Epoch 800 MSE = 0.53406775
Epoch 900 MSE = 0.53214717
In [18]:
print(best_theta)
[[ 2.0685525 ]
 [ 0.8874027 ]
 [ 0.14401658]
 [-0.3477088 ]
 [ 0.36178368]
 [ 0.00393811]
 [-0.04269556]
 [-0.6614529 ]
 [-0.6375278 ]]

Plan D: TF Optimizer

TF can automatically add the gradient update operation

This is handy because there are many possible options there (momentum, acceleration, etc.)

https://www.tensorflow.org/api_docs/python/tf/optimizers

In [19]:
# redefine graph up to the MSE calculation node

reset_graph()

n_epochs = 1000
learning_rate = 0.01

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")
In [20]:
# new lines

optimizer  = tf.train.GradientDescentOptimizer(learning_rate=learning_rate) 
#optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,momentum=0.9) # alternative approch
training_op = optimizer.minimize(mse)
In [21]:
init = tf.global_variables_initializer()

with tf.Session() as sess:
    sess.run(init)

    for epoch in range(n_epochs):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())
        sess.run(training_op)
    
    best_theta = theta.eval()
Epoch 0 MSE = 9.161543
Epoch 100 MSE = 0.7145006
Epoch 200 MSE = 0.56670463
Epoch 300 MSE = 0.5555716
Epoch 400 MSE = 0.5488117
Epoch 500 MSE = 0.5436362
Epoch 600 MSE = 0.5396292
Epoch 700 MSE = 0.53650916
Epoch 800 MSE = 0.53406775
Epoch 900 MSE = 0.53214717
In [22]:
print("Best theta:")
print(best_theta)
Best theta:
[[ 2.0685525 ]
 [ 0.8874027 ]
 [ 0.14401658]
 [-0.3477088 ]
 [ 0.36178368]
 [ 0.00393811]
 [-0.04269556]
 [-0.6614529 ]
 [-0.6375278 ]]

Feeding Data for Training

Thus far we have used the entire dataset for each iteration

For batch stochastic gradient descent we want to use a different subset each iteration

Recall the network that operates on one sample at a time

Can use TF feed_dict to feed input data at time evaluation to a node rather than computing it

Use placeholder node if value will always be fed

In [23]:
# tiny example of feeding data to placeholder node at time of evaluation of node

reset_graph()

A = tf.placeholder(tf.float32, shape=(None, 3))
B = A + 5
with tf.Session() as sess:
    B_val_1 = B.eval(feed_dict={A: [[1, 2, 3]]})
    B_val_2 = B.eval(feed_dict={A: [[4, 5, 6], [7, 8, 9]]})

print(B_val_1)
[[6. 7. 8.]]
In [43]:
print(B_val_2)
[[ 9. 10. 11.]
 [12. 13. 14.]]

Mini-batch Gradient Descent

In [44]:
# now make X and y in our regression graph into placeholders

reset_graph()

X = tf.placeholder(tf.float32, shape=(None, n + 1), name="X")
y = tf.placeholder(tf.float32, shape=(None, 1), name="y")
In [45]:
# construct rest of graph and optimizer same as before

learning_rate = 0.01

theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")

optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(mse)

init = tf.global_variables_initializer()
In [48]:
# homemade function to return batches of data

def fetch_batch(epoch, batch_index, batch_size):
    np.random.seed(epoch * n_batches + batch_index)  
    indices = np.random.randint(m, size=batch_size)  
    X_batch = scaled_housing_data_plus_bias[indices] 
    y_batch = housing.target.reshape(-1, 1)[indices] 
    return X_batch, y_batch
In [46]:
n_epochs = 10
In [47]:
batch_size = 100
n_batches = int(np.ceil(m / batch_size))
In [49]:
# loop through data feeding batches

with tf.Session() as sess:
    sess.run(init)
    for epoch in range(n_epochs):
        for batch_index in range(n_batches):
            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})

    best_theta = theta.eval()

print(best_theta)
[[ 2.0703337 ]
 [ 0.86371446]
 [ 0.12255151]
 [-0.31211877]
 [ 0.38510376]
 [ 0.00434168]
 [-0.01232954]
 [-0.83376896]
 [-0.8030471 ]]

Saving and Restoring Models

  • Save the parameters you worked so hard to optimize when done
  • Also save intermediate values to analyze or go back
In [ ]:
# create a saver node and call during training

reset_graph()

n_epochs = 1000                                                                 
learning_rate = 0.01                                                               

X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name="X")          
y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name="y")            
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")                                     
error = y_pred - y                                                                  
mse = tf.reduce_mean(tf.square(error), name="mse")                                    
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)            
training_op = optimizer.minimize(mse)                                                

init = tf.global_variables_initializer()

saver = tf.train.Saver()
In [72]:
with tf.Session() as sess:
    sess.run(init)

    for epoch in range(n_epochs):
        if epoch % 100 == 0:
            print("Epoch", epoch, "MSE =", mse.eval())                            
            save_path = saver.save(sess, "./my_model.ckpt")
        sess.run(training_op)
    
    best_theta = theta.eval()
    save_path = saver.save(sess, "./my_model_final.ckpt")
Epoch 0 MSE = 9.16154
Epoch 100 MSE = 0.7145004
Epoch 200 MSE = 0.56670487
Epoch 300 MSE = 0.55557173
Epoch 400 MSE = 0.5488112
Epoch 500 MSE = 0.54363626
Epoch 600 MSE = 0.53962904
Epoch 700 MSE = 0.5365092
Epoch 800 MSE = 0.53406775
Epoch 900 MSE = 0.5321473
In [51]:
# load model

with tf.Session() as sess:
    saver.restore(sess, "./my_model_final.ckpt")
    best_theta_restored = theta.eval() # not shown in the book
INFO:tensorflow:Restoring parameters from ./my_model_final.ckpt

Visualization

Thus far we've been essentially using "printf" debugging

Graphical tools:

  • Tensorboard
  • tfgraphviz

Tensorboard

Step 1. Logging

Need to tell your program to log the data

note TB will merge logs so must separate them into different directories if needed.

In [53]:
from datetime import datetime

# For TB: put this at beginning
now = datetime.utcnow().strftime("%Y%m%d%H%M%S")
root_logdir = "tf_logs"
logdir = "{}/run-{}/".format(root_logdir, now)
In [54]:
# now define graph again

n_epochs = 1000
learning_rate = 0.01

X = tf.placeholder(tf.float32, shape=(None, n + 1), name="X")
y = tf.placeholder(tf.float32, shape=(None, 1), name="y")
theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name="theta")
y_pred = tf.matmul(X, theta, name="predictions")
error = y_pred - y
mse = tf.reduce_mean(tf.square(error), name="mse")
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)
training_op = optimizer.minimize(mse)

init = tf.global_variables_initializer()
In [60]:
# For TB: put this after graph defined 

mse_summary = tf.summary.scalar('MSE', mse) # add node which saves MSE to log

# initialize filewriter object
file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())
In [61]:
# Run model and evaluate logging node every 10 batches (to reduce computational cost)

n_epochs = 10
batch_size = 100
n_batches = int(np.ceil(m / batch_size))

with tf.Session() as sess:                                                   
    sess.run(init)                                                              

    for epoch in range(n_epochs):                                          
        for batch_index in range(n_batches):
            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)
            if batch_index % 10 == 0:
                summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})
                step = epoch * n_batches + batch_index
                file_writer.add_summary(summary_str, step)
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})

    best_theta = theta.eval()                                               
In [62]:
file_writer.close()
In [58]:
best_theta
Out[58]:
array([[ 2.0703337 ],
       [ 0.86371446],
       [ 0.12255151],
       [-0.31211877],
       [ 0.38510376],
       [ 0.00434168],
       [-0.01232954],
       [-0.83376896],
       [-0.8030471 ]], dtype=float32)

Should be able to see a new log directory tf_logs/run*

If you run the program a second time, you should see a second directory in the tf_logs/ directory

Step 2. Visualizing logs

Book site refers to TensorBoard server available online at https://tensorboard.appspot.com/

But site not found...

  • Run own server using Anaconda prompt (be sure to use proper environment to find TF)
  • Must give logdir as argument.
  • Navigate to link given in a web browser
drawing
drawing

Click on the 'Graphs' tab to see visualizations of the graph

drawing

Code to display graphs in Jupyter, contains wrapper around web-based version of TB: https://github.com/ageron/handson-ml/blob/master/tensorflow_graph_in_jupyter.py

In [73]:
from tensorflow_graph_in_jupyter import show_graph

show_graph(tf.get_default_graph())

Name Scopes

  • Group related nodes for clarity
  • Creates prefix for node names
In [65]:
with tf.name_scope("loss") as scope:    
    error = y_pred - y    
    mse = tf.reduce_mean(tf.square(error), name="mse") 
In [67]:
print(error.op.name) 
print(mse.op.name) 
loss/sub
loss/mse

Name scopes are collapsed within TB

drawing

Modularity

Use functions to reuse code defining graph structure

TF will automatically add numbers to end repeated names

In [24]:
reset_graph()

with tf.variable_scope("my_scope"):
    x0 = tf.get_variable("x", shape=(), initializer=tf.constant_initializer(0.))
    x1 = tf.Variable(0., name="x")
    x2 = tf.Variable(0., name="x")

with tf.variable_scope("my_scope", reuse=True):
    x3 = tf.get_variable("x")
    x4 = tf.Variable(0., name="x")

with tf.variable_scope("", default_name="", reuse=True):
    x5 = tf.get_variable("my_scope/x")
In [25]:
print("x0:", x0.op.name)
print("x1:", x1.op.name)
print("x2:", x2.op.name)
print("x3:", x3.op.name)
print("x4:", x4.op.name)
print("x5:", x5.op.name)
print(x0 is x3 and x3 is x5)
x0: my_scope/x
x1: my_scope/x_1
x2: my_scope/x_2
x3: my_scope/x
x4: my_scope_1/x
x5: my_scope/x
True
In [ ]:
with tf.variable_scope("my_scope"):
    x0 = tf.get_variable("x", shape=(), initializer=tf.constant_initializer(0.))
    x1 = tf.Variable(0., name="x")
    x2 = tf.Variable(0., name="x")
  • creates the shared variable x0, named my_scope/x.
  • For all operations other than shared variables (including non-shared variables), the variable scope acts like a regular name scope, which is why the two variables x1 and x2 have a name with a prefix my_scope/.
  • TensorFlow makes their names unique by adding an index: my_scope/x_1 and my_scope/x_2.
In [26]:
print("x0:", x0.op.name)
print("x1:", x1.op.name)
print("x2:", x2.op.name)
x0: my_scope/x
x1: my_scope/x_1
x2: my_scope/x_2
In [ ]:
with tf.variable_scope("my_scope", reuse=True):
    x3 = tf.get_variable("x")
    x4 = tf.Variable(0., name="x")
  • reuses the shared variables in scope my_scope, which is why x0 is x3. O
  • again, for all operations other than shared variables it acts as a named scope
  • since it's a separate block from the first one, the name of the scope is made unique by TensorFlow (my_scope_1) and thus the variable x4 is named my_scope_1/x.
In [27]:
print("x3:", x3.op.name)
print("x4:", x4.op.name)
x3: my_scope/x
x4: my_scope_1/x
In [ ]:
with tf.variable_scope("", default_name="", reuse=True):
    x5 = tf.get_variable("my_scope/x")
  • shows another way to get a handle on the shared variable my_scope/x by creating a variable_scope() at the root scope (whose name is an empty string)
  • then calling get_variable() with the full name of the shared variable (i.e. "my_scope/x").
In [28]:
print("x5:", x5.op.name)
print(x0 is x3 and x3 is x5)
x5: my_scope/x
True

Example network with multiple ReLU functions

In [ ]:
# Plan 1: Repeated-code version

reset_graph()

n_features = 3
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")

w1 = tf.Variable(tf.random_normal((n_features, 1)), name="weights1")
w2 = tf.Variable(tf.random_normal((n_features, 1)), name="weights2")
b1 = tf.Variable(0.0, name="bias1")
b2 = tf.Variable(0.0, name="bias2")

z1 = tf.add(tf.matmul(X, w1), b1, name="z1")
z2 = tf.add(tf.matmul(X, w2), b2, name="z2")

relu1 = tf.maximum(z1, 0., name="relu1")
relu2 = tf.maximum(z1, 0., name="relu2")  # Oops, cut&paste error! Did you spot it?

output = tf.add(relu1, relu2, name="output")
In [ ]:
# Plan 2: Function version

# relies on TF to rename the nodes

reset_graph()

def relu(X):
    w_shape = (int(X.get_shape()[1]), 1)
    w = tf.Variable(tf.random_normal(w_shape), name="weights")
    b = tf.Variable(0.0, name="bias")
    z = tf.add(tf.matmul(X, w), b, name="z")
    return tf.maximum(z, 0., name="relu")

n_features = 3
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
relus = [relu(X) for i in range(5)]
output = tf.add_n(relus, name="output")
In [ ]:
# Plan 3: Name scope function version

reset_graph()

def relu(X):
    with tf.name_scope("relu"):
        w_shape = (int(X.get_shape()[1]), 1)                      
        w = tf.Variable(tf.random_normal(w_shape), name="weights")    
        b = tf.Variable(0.0, name="bias")                            
        z = tf.add(tf.matmul(X, w), b, name="z")                     
        return tf.maximum(z, 0., name="max")                        
    
n_features = 3
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
relus = [relu(X) for i in range(5)]
output = tf.add_n(relus, name="output")

file_writer = tf.summary.FileWriter("logs/relu2", tf.get_default_graph())
file_writer.close()

Sharing Variables

If your model enforces the use of the same value for multiple parameters, there are many ways to achieve this:

  • create a Python dictionary containing all the variables in their model, and pass it around to every function.
  • create a class for each module (e.g., a ReLU class using class variables to handle the shared parameter)
  • set the shared variable as an attribute of the relu() function upon the first call
In [ ]:
# Plan X: Sharing a variable the classic way:
# 1. defining it outside of the relu() function 
# 2. passing it as a parameter:

reset_graph()

def relu(X, threshold):
    with tf.name_scope("relu"):
        w_shape = (int(X.get_shape()[1]), 1)                        # not shown in the book
        w = tf.Variable(tf.random_normal(w_shape), name="weights")  # not shown
        b = tf.Variable(0.0, name="bias")                           # not shown
        z = tf.add(tf.matmul(X, w), b, name="z")                    # not shown
        return tf.maximum(z, threshold, name="max")

threshold = tf.Variable(0.0, name="threshold")
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
relus = [relu(X, threshold) for i in range(5)]
output = tf.add_n(relus, name="output")
In [ ]:
# Plan Y: Sharing a variable by setting it as an attribute

reset_graph()

def relu(X):
    with tf.name_scope("relu"):
        if not hasattr(relu, "threshold"):
            relu.threshold = tf.Variable(0.0, name="threshold")
        w_shape = int(X.get_shape()[1]), 1                          
        w = tf.Variable(tf.random_normal(w_shape), name="weights")  
        b = tf.Variable(0.0, name="bias")                           
        z = tf.add(tf.matmul(X, w), b, name="z")                    
        return tf.maximum(z, relu.threshold, name="max")
X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")

relus = [relu(X) for i in range(5)]
output = tf.add_n(relus, name="output")

Plan Z: Built-in TF option:

  • use the get_variable() function
  • to create the shared variable if it does not exist yet,
  • or reuse it if it already exists
In [ ]:
reset_graph()

with tf.variable_scope("relu"):
    threshold = tf.get_variable("threshold", shape=(), initializer=tf.constant_initializer(0.0))

with tf.variable_scope("relu", reuse=True):
    threshold = tf.get_variable("threshold")
    
with tf.variable_scope("relu") as scope:
    scope.reuse_variables()
    threshold = tf.get_variable("threshold")
In [ ]:
reset_graph()

def relu(X):
    with tf.variable_scope("relu", reuse=True):
        threshold = tf.get_variable("threshold")
        w_shape = int(X.get_shape()[1]), 1                          # not shown
        w = tf.Variable(tf.random_normal(w_shape), name="weights")  # not shown
        b = tf.Variable(0.0, name="bias")                           # not shown
        z = tf.add(tf.matmul(X, w), b, name="z")                    # not shown
        return tf.maximum(z, threshold, name="max")

X = tf.placeholder(tf.float32, shape=(None, n_features), name="X")
with tf.variable_scope("relu"):
    threshold = tf.get_variable("threshold", shape=(),
                                initializer=tf.constant_initializer(0.0))
relus = [relu(X) for relu_index in range(5)]
output = tf.add_n(relus, name="output")
In [ ]:
 
In [ ]:
 
In [ ]:
 
In [18]:
# SETUP

# To support both python 2 and python 3
from __future__ import division, print_function, unicode_literals

# Common imports
import numpy as np
import os

# to make this notebook's output stable across runs
def reset_graph(seed=42):
    tf.reset_default_graph()
    tf.set_random_seed(seed)
    np.random.seed(seed)

# To plot pretty figures
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12

# Where to save the figures
PROJECT_ROOT_DIR = "."
CHAPTER_ID = "ann"

def save_fig(fig_id, tight_layout=True):
    path = os.path.join(PROJECT_ROOT_DIR, "images", CHAPTER_ID, fig_id + ".png")
    print("Saving figure", fig_id)
    if tight_layout:
        plt.tight_layout()
    plt.savefig(path, format='png', dpi=300)
In [ ]:
 
In [ ]:
 

IV. Multi-Layer Perceptron with TF

Plan A: TF MLP with High-Level API

TF.Learn = TensorFlow’s High-Level API

Quite similar to Scikit-Learn’s API:

  1. call constructor for model giving parameters
  2. fit() to optimize model using training data
  3. evaluate() to compute accuracy on test data
  4. predict() to estimate target for a sample

DNNClassifier class

  • makes it trivial to train a deep neural network with any number of hidden layers,
  • and a softmax output layer to output estimated class probabilities.
In [8]:
# train a DNN for classification with two hidden layers 
# one with 300 neurons, and the other with 100 neurons
# and a softmax output layer with 10 neurons:

import tensorflow as tf

# Fetch the data and split into training, test, and validation sets

(X_train, y_train), (X_test, y_test) = tf.keras.datasets.mnist.load_data()
X_train = X_train.astype(np.float32).reshape(-1, 28*28) / 255.0
X_test = X_test.astype(np.float32).reshape(-1, 28*28) / 255.0
y_train = y_train.astype(np.int32)
y_test = y_test.astype(np.int32)
X_valid, X_train = X_train[:5000], X_train[5000:]
y_valid, y_train = y_train[:5000], y_train[5000:]
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz
11493376/11490434 [==============================] - 2s 0us/step
In [14]:
import tensorflow as tf
feature_columns = tf.contrib.learn.infer_real_valued_columns_from_input(X_train) 
dnn_clf = tf.contrib.learn.DNNClassifier(hidden_units=[300, 100], n_classes=10,feature_columns=feature_columns) 
dnn_clf.fit(x=X_train, y=y_train, batch_size=50, steps=40000) 
WARNING: The TensorFlow contrib module will not be included in TensorFlow 2.0.
For more information, please see:
  * https://github.com/tensorflow/community/blob/master/rfcs/20180907-contrib-sunset.md
  * https://github.com/tensorflow/addons
If you depend on functionality not listed there, please file an issue.

WARNING:tensorflow:From <ipython-input-14-e9d33b98135b>:2: infer_real_valued_columns_from_input (from tensorflow.contrib.learn.python.learn.estimators.estimator) is deprecated and will be removed in a future version.
Instructions for updating:
Please specify feature columns explicitly.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\estimators\estimator.py:143: setup_train_data_feeder (from tensorflow.contrib.learn.python.learn.learn_io.data_feeder) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tensorflow/transform or tf.data.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\learn_io\data_feeder.py:100: extract_pandas_data (from tensorflow.contrib.learn.python.learn.learn_io.pandas_io) is deprecated and will be removed in a future version.
Instructions for updating:
Please access pandas data directly.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\learn_io\data_feeder.py:159: DataFeeder.__init__ (from tensorflow.contrib.learn.python.learn.learn_io.data_feeder) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tensorflow/transform or tf.data.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\learn_io\data_feeder.py:340: check_array (from tensorflow.contrib.learn.python.learn.learn_io.data_feeder) is deprecated and will be removed in a future version.
Instructions for updating:
Please convert numpy dtypes explicitly.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\estimators\estimator.py:183: infer_real_valued_columns_from_input_fn (from tensorflow.contrib.learn.python.learn.estimators.estimator) is deprecated and will be removed in a future version.
Instructions for updating:
Please specify feature columns explicitly.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\estimators\dnn.py:378: multi_class_head (from tensorflow.contrib.learn.python.learn.estimators.head) is deprecated and will be removed in a future version.
Instructions for updating:
Please switch to tf.contrib.estimator.*_head.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\estimators\estimator.py:1179: BaseEstimator.__init__ (from tensorflow.contrib.learn.python.learn.estimators.estimator) is deprecated and will be removed in a future version.
Instructions for updating:
Please replace uses of any Estimator from tf.contrib.learn with an Estimator from tf.estimator.*
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\estimators\estimator.py:427: RunConfig.__init__ (from tensorflow.contrib.learn.python.learn.estimators.run_config) is deprecated and will be removed in a future version.
Instructions for updating:
When switching to tf.estimator.Estimator, use tf.estimator.RunConfig instead.
INFO:tensorflow:Using default config.
WARNING:tensorflow:Using temporary folder as model directory: C:\Users\Keith\AppData\Local\Temp\tmp1qywvh85
INFO:tensorflow:Using config: {'_task_type': None, '_task_id': 0, '_cluster_spec': <tensorflow.python.training.server_lib.ClusterSpec object at 0x000001ACC34CF588>, '_master': '', '_num_ps_replicas': 0, '_num_worker_replicas': 0, '_environment': 'local', '_is_chief': True, '_evaluation_master': '', '_train_distribute': None, '_eval_distribute': None, '_device_fn': None, '_tf_config': gpu_options {
  per_process_gpu_memory_fraction: 1.0
}
, '_tf_random_seed': None, '_save_summary_steps': 100, '_save_checkpoints_secs': 600, '_log_step_count_steps': 100, '_protocol': None, '_session_config': None, '_save_checkpoints_steps': None, '_keep_checkpoint_max': 5, '_keep_checkpoint_every_n_hours': 10000, '_model_dir': 'C:\\Users\\Keith\\AppData\\Local\\Temp\\tmp1qywvh85'}
WARNING:tensorflow:From <ipython-input-14-e9d33b98135b>:4: calling BaseEstimator.fit (from tensorflow.contrib.learn.python.learn.estimators.estimator) with x is deprecated and will be removed after 2016-12-01.
Instructions for updating:
Estimator is decoupled from Scikit Learn interface by moving into
separate class SKCompat. Arguments x, y and batch_size are only
available in the SKCompat class, Estimator will only accept input_fn.
Example conversion:
  est = Estimator(...) -> est = SKCompat(Estimator(...))
WARNING:tensorflow:From <ipython-input-14-e9d33b98135b>:4: calling BaseEstimator.fit (from tensorflow.contrib.learn.python.learn.estimators.estimator) with y is deprecated and will be removed after 2016-12-01.
Instructions for updating:
Estimator is decoupled from Scikit Learn interface by moving into
separate class SKCompat. Arguments x, y and batch_size are only
available in the SKCompat class, Estimator will only accept input_fn.
Example conversion:
  est = Estimator(...) -> est = SKCompat(Estimator(...))
WARNING:tensorflow:From <ipython-input-14-e9d33b98135b>:4: calling BaseEstimator.fit (from tensorflow.contrib.learn.python.learn.estimators.estimator) with batch_size is deprecated and will be removed after 2016-12-01.
Instructions for updating:
Estimator is decoupled from Scikit Learn interface by moving into
separate class SKCompat. Arguments x, y and batch_size are only
available in the SKCompat class, Estimator will only accept input_fn.
Example conversion:
  est = Estimator(...) -> est = SKCompat(Estimator(...))
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\estimators\estimator.py:508: SKCompat.__init__ (from tensorflow.contrib.learn.python.learn.estimators.estimator) is deprecated and will be removed in a future version.
Instructions for updating:
Please switch to the Estimator interface.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\learn_io\data_feeder.py:102: extract_pandas_labels (from tensorflow.contrib.learn.python.learn.learn_io.pandas_io) is deprecated and will be removed in a future version.
Instructions for updating:
Please access pandas data directly.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\estimators\head.py:677: ModelFnOps.__new__ (from tensorflow.contrib.learn.python.learn.estimators.model_fn) is deprecated and will be removed in a future version.
Instructions for updating:
When switching to tf.estimator.Estimator, use tf.estimator.EstimatorSpec. You can use the `estimator_spec` method to create an equivalent one.
INFO:tensorflow:Create CheckpointSaverHook.
INFO:tensorflow:Graph was finalized.
INFO:tensorflow:Running local_init_op.
INFO:tensorflow:Done running local_init_op.
INFO:tensorflow:Saving checkpoints for 0 into C:\Users\Keith\AppData\Local\Temp\tmp1qywvh85\model.ckpt.
INFO:tensorflow:loss = 2.3020055, step = 1
INFO:tensorflow:global_step/sec: 77.3472
INFO:tensorflow:loss = 0.2862603, step = 101 (1.287 sec)
INFO:tensorflow:global_step/sec: 108.696
INFO:tensorflow:loss = 0.2626466, step = 201 (0.917 sec)
INFO:tensorflow:global_step/sec: 131.665
INFO:tensorflow:loss = 0.37034413, step = 301 (0.762 sec)
INFO:tensorflow:global_step/sec: 110.132
INFO:tensorflow:loss = 0.2160385, step = 401 (0.907 sec)
INFO:tensorflow:global_step/sec: 129.955
INFO:tensorflow:loss = 0.25369272, step = 501 (0.769 sec)
INFO:tensorflow:global_step/sec: 119.976
INFO:tensorflow:loss = 0.054453988, step = 601 (0.838 sec)
INFO:tensorflow:global_step/sec: 136.612
INFO:tensorflow:loss = 0.14657785, step = 701 (0.732 sec)
INFO:tensorflow:global_step/sec: 131.84
INFO:tensorflow:loss = 0.23870543, step = 801 (0.754 sec)
INFO:tensorflow:global_step/sec: 100.1
INFO:tensorflow:loss = 0.1002015, step = 901 (1.000 sec)
INFO:tensorflow:global_step/sec: 133.869
INFO:tensorflow:loss = 0.2069863, step = 1001 (0.746 sec)
INFO:tensorflow:global_step/sec: 146.413
INFO:tensorflow:loss = 0.14901677, step = 1101 (0.682 sec)
INFO:tensorflow:global_step/sec: 139.567
INFO:tensorflow:loss = 0.14633244, step = 1201 (0.717 sec)
INFO:tensorflow:global_step/sec: 148.258
INFO:tensorflow:loss = 0.12762839, step = 1301 (0.675 sec)
INFO:tensorflow:global_step/sec: 136.705
INFO:tensorflow:loss = 0.07708808, step = 1401 (0.732 sec)
INFO:tensorflow:global_step/sec: 117.509
INFO:tensorflow:loss = 0.111827396, step = 1501 (0.850 sec)
INFO:tensorflow:global_step/sec: 142.755
INFO:tensorflow:loss = 0.15285447, step = 1601 (0.700 sec)
INFO:tensorflow:global_step/sec: 129.115
INFO:tensorflow:loss = 0.03738655, step = 1701 (0.776 sec)
INFO:tensorflow:global_step/sec: 124.533
INFO:tensorflow:loss = 0.13448748, step = 1801 (0.807 sec)
INFO:tensorflow:global_step/sec: 133.422
INFO:tensorflow:loss = 0.14104086, step = 1901 (0.745 sec)
INFO:tensorflow:global_step/sec: 140.746
INFO:tensorflow:loss = 0.09909964, step = 2001 (0.711 sec)
INFO:tensorflow:global_step/sec: 115.674
INFO:tensorflow:loss = 0.017417703, step = 2101 (0.864 sec)
INFO:tensorflow:global_step/sec: 147.929
INFO:tensorflow:loss = 0.026840923, step = 2201 (0.676 sec)
INFO:tensorflow:global_step/sec: 115.674
INFO:tensorflow:loss = 0.03675856, step = 2301 (0.864 sec)
INFO:tensorflow:global_step/sec: 116.618
INFO:tensorflow:loss = 0.06779099, step = 2401 (0.858 sec)
INFO:tensorflow:global_step/sec: 106.327
INFO:tensorflow:loss = 0.07686894, step = 2501 (0.950 sec)
INFO:tensorflow:global_step/sec: 121.951
INFO:tensorflow:loss = 0.049974646, step = 2601 (0.813 sec)
INFO:tensorflow:global_step/sec: 122.026
INFO:tensorflow:loss = 0.021585865, step = 2701 (0.818 sec)
INFO:tensorflow:global_step/sec: 130.208
INFO:tensorflow:loss = 0.03496332, step = 2801 (0.769 sec)
INFO:tensorflow:global_step/sec: 121.359
INFO:tensorflow:loss = 0.16399623, step = 2901 (0.823 sec)
INFO:tensorflow:global_step/sec: 118.765
INFO:tensorflow:loss = 0.017933732, step = 3001 (0.841 sec)
INFO:tensorflow:global_step/sec: 130.89
INFO:tensorflow:loss = 0.051229175, step = 3101 (0.764 sec)
INFO:tensorflow:global_step/sec: 120.627
INFO:tensorflow:loss = 0.010760326, step = 3201 (0.831 sec)
INFO:tensorflow:global_step/sec: 133.333
INFO:tensorflow:loss = 0.030692268, step = 3301 (0.750 sec)
INFO:tensorflow:global_step/sec: 105.374
INFO:tensorflow:loss = 0.15963605, step = 3401 (0.947 sec)
INFO:tensorflow:global_step/sec: 98.4252
INFO:tensorflow:loss = 0.10293282, step = 3501 (1.016 sec)
INFO:tensorflow:global_step/sec: 107.066
INFO:tensorflow:loss = 0.15774502, step = 3601 (0.934 sec)
INFO:tensorflow:global_step/sec: 138.986
INFO:tensorflow:loss = 0.04898131, step = 3701 (0.730 sec)
INFO:tensorflow:global_step/sec: 87.5655
INFO:tensorflow:loss = 0.008499086, step = 3801 (1.131 sec)
INFO:tensorflow:global_step/sec: 138.986
INFO:tensorflow:loss = 0.1360391, step = 3901 (0.720 sec)
INFO:tensorflow:global_step/sec: 140.35
INFO:tensorflow:loss = 0.15725328, step = 4001 (0.712 sec)
INFO:tensorflow:global_step/sec: 131.84
INFO:tensorflow:loss = 0.03170229, step = 4101 (0.758 sec)
INFO:tensorflow:global_step/sec: 119.689
INFO:tensorflow:loss = 0.042345375, step = 4201 (0.837 sec)
INFO:tensorflow:global_step/sec: 130.634
INFO:tensorflow:loss = 0.17799649, step = 4301 (0.765 sec)
INFO:tensorflow:global_step/sec: 123.153
INFO:tensorflow:loss = 0.13895029, step = 4401 (0.811 sec)
INFO:tensorflow:global_step/sec: 106.27
INFO:tensorflow:loss = 0.019976946, step = 4501 (0.941 sec)
INFO:tensorflow:global_step/sec: 132.275
INFO:tensorflow:loss = 0.025137002, step = 4601 (0.756 sec)
INFO:tensorflow:global_step/sec: 127.47
INFO:tensorflow:loss = 0.010976082, step = 4701 (0.786 sec)
INFO:tensorflow:global_step/sec: 115.075
INFO:tensorflow:loss = 0.018930476, step = 4801 (0.868 sec)
INFO:tensorflow:global_step/sec: 127.959
INFO:tensorflow:loss = 0.052622423, step = 4901 (0.781 sec)
INFO:tensorflow:global_step/sec: 130.124
INFO:tensorflow:loss = 0.07966899, step = 5001 (0.770 sec)
INFO:tensorflow:global_step/sec: 118.765
INFO:tensorflow:loss = 0.007830083, step = 5101 (0.841 sec)
INFO:tensorflow:global_step/sec: 108.342
INFO:tensorflow:loss = 0.031254422, step = 5201 (0.926 sec)
INFO:tensorflow:global_step/sec: 137.269
INFO:tensorflow:loss = 0.045173597, step = 5301 (0.725 sec)
INFO:tensorflow:global_step/sec: 124.611
INFO:tensorflow:loss = 0.05819138, step = 5401 (0.802 sec)
INFO:tensorflow:global_step/sec: 131.406
INFO:tensorflow:loss = 0.020733682, step = 5501 (0.766 sec)
INFO:tensorflow:global_step/sec: 136.612
INFO:tensorflow:loss = 0.07951477, step = 5601 (0.727 sec)
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INFO:tensorflow:global_step/sec: 95.511
INFO:tensorflow:loss = 0.0002034077, step = 25001 (1.045 sec)
INFO:tensorflow:global_step/sec: 138.889
INFO:tensorflow:loss = 0.0011735616, step = 25101 (0.723 sec)
INFO:tensorflow:global_step/sec: 108.696
INFO:tensorflow:loss = 0.0019028622, step = 25201 (0.917 sec)
INFO:tensorflow:global_step/sec: 144.509
INFO:tensorflow:loss = 0.00025500354, step = 25301 (0.693 sec)
INFO:tensorflow:global_step/sec: 127.307
INFO:tensorflow:loss = 0.00053306523, step = 25401 (0.787 sec)
INFO:tensorflow:global_step/sec: 110.193
INFO:tensorflow:loss = 0.0011538606, step = 25501 (0.910 sec)
INFO:tensorflow:global_step/sec: 116.279
INFO:tensorflow:loss = 0.00091025425, step = 25601 (0.863 sec)
INFO:tensorflow:global_step/sec: 107.181
INFO:tensorflow:loss = 0.0007047773, step = 25701 (0.926 sec)
INFO:tensorflow:global_step/sec: 144.196
INFO:tensorflow:loss = 0.0017489574, step = 25801 (0.693 sec)
INFO:tensorflow:global_step/sec: 107.817
INFO:tensorflow:loss = 0.0012627325, step = 25901 (0.929 sec)
INFO:tensorflow:global_step/sec: 86.2813
INFO:tensorflow:loss = 2.7895816e-05, step = 26001 (1.162 sec)
INFO:tensorflow:global_step/sec: 143.472
INFO:tensorflow:loss = 0.00081551576, step = 26101 (0.693 sec)
INFO:tensorflow:global_step/sec: 98.7655
INFO:tensorflow:loss = 0.00044112458, step = 26201 (1.013 sec)
INFO:tensorflow:global_step/sec: 119.189
INFO:tensorflow:loss = 0.0013754423, step = 26301 (0.839 sec)
INFO:tensorflow:global_step/sec: 121.359
INFO:tensorflow:loss = 0.001274162, step = 26401 (0.834 sec)
INFO:tensorflow:global_step/sec: 111.049
INFO:tensorflow:loss = 0.0011931465, step = 26501 (0.891 sec)
INFO:tensorflow:global_step/sec: 114.679
INFO:tensorflow:loss = 0.00075240486, step = 26601 (0.873 sec)
INFO:tensorflow:global_step/sec: 131.062
INFO:tensorflow:loss = 7.9561396e-05, step = 26701 (0.762 sec)
INFO:tensorflow:global_step/sec: 83.6819
INFO:tensorflow:loss = 0.0005915101, step = 26801 (1.196 sec)
INFO:tensorflow:global_step/sec: 81.7662
INFO:tensorflow:loss = 0.0009753166, step = 26901 (1.227 sec)
INFO:tensorflow:global_step/sec: 138.122
INFO:tensorflow:loss = 0.0008363343, step = 27001 (0.719 sec)
INFO:tensorflow:global_step/sec: 118.624
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INFO:tensorflow:loss = 0.0014865395, step = 27301 (0.844 sec)
INFO:tensorflow:global_step/sec: 117.44
INFO:tensorflow:loss = 0.0001604248, step = 27401 (0.852 sec)
INFO:tensorflow:global_step/sec: 94.2951
INFO:tensorflow:loss = 0.0013539345, step = 27501 (1.057 sec)
INFO:tensorflow:global_step/sec: 114.943
INFO:tensorflow:loss = 0.00086933636, step = 27601 (0.870 sec)
INFO:tensorflow:global_step/sec: 123.304
INFO:tensorflow:loss = 0.00035710738, step = 27701 (0.813 sec)
INFO:tensorflow:global_step/sec: 126.502
INFO:tensorflow:loss = 0.00021270115, step = 27801 (0.789 sec)
INFO:tensorflow:global_step/sec: 128.041
INFO:tensorflow:loss = 0.00046022166, step = 27901 (0.780 sec)
INFO:tensorflow:global_step/sec: 134.228
INFO:tensorflow:loss = 0.0014472507, step = 28001 (0.751 sec)
INFO:tensorflow:global_step/sec: 134.409
INFO:tensorflow:loss = 0.0010157593, step = 28101 (0.738 sec)
INFO:tensorflow:global_step/sec: 149.813
INFO:tensorflow:loss = 0.0009422499, step = 28201 (0.667 sec)
INFO:tensorflow:global_step/sec: 132.1
INFO:tensorflow:loss = 0.0008113724, step = 28301 (0.757 sec)
INFO:tensorflow:global_step/sec: 148.369
INFO:tensorflow:loss = 0.0011808894, step = 28401 (0.674 sec)
INFO:tensorflow:global_step/sec: 121.803
INFO:tensorflow:loss = 0.0004191447, step = 28501 (0.822 sec)
INFO:tensorflow:global_step/sec: 144.196
INFO:tensorflow:loss = 0.00023940473, step = 28601 (0.692 sec)
INFO:tensorflow:global_step/sec: 123.533
INFO:tensorflow:loss = 0.0009539034, step = 28701 (0.812 sec)
INFO:tensorflow:global_step/sec: 136.986
INFO:tensorflow:loss = 0.0014368035, step = 28801 (0.727 sec)
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INFO:tensorflow:loss = 0.0004228819, step = 28901 (0.703 sec)
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INFO:tensorflow:loss = 0.0013138631, step = 29101 (0.693 sec)
INFO:tensorflow:global_step/sec: 117.647
INFO:tensorflow:loss = 0.0017235178, step = 29201 (0.852 sec)
INFO:tensorflow:global_step/sec: 147.275
INFO:tensorflow:loss = 0.0019783506, step = 29301 (0.679 sec)
INFO:tensorflow:global_step/sec: 120.846
INFO:tensorflow:loss = 0.0012705141, step = 29401 (0.826 sec)
INFO:tensorflow:global_step/sec: 140.154
INFO:tensorflow:loss = 0.001259031, step = 29501 (0.713 sec)
INFO:tensorflow:global_step/sec: 113.379
INFO:tensorflow:loss = 0.00026371985, step = 29601 (0.882 sec)
INFO:tensorflow:global_step/sec: 84.6381
INFO:tensorflow:loss = 0.00015156495, step = 29701 (1.190 sec)
INFO:tensorflow:global_step/sec: 90.4568
INFO:tensorflow:loss = 0.0008930695, step = 29801 (1.097 sec)
INFO:tensorflow:global_step/sec: 109.17
INFO:tensorflow:loss = 0.0010357066, step = 29901 (0.919 sec)
INFO:tensorflow:global_step/sec: 106.667
INFO:tensorflow:loss = 7.300196e-05, step = 30001 (0.934 sec)
INFO:tensorflow:global_step/sec: 151.401
INFO:tensorflow:loss = 0.00081866817, step = 30101 (0.661 sec)
INFO:tensorflow:global_step/sec: 130.378
INFO:tensorflow:loss = 0.00026443027, step = 30201 (0.766 sec)
INFO:tensorflow:global_step/sec: 148.809
INFO:tensorflow:loss = 0.001075211, step = 30301 (0.673 sec)
INFO:tensorflow:global_step/sec: 112.93
INFO:tensorflow:loss = 0.001637378, step = 30401 (0.886 sec)
INFO:tensorflow:global_step/sec: 152.789
INFO:tensorflow:loss = 0.00090330286, step = 30501 (0.655 sec)
INFO:tensorflow:global_step/sec: 101.575
INFO:tensorflow:loss = 0.001213835, step = 30601 (0.985 sec)
INFO:tensorflow:global_step/sec: 99.1079
INFO:tensorflow:loss = 0.0007986991, step = 30701 (1.008 sec)
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INFO:tensorflow:loss = 0.0009841413, step = 30801 (0.759 sec)
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INFO:tensorflow:loss = 0.0012120056, step = 30901 (0.868 sec)
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INFO:tensorflow:loss = 0.0010039705, step = 31001 (0.872 sec)
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INFO:tensorflow:loss = 0.0013885555, step = 31101 (0.744 sec)
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INFO:tensorflow:loss = 0.00086156954, step = 31901 (0.787 sec)
INFO:tensorflow:global_step/sec: 150.489
INFO:tensorflow:loss = 0.00025417472, step = 32001 (0.665 sec)
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INFO:tensorflow:loss = 0.0013063625, step = 32201 (0.698 sec)
INFO:tensorflow:global_step/sec: 93.6768
INFO:tensorflow:loss = 0.00048622716, step = 32301 (1.067 sec)
INFO:tensorflow:global_step/sec: 98.4737
INFO:tensorflow:loss = 0.00017239567, step = 32401 (1.015 sec)
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INFO:tensorflow:loss = 7.541974e-05, step = 32601 (0.862 sec)
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INFO:tensorflow:global_step/sec: 108.636
INFO:tensorflow:loss = 0.00053583144, step = 33001 (0.920 sec)
INFO:tensorflow:global_step/sec: 116.279
INFO:tensorflow:loss = 0.0018361495, step = 33101 (0.864 sec)
INFO:tensorflow:global_step/sec: 132.714
INFO:tensorflow:loss = 0.00097217935, step = 33201 (0.750 sec)
INFO:tensorflow:global_step/sec: 127.877
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INFO:tensorflow:global_step/sec: 117.716
INFO:tensorflow:loss = 0.0008713158, step = 33401 (0.851 sec)
INFO:tensorflow:global_step/sec: 143.781
INFO:tensorflow:loss = 0.0004174811, step = 33501 (0.695 sec)
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INFO:tensorflow:loss = 0.0005641377, step = 33601 (0.961 sec)
INFO:tensorflow:global_step/sec: 140.449
INFO:tensorflow:loss = 0.0008594606, step = 33701 (0.712 sec)
INFO:tensorflow:global_step/sec: 132.363
INFO:tensorflow:loss = 0.00065256713, step = 33801 (0.755 sec)
INFO:tensorflow:global_step/sec: 118.133
INFO:tensorflow:loss = 0.0011786317, step = 33901 (0.847 sec)
INFO:tensorflow:global_step/sec: 141.343
INFO:tensorflow:loss = 0.0006465435, step = 34001 (0.707 sec)
INFO:tensorflow:global_step/sec: 123.153
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INFO:tensorflow:loss = 0.000840514, step = 34201 (0.840 sec)
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INFO:tensorflow:loss = 0.00016195442, step = 34301 (0.834 sec)
INFO:tensorflow:global_step/sec: 94.5178
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INFO:tensorflow:global_step/sec: 123.533
INFO:tensorflow:loss = 0.00050370645, step = 34801 (0.809 sec)
INFO:tensorflow:global_step/sec: 69.1564
INFO:tensorflow:loss = 0.000500097, step = 34901 (1.445 sec)
INFO:tensorflow:global_step/sec: 75.3013
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INFO:tensorflow:global_step/sec: 125.945
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INFO:tensorflow:global_step/sec: 143.472
INFO:tensorflow:loss = 0.00020615419, step = 35601 (0.698 sec)
INFO:tensorflow:global_step/sec: 119.832
INFO:tensorflow:loss = 0.0009566247, step = 35701 (0.835 sec)
INFO:tensorflow:global_step/sec: 119.546
INFO:tensorflow:loss = 0.00049882993, step = 35801 (0.837 sec)
INFO:tensorflow:global_step/sec: 121.581
INFO:tensorflow:loss = 0.0005369179, step = 35901 (0.821 sec)
INFO:tensorflow:global_step/sec: 94.4288
INFO:tensorflow:loss = 0.0002706097, step = 36001 (1.058 sec)
INFO:tensorflow:global_step/sec: 110.132
INFO:tensorflow:loss = 0.0015542519, step = 36101 (0.909 sec)
INFO:tensorflow:global_step/sec: 124.07
INFO:tensorflow:loss = 0.0008960398, step = 36201 (0.806 sec)
INFO:tensorflow:global_step/sec: 123.229
INFO:tensorflow:loss = 0.00022922695, step = 36301 (0.811 sec)
INFO:tensorflow:global_step/sec: 139.665
INFO:tensorflow:loss = 0.00085951836, step = 36401 (0.716 sec)
INFO:tensorflow:global_step/sec: 117.233
INFO:tensorflow:loss = 0.00020592193, step = 36501 (0.853 sec)
INFO:tensorflow:global_step/sec: 104.767
INFO:tensorflow:loss = 0.0003545551, step = 36601 (0.955 sec)
INFO:tensorflow:global_step/sec: 109.409
INFO:tensorflow:loss = 0.00057728734, step = 36701 (0.913 sec)
INFO:tensorflow:global_step/sec: 122.7
INFO:tensorflow:loss = 0.000992248, step = 36801 (0.815 sec)
INFO:tensorflow:global_step/sec: 149.031
INFO:tensorflow:loss = 0.000450318, step = 36901 (0.672 sec)
INFO:tensorflow:global_step/sec: 110.437
INFO:tensorflow:loss = 0.00051883946, step = 37001 (0.904 sec)
INFO:tensorflow:global_step/sec: 127.551
INFO:tensorflow:loss = 0.00034029438, step = 37101 (0.786 sec)
INFO:tensorflow:global_step/sec: 131.406
INFO:tensorflow:loss = 0.00020198344, step = 37201 (0.763 sec)
INFO:tensorflow:global_step/sec: 121.654
INFO:tensorflow:loss = 0.0006564577, step = 37301 (0.819 sec)
INFO:tensorflow:global_step/sec: 142.349
INFO:tensorflow:loss = 0.00030728127, step = 37401 (0.702 sec)
INFO:tensorflow:global_step/sec: 122.175
INFO:tensorflow:loss = 0.00028253082, step = 37501 (0.821 sec)
INFO:tensorflow:global_step/sec: 129.282
INFO:tensorflow:loss = 0.0003703754, step = 37601 (0.771 sec)
INFO:tensorflow:global_step/sec: 118.413
INFO:tensorflow:loss = 7.766451e-05, step = 37701 (0.848 sec)
INFO:tensorflow:global_step/sec: 86.9187
INFO:tensorflow:loss = 0.00029408635, step = 37801 (1.147 sec)
INFO:tensorflow:global_step/sec: 55.371
INFO:tensorflow:loss = 0.0013713894, step = 37901 (1.807 sec)
INFO:tensorflow:global_step/sec: 111.421
INFO:tensorflow:loss = 6.9400805e-05, step = 38001 (0.897 sec)
INFO:tensorflow:global_step/sec: 125.707
INFO:tensorflow:loss = 0.0011137301, step = 38101 (0.794 sec)
INFO:tensorflow:global_step/sec: 125.865
INFO:tensorflow:loss = 0.0007855168, step = 38201 (0.796 sec)
INFO:tensorflow:global_step/sec: 112.36
INFO:tensorflow:loss = 0.00011839019, step = 38301 (0.890 sec)
INFO:tensorflow:global_step/sec: 118.413
INFO:tensorflow:loss = 0.00023116679, step = 38401 (0.845 sec)
INFO:tensorflow:global_step/sec: 142.552
INFO:tensorflow:loss = 0.00045502023, step = 38501 (0.700 sec)
INFO:tensorflow:global_step/sec: 90.1307
INFO:tensorflow:loss = 0.000670968, step = 38601 (1.110 sec)
INFO:tensorflow:global_step/sec: 142.857
INFO:tensorflow:loss = 0.00068076863, step = 38701 (0.700 sec)
INFO:tensorflow:global_step/sec: 123.077
INFO:tensorflow:loss = 0.0002746721, step = 38801 (0.812 sec)
INFO:tensorflow:global_step/sec: 122.699
INFO:tensorflow:loss = 0.0016101614, step = 38901 (0.815 sec)
INFO:tensorflow:global_step/sec: 133.779
INFO:tensorflow:loss = 0.0002800584, step = 39001 (0.748 sec)
INFO:tensorflow:global_step/sec: 56.6251
INFO:tensorflow:loss = 0.0007799863, step = 39101 (1.765 sec)
INFO:tensorflow:global_step/sec: 117.716
INFO:tensorflow:loss = 0.00031419814, step = 39201 (0.851 sec)
INFO:tensorflow:global_step/sec: 117.647
INFO:tensorflow:loss = 0.00022067601, step = 39301 (0.850 sec)
INFO:tensorflow:global_step/sec: 111.857
INFO:tensorflow:loss = 0.0008232528, step = 39401 (0.895 sec)
INFO:tensorflow:global_step/sec: 138.6
INFO:tensorflow:loss = 0.00012726654, step = 39501 (0.721 sec)
INFO:tensorflow:global_step/sec: 127.065
INFO:tensorflow:loss = 0.00054408016, step = 39601 (0.787 sec)
INFO:tensorflow:global_step/sec: 136.706
INFO:tensorflow:loss = 0.0001087566, step = 39701 (0.733 sec)
INFO:tensorflow:global_step/sec: 122.399
INFO:tensorflow:loss = 0.0010954234, step = 39801 (0.816 sec)
INFO:tensorflow:global_step/sec: 126.743
INFO:tensorflow:loss = 0.0010776151, step = 39901 (0.790 sec)
INFO:tensorflow:Saving checkpoints for 40000 into C:\Users\Keith\AppData\Local\Temp\tmp1qywvh85\model.ckpt.
INFO:tensorflow:Loss for final step: 0.00041501672.
Out[14]:
DNNClassifier(params={'head': <tensorflow.contrib.learn.python.learn.estimators.head._MultiClassHead object at 0x000001ACC1A20F98>, 'hidden_units': [300, 100], 'feature_columns': (_RealValuedColumn(column_name='', dimension=784, default_value=None, dtype=tf.float32, normalizer=None),), 'optimizer': None, 'activation_fn': <function relu at 0x000001ACBEEA1B70>, 'dropout': None, 'gradient_clip_norm': None, 'embedding_lr_multipliers': None, 'input_layer_min_slice_size': None})
In [9]:
feature_cols = [tf.feature_column.numeric_column("X", shape=[28 * 28])]
dnn_clf = tf.estimator.DNNClassifier(hidden_units=[300,100], n_classes=10,feature_columns=feature_cols)

input_fn = tf.estimator.inputs.numpy_input_fn(x={"X": X_train}, y=y_train, num_epochs=40, batch_size=50, shuffle=True)
dnn_clf.train(input_fn=input_fn)
INFO:tensorflow:Using default config.
WARNING:tensorflow:Using temporary folder as model directory: C:\Users\Keith\AppData\Local\Temp\tmpuu5938j6
INFO:tensorflow:Using config: {'_model_dir': 'C:\\Users\\Keith\\AppData\\Local\\Temp\\tmpuu5938j6', '_tf_random_seed': None, '_save_summary_steps': 100, '_save_checkpoints_steps': None, '_save_checkpoints_secs': 600, '_session_config': allow_soft_placement: true
graph_options {
  rewrite_options {
    meta_optimizer_iterations: ONE
  }
}
, '_keep_checkpoint_max': 5, '_keep_checkpoint_every_n_hours': 10000, '_log_step_count_steps': 100, '_train_distribute': None, '_device_fn': None, '_protocol': None, '_eval_distribute': None, '_experimental_distribute': None, '_service': None, '_cluster_spec': <tensorflow.python.training.server_lib.ClusterSpec object at 0x000001ACBE1D3518>, '_task_type': 'worker', '_task_id': 0, '_global_id_in_cluster': 0, '_master': '', '_evaluation_master': '', '_is_chief': True, '_num_ps_replicas': 0, '_num_worker_replicas': 1}
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\python\framework\op_def_library.py:263: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.
Instructions for updating:
Colocations handled automatically by placer.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow_estimator\python\estimator\inputs\queues\feeding_queue_runner.py:62: QueueRunner.__init__ (from tensorflow.python.training.queue_runner_impl) is deprecated and will be removed in a future version.
Instructions for updating:
To construct input pipelines, use the `tf.data` module.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow_estimator\python\estimator\inputs\queues\feeding_functions.py:500: add_queue_runner (from tensorflow.python.training.queue_runner_impl) is deprecated and will be removed in a future version.
Instructions for updating:
To construct input pipelines, use the `tf.data` module.
INFO:tensorflow:Calling model_fn.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\python\feature_column\feature_column_v2.py:2703: to_float (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.
Instructions for updating:
Use tf.cast instead.
INFO:tensorflow:Done calling model_fn.
INFO:tensorflow:Create CheckpointSaverHook.
INFO:tensorflow:Graph was finalized.
INFO:tensorflow:Running local_init_op.
INFO:tensorflow:Done running local_init_op.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\python\training\monitored_session.py:809: start_queue_runners (from tensorflow.python.training.queue_runner_impl) is deprecated and will be removed in a future version.
Instructions for updating:
To construct input pipelines, use the `tf.data` module.
INFO:tensorflow:Saving checkpoints for 0 into C:\Users\Keith\AppData\Local\Temp\tmpuu5938j6\model.ckpt.
INFO:tensorflow:loss = 115.729485, step = 1
INFO:tensorflow:global_step/sec: 65.7787
INFO:tensorflow:loss = 28.141819, step = 101 (1.533 sec)
INFO:tensorflow:global_step/sec: 92.5926
INFO:tensorflow:loss = 16.46119, step = 201 (1.075 sec)
INFO:tensorflow:global_step/sec: 101.678
INFO:tensorflow:loss = 9.773326, step = 301 (0.986 sec)
INFO:tensorflow:global_step/sec: 98.522
INFO:tensorflow:loss = 12.619308, step = 401 (1.011 sec)
INFO:tensorflow:global_step/sec: 110.558
INFO:tensorflow:loss = 3.8767097, step = 501 (0.906 sec)
INFO:tensorflow:global_step/sec: 104.877
INFO:tensorflow:loss = 3.317923, step = 601 (0.956 sec)
INFO:tensorflow:global_step/sec: 115.141
INFO:tensorflow:loss = 9.805412, step = 701 (0.866 sec)
INFO:tensorflow:global_step/sec: 111.67
INFO:tensorflow:loss = 3.3052614, step = 801 (0.895 sec)
INFO:tensorflow:global_step/sec: 118.765
INFO:tensorflow:loss = 2.3905637, step = 901 (0.843 sec)
INFO:tensorflow:global_step/sec: 110.681
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INFO:tensorflow:loss = 0.01627255, step = 39701 (0.788 sec)
INFO:tensorflow:global_step/sec: 113.507
INFO:tensorflow:loss = 0.0051577385, step = 39801 (0.881 sec)
INFO:tensorflow:global_step/sec: 103.95
INFO:tensorflow:loss = 0.011494853, step = 39901 (0.962 sec)
INFO:tensorflow:global_step/sec: 126.183
INFO:tensorflow:loss = 0.022883069, step = 40001 (0.794 sec)
INFO:tensorflow:global_step/sec: 109.89
INFO:tensorflow:loss = 0.011489254, step = 40101 (0.910 sec)
INFO:tensorflow:global_step/sec: 118.343
INFO:tensorflow:loss = 0.0057439134, step = 40201 (0.845 sec)
INFO:tensorflow:global_step/sec: 118.765
INFO:tensorflow:loss = 0.011379017, step = 40301 (0.842 sec)
INFO:tensorflow:global_step/sec: 113.315
INFO:tensorflow:loss = 0.026006846, step = 40401 (0.882 sec)
INFO:tensorflow:global_step/sec: 127.632
INFO:tensorflow:loss = 0.0068370886, step = 40501 (0.784 sec)
INFO:tensorflow:global_step/sec: 117.994
INFO:tensorflow:loss = 0.01719052, step = 40601 (0.847 sec)
INFO:tensorflow:global_step/sec: 115.54
INFO:tensorflow:loss = 0.0060382364, step = 40701 (0.889 sec)
INFO:tensorflow:global_step/sec: 125.235
INFO:tensorflow:loss = 0.027376682, step = 40801 (0.776 sec)
INFO:tensorflow:global_step/sec: 114.547
INFO:tensorflow:loss = 0.0076563885, step = 40901 (0.873 sec)
INFO:tensorflow:global_step/sec: 119.048
INFO:tensorflow:loss = 0.021976072, step = 41001 (0.840 sec)
INFO:tensorflow:global_step/sec: 122.775
INFO:tensorflow:loss = 0.004605875, step = 41101 (0.814 sec)
INFO:tensorflow:global_step/sec: 115.875
INFO:tensorflow:loss = 0.010491568, step = 41201 (0.863 sec)
INFO:tensorflow:global_step/sec: 125.157
INFO:tensorflow:loss = 0.011319036, step = 41301 (0.800 sec)
INFO:tensorflow:global_step/sec: 117.716
INFO:tensorflow:loss = 0.0047789407, step = 41401 (0.848 sec)
INFO:tensorflow:global_step/sec: 115.808
INFO:tensorflow:loss = 0.07915461, step = 41501 (0.867 sec)
INFO:tensorflow:global_step/sec: 128.452
INFO:tensorflow:loss = 0.021174006, step = 41601 (0.776 sec)
INFO:tensorflow:global_step/sec: 115.875
INFO:tensorflow:loss = 0.01423851, step = 41701 (0.862 sec)
INFO:tensorflow:global_step/sec: 121.654
INFO:tensorflow:loss = 0.011738154, step = 41801 (0.823 sec)
INFO:tensorflow:global_step/sec: 123.229
INFO:tensorflow:loss = 0.028652744, step = 41901 (0.811 sec)
INFO:tensorflow:global_step/sec: 116.076
INFO:tensorflow:loss = 0.027635824, step = 42001 (0.861 sec)
INFO:tensorflow:global_step/sec: 122.249
INFO:tensorflow:loss = 0.028343944, step = 42101 (0.818 sec)
INFO:tensorflow:global_step/sec: 116.55
INFO:tensorflow:loss = 0.011847503, step = 42201 (0.858 sec)
INFO:tensorflow:global_step/sec: 115.942
INFO:tensorflow:loss = 0.0061660428, step = 42301 (0.863 sec)
INFO:tensorflow:global_step/sec: 130.548
INFO:tensorflow:loss = 0.008715527, step = 42401 (0.765 sec)
INFO:tensorflow:global_step/sec: 115.607
INFO:tensorflow:loss = 0.0015957085, step = 42501 (0.865 sec)
INFO:tensorflow:global_step/sec: 122.249
INFO:tensorflow:loss = 0.03562484, step = 42601 (0.818 sec)
INFO:tensorflow:global_step/sec: 122.175
INFO:tensorflow:loss = 0.006041453, step = 42701 (0.819 sec)
INFO:tensorflow:global_step/sec: 115.808
INFO:tensorflow:loss = 0.0166457, step = 42801 (0.863 sec)
INFO:tensorflow:global_step/sec: 128.7
INFO:tensorflow:loss = 0.037997406, step = 42901 (0.777 sec)
INFO:tensorflow:global_step/sec: 116.686
INFO:tensorflow:loss = 0.0022429582, step = 43001 (0.857 sec)
INFO:tensorflow:global_step/sec: 119.119
INFO:tensorflow:loss = 0.00827532, step = 43101 (0.839 sec)
INFO:tensorflow:global_step/sec: 125
INFO:tensorflow:loss = 0.015670553, step = 43201 (0.800 sec)
INFO:tensorflow:global_step/sec: 116.347
INFO:tensorflow:loss = 0.016489763, step = 43301 (0.859 sec)
INFO:tensorflow:global_step/sec: 128.949
INFO:tensorflow:loss = 0.0030419256, step = 43401 (0.775 sec)
INFO:tensorflow:global_step/sec: 116.959
INFO:tensorflow:loss = 0.019323621, step = 43501 (0.855 sec)
INFO:tensorflow:global_step/sec: 118.064
INFO:tensorflow:loss = 0.0038687144, step = 43601 (0.847 sec)
INFO:tensorflow:global_step/sec: 126.984
INFO:tensorflow:loss = 0.011646051, step = 43701 (0.787 sec)
INFO:tensorflow:global_step/sec: 115.473
INFO:tensorflow:loss = 0.04324679, step = 43801 (0.866 sec)
INFO:tensorflow:global_step/sec: 123.381
INFO:tensorflow:loss = 0.052263252, step = 43901 (0.811 sec)
INFO:tensorflow:Saving checkpoints for 44000 into C:\Users\Keith\AppData\Local\Temp\tmpuu5938j6\model.ckpt.
INFO:tensorflow:Loss for final step: 0.04805707.
Out[9]:
<tensorflow_estimator.python.estimator.canned.dnn.DNNClassifier at 0x1acbe22f470>
In [10]:
test_input_fn = tf.estimator.inputs.numpy_input_fn(x={"X": X_test}, y=y_test, shuffle=False)
eval_results = dnn_clf.evaluate(input_fn=test_input_fn)
INFO:tensorflow:Calling model_fn.
INFO:tensorflow:Done calling model_fn.
INFO:tensorflow:Starting evaluation at 2019-08-15T14:51:53Z
INFO:tensorflow:Graph was finalized.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\python\training\saver.py:1266: checkpoint_exists (from tensorflow.python.training.checkpoint_management) is deprecated and will be removed in a future version.
Instructions for updating:
Use standard file APIs to check for files with this prefix.
INFO:tensorflow:Restoring parameters from C:\Users\Keith\AppData\Local\Temp\tmpuu5938j6\model.ckpt-44000
INFO:tensorflow:Running local_init_op.
INFO:tensorflow:Done running local_init_op.
INFO:tensorflow:Finished evaluation at 2019-08-15-14:51:57
INFO:tensorflow:Saving dict for global step 44000: accuracy = 0.9789, average_loss = 0.10475795, global_step = 44000, loss = 13.2605
INFO:tensorflow:Saving 'checkpoint_path' summary for global step 44000: C:\Users\Keith\AppData\Local\Temp\tmpuu5938j6\model.ckpt-44000
In [11]:
eval_results
Out[11]:
{'accuracy': 0.9789,
 'average_loss': 0.10475795,
 'loss': 13.2605,
 'global_step': 44000}
In [12]:
y_pred_iter = dnn_clf.predict(input_fn=test_input_fn)
y_pred = list(y_pred_iter)
y_pred[0]
INFO:tensorflow:Calling model_fn.
INFO:tensorflow:Done calling model_fn.
INFO:tensorflow:Graph was finalized.
INFO:tensorflow:Restoring parameters from C:\Users\Keith\AppData\Local\Temp\tmpuu5938j6\model.ckpt-44000
INFO:tensorflow:Running local_init_op.
INFO:tensorflow:Done running local_init_op.
Out[12]:
{'logits': array([-15.512893  ,  -3.028629  ,  -1.4320402 ,   1.4622402 ,
         -8.765881  , -15.658692  , -27.722343  ,  28.068766  ,
        -14.659092  ,   0.86577505], dtype=float32),
 'probabilities': array([1.1822973e-19, 3.1230071e-14, 1.5415699e-13, 2.7856903e-12,
        1.0067359e-16, 1.0218940e-19, 5.8915559e-25, 1.0000000e+00,
        2.7766835e-19, 1.5342315e-12], dtype=float32),
 'class_ids': array([7], dtype=int64),
 'classes': array([b'7'], dtype=object)}

Under the hood,

  • DNNClassifier class creates all the neuron layers
  • Uses ReLU activation function (can change by setting the activation_fn hyperparameter)
  • Output layer relies on the softmax function, and the cost function is cross entropy

Plan B: TF MLP with Low-Level API

Step 1. Construction Phase

In [24]:
import tensorflow as tf

n_inputs = 28*28  # MNIST
n_hidden1 = 300
n_hidden2 = 100
n_outputs = 10
In [25]:
# Create placeholder nodes to represent the training data (inputs) and target (output class)
# 'None' means we don't know/care what the dimension is (and don't need to give it yet)

reset_graph()

X = tf.placeholder(tf.float32, shape=(None, n_inputs), name="X")
y = tf.placeholder(tf.int32, shape=(None), name="y")
In [26]:
# function which creates a graph for a layer

def neuron_layer(X, n_neurons, name, activation=None):
    with tf.name_scope(name):
        n_inputs = int(X.get_shape()[1])
        stddev = 2 / np.sqrt(n_inputs)
        init = tf.truncated_normal((n_inputs, n_neurons), stddev=stddev)
        W = tf.Variable(init, name="kernel")
        b = tf.Variable(tf.zeros([n_neurons]), name="bias")
        Z = tf.matmul(X, W) + b
        if activation is not None:
            return activation(Z)
        else:
            return Z

Detailed Steps

  1. Create a name scope using the name of the layer: will contain all the computation nodes for this neuron layer. This is optional, but the graph will look much nicer in TensorBoard if its nodes are well organized.
  2. Get the number of inputs by looking up the input matrix’s shape and getting the size of the second dimension (the first dimension is for instances).
  3. Create and initialize a W variable that will hold the weights matrix.
    • 2D tensor containing all the connection weights between each input and each neuron; hence, its shape will be (n_inputs, n_neurons).
    • Initialized randomly, using a truncated normal (Gaussian) distribution with a standard deviation of $2/\sqrt{n_{inputs}}$.
    • Using this specific standard deviation helps the algorithm converge much faster.
    • It is important to initialize connection weights randomly for all hidden layers to avoid any symmetries that the Gradient Descent algorithm would be unable to break.
  4. Create a $b$ variable for biases, initialized to 0 (no symmetry issue in this case), with one bias parameter per neuron.
  5. Create a subgraph to compute $\mathbf z = \mathbf X · \mathbf W + \mathbf b$. This vectorized implementation will efficiently compute the weighted sums of the inputs plus the bias term for each and every neuron in the layer, for all the instances in the batch in just one shot.
  6. Finally, if the activation parameter is set to "relu", the code returns relu($z$) (i.e., $\max (0, z)$), or else it just returns $z$.
In [27]:
# Create network using our layer function

with tf.name_scope("dnn"):
    hidden1 = neuron_layer(X, n_hidden1, name="hidden1", activation=tf.nn.relu)
    hidden2 = neuron_layer(hidden1, n_hidden2, name="hidden2", activation=tf.nn.relu)
    logits = neuron_layer(hidden2, n_outputs, name="outputs")
  1. The first hidden layer takes X as its input.
  2. The second takes the output of the first hidden layer as its input.
  3. the output layer takes the output of the second hidden layer as its input.

Note that the last layer has no activation yet

Plan C: Create equivalent network using TF built-in functions

  1. contrib.layers.fully_connected - old & experimental
  2. dense() - new function added after publication

The tensorflow.contrib package

  • contains many useful functions,
  • but it is a place for experimental code that has not yet graduated to be part of the main TensorFlow API.
  • So the fully_connected() function (and any other contrib code) may change or move in the future.

See https://github.com/ageron/handson-ml/blob/master/10_introduction_to_artificial_neural_networks.ipynb cell 29+ for use of new dense() function instead.

# contrib.layers.fully_connected from tensorflow.contrib.layers import fully_connected with tf.name_scope("dnn"): hidden1 = fully_connected(X, n_hidden1, scope="hidden1") hidden2 = fully_connected(hidden1, n_hidden2, scope="hidden2") logits = fully_connected(hidden2, n_outputs, scope="outputs", activation_fn=None)
# tf.layers.dense with tf.name_scope("dnn"): hidden1 = tf.layers.dense(X, n_hidden1, name="hidden1", activation=tf.nn.relu) hidden2 = tf.layers.dense(hidden1, n_hidden2, name="hidden2", activation=tf.nn.relu) logits = tf.layers.dense(hidden2, n_outputs, name="outputs") y_proba = tf.nn.softmax(logits)

Define Loss function

  • Cross-entropy - for probabilistic estimate (logistic or softmax decision)
  • Logits - means it uses the continuous values before activation for loss
  • Sparse - Labels expected to be integers between 0 and $N-1$, rather than a one-hot vector indicating class
In [28]:
with tf.name_scope("loss"):
    xentropy = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=y, logits=logits)
    loss = tf.reduce_mean(xentropy, name="loss")
  1. xentropy is a list of cross-entropies for the samples
  2. Loss computes a mean over the samples

Create Optimizer

will adjust parameters to minimize the cost function

In [29]:
learning_rate = 0.01

with tf.name_scope("train"):
    optimizer = tf.train.GradientDescentOptimizer(learning_rate)
    training_op = optimizer.minimize(loss)

Model Evaluation

  1. First, for each instance, determine if the neural network’s prediction is correct by checking whether or not the highest logit corresponds to the target class. For this you can use the in_top_k() function.
  2. This returns a 1D tensor full of boolean values, so we need to cast these booleans to floats and then compute the average. This will give us the network’s overall accuracy.
In [30]:
with tf.name_scope("eval"):
    correct = tf.nn.in_top_k(logits, y, 1)
    accuracy = tf.reduce_mean(tf.cast(correct, tf.float32))

And, as usual, create a node to initialize all variables

also create a Saver to save our trained model parameters to disk

In [31]:
init = tf.global_variables_initializer()
saver = tf.train.Saver()

Execution phase

  • First, load MNIST.
  • could use ScikitLearn for that as we did in previous chapters, but TensorFlow offers its own helper that fetches the data, scales it (between 0 and 1), shuffles it, and provides a simple function to load one mini-batches a time.
In [32]:
from tensorflow.examples.tutorials.mnist import input_data 
mnist = input_data.read_data_sets("/tmp/data/") 
WARNING:tensorflow:From <ipython-input-32-2e6e2ea27661>:2: read_data_sets (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use alternatives such as official/mnist/dataset.py from tensorflow/models.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:260: maybe_download (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.
Instructions for updating:
Please write your own downloading logic.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\base.py:252: _internal_retry.<locals>.wrap.<locals>.wrapped_fn (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.
Instructions for updating:
Please use urllib or similar directly.
Successfully downloaded train-images-idx3-ubyte.gz 9912422 bytes.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:262: extract_images (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tf.data to implement this functionality.
Extracting /tmp/data/train-images-idx3-ubyte.gz
Successfully downloaded train-labels-idx1-ubyte.gz 28881 bytes.
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:267: extract_labels (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tf.data to implement this functionality.
Extracting /tmp/data/train-labels-idx1-ubyte.gz
Successfully downloaded t10k-images-idx3-ubyte.gz 1648877 bytes.
Extracting /tmp/data/t10k-images-idx3-ubyte.gz
Successfully downloaded t10k-labels-idx1-ubyte.gz 4542 bytes.
Extracting /tmp/data/t10k-labels-idx1-ubyte.gz
WARNING:tensorflow:From C:\Users\Keith\Anaconda3\envs\ML37\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:290: DataSet.__init__ (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use alternatives such as official/mnist/dataset.py from tensorflow/models.
In [35]:
# training using TF built-in helper

n_epochs = 10
batch_size = 50

with tf.Session() as sess:    
    init.run()    
    for epoch in range(n_epochs):        
        for iteration in range(mnist.train.num_examples // batch_size):            
            X_batch, y_batch = mnist.train.next_batch(batch_size)            
            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})        
            acc_train = accuracy.eval(feed_dict={X: X_batch, y: y_batch})        
            acc_test = accuracy.eval(feed_dict={X: mnist.test.images,                                            
                                                y: mnist.test.labels})        
            print(epoch, "Train accuracy:", acc_train, "Test accuracy:", acc_test)
    save_path = saver.save(sess, "./my_model_final.ckpt")
0 Train accuracy: 0.04 Test accuracy: 0.0574
0 Train accuracy: 0.06 Test accuracy: 0.0633
0 Train accuracy: 0.14 Test accuracy: 0.0643
0 Train accuracy: 0.08 Test accuracy: 0.0771
0 Train accuracy: 0.12 Test accuracy: 0.0848
0 Train accuracy: 0.08 Test accuracy: 0.094
0 Train accuracy: 0.12 Test accuracy: 0.1079
0 Train accuracy: 0.2 Test accuracy: 0.1244
0 Train accuracy: 0.16 Test accuracy: 0.1378
0 Train accuracy: 0.14 Test accuracy: 0.1575
0 Train accuracy: 0.22 Test accuracy: 0.1763
0 Train accuracy: 0.22 Test accuracy: 0.1945
0 Train accuracy: 0.28 Test accuracy: 0.2086
0 Train accuracy: 0.34 Test accuracy: 0.2235
0 Train accuracy: 0.28 Test accuracy: 0.2374
0 Train accuracy: 0.28 Test accuracy: 0.2513
0 Train accuracy: 0.26 Test accuracy: 0.2558
0 Train accuracy: 0.26 Test accuracy: 0.2695
0 Train accuracy: 0.4 Test accuracy: 0.2888
0 Train accuracy: 0.36 Test accuracy: 0.299
0 Train accuracy: 0.34 Test accuracy: 0.3168
0 Train accuracy: 0.28 Test accuracy: 0.3236
0 Train accuracy: 0.42 Test accuracy: 0.3417
0 Train accuracy: 0.46 Test accuracy: 0.3563
0 Train accuracy: 0.4 Test accuracy: 0.365
0 Train accuracy: 0.4 Test accuracy: 0.3796
0 Train accuracy: 0.52 Test accuracy: 0.3952
0 Train accuracy: 0.38 Test accuracy: 0.4044
0 Train accuracy: 0.32 Test accuracy: 0.4132
0 Train accuracy: 0.48 Test accuracy: 0.4274
0 Train accuracy: 0.44 Test accuracy: 0.4347
0 Train accuracy: 0.42 Test accuracy: 0.4529
0 Train accuracy: 0.46 Test accuracy: 0.4698
0 Train accuracy: 0.46 Test accuracy: 0.4788
0 Train accuracy: 0.58 Test accuracy: 0.4913
0 Train accuracy: 0.5 Test accuracy: 0.5061
0 Train accuracy: 0.64 Test accuracy: 0.5145
0 Train accuracy: 0.6 Test accuracy: 0.5228
0 Train accuracy: 0.56 Test accuracy: 0.5309
0 Train accuracy: 0.58 Test accuracy: 0.5429
0 Train accuracy: 0.6 Test accuracy: 0.5561
0 Train accuracy: 0.54 Test accuracy: 0.5636
0 Train accuracy: 0.54 Test accuracy: 0.5738
0 Train accuracy: 0.56 Test accuracy: 0.5777
0 Train accuracy: 0.48 Test accuracy: 0.582
0 Train accuracy: 0.7 Test accuracy: 0.5872
0 Train accuracy: 0.48 Test accuracy: 0.596
0 Train accuracy: 0.52 Test accuracy: 0.5947
0 Train accuracy: 0.54 Test accuracy: 0.6002
0 Train accuracy: 0.58 Test accuracy: 0.6072
0 Train accuracy: 0.52 Test accuracy: 0.6093
0 Train accuracy: 0.54 Test accuracy: 0.6148
0 Train accuracy: 0.74 Test accuracy: 0.6198
0 Train accuracy: 0.58 Test accuracy: 0.6261
0 Train accuracy: 0.64 Test accuracy: 0.6254
0 Train accuracy: 0.6 Test accuracy: 0.6312
0 Train accuracy: 0.58 Test accuracy: 0.6319
0 Train accuracy: 0.6 Test accuracy: 0.6353
0 Train accuracy: 0.68 Test accuracy: 0.6324
0 Train accuracy: 0.74 Test accuracy: 0.6455
0 Train accuracy: 0.6 Test accuracy: 0.6495
0 Train accuracy: 0.66 Test accuracy: 0.651
0 Train accuracy: 0.6 Test accuracy: 0.6586
0 Train accuracy: 0.48 Test accuracy: 0.6623
0 Train accuracy: 0.68 Test accuracy: 0.666
0 Train accuracy: 0.72 Test accuracy: 0.6674
0 Train accuracy: 0.6 Test accuracy: 0.6723
0 Train accuracy: 0.74 Test accuracy: 0.6791
0 Train accuracy: 0.72 Test accuracy: 0.6807
0 Train accuracy: 0.74 Test accuracy: 0.6799
0 Train accuracy: 0.74 Test accuracy: 0.6767
0 Train accuracy: 0.62 Test accuracy: 0.6855
0 Train accuracy: 0.68 Test accuracy: 0.687
0 Train accuracy: 0.58 Test accuracy: 0.6934
0 Train accuracy: 0.8 Test accuracy: 0.6955
0 Train accuracy: 0.64 Test accuracy: 0.7004
0 Train accuracy: 0.76 Test accuracy: 0.7037
0 Train accuracy: 0.66 Test accuracy: 0.7065
0 Train accuracy: 0.74 Test accuracy: 0.711
0 Train accuracy: 0.74 Test accuracy: 0.7123
0 Train accuracy: 0.82 Test accuracy: 0.7154
0 Train accuracy: 0.74 Test accuracy: 0.7179
0 Train accuracy: 0.7 Test accuracy: 0.7175
0 Train accuracy: 0.76 Test accuracy: 0.7182
0 Train accuracy: 0.6 Test accuracy: 0.7246
0 Train accuracy: 0.66 Test accuracy: 0.7306
0 Train accuracy: 0.76 Test accuracy: 0.7304
0 Train accuracy: 0.68 Test accuracy: 0.7347
0 Train accuracy: 0.76 Test accuracy: 0.737
0 Train accuracy: 0.76 Test accuracy: 0.7405
0 Train accuracy: 0.8 Test accuracy: 0.7435
0 Train accuracy: 0.6 Test accuracy: 0.743
0 Train accuracy: 0.62 Test accuracy: 0.7459
0 Train accuracy: 0.64 Test accuracy: 0.7422
0 Train accuracy: 0.76 Test accuracy: 0.7452
0 Train accuracy: 0.7 Test accuracy: 0.745
0 Train accuracy: 0.8 Test accuracy: 0.7484
0 Train accuracy: 0.68 Test accuracy: 0.752
0 Train accuracy: 0.8 Test accuracy: 0.7506
0 Train accuracy: 0.82 Test accuracy: 0.7468
0 Train accuracy: 0.74 Test accuracy: 0.7526
0 Train accuracy: 0.84 Test accuracy: 0.7558
0 Train accuracy: 0.66 Test accuracy: 0.7595
0 Train accuracy: 0.68 Test accuracy: 0.758
0 Train accuracy: 0.72 Test accuracy: 0.7581
0 Train accuracy: 0.7 Test accuracy: 0.7624
0 Train accuracy: 0.76 Test accuracy: 0.7651
0 Train accuracy: 0.7 Test accuracy: 0.7652
0 Train accuracy: 0.84 Test accuracy: 0.7654
0 Train accuracy: 0.86 Test accuracy: 0.7647
0 Train accuracy: 0.82 Test accuracy: 0.7654
0 Train accuracy: 0.74 Test accuracy: 0.7708
0 Train accuracy: 0.78 Test accuracy: 0.768
0 Train accuracy: 0.74 Test accuracy: 0.7697
0 Train accuracy: 0.76 Test accuracy: 0.7738
0 Train accuracy: 0.8 Test accuracy: 0.7751
0 Train accuracy: 0.8 Test accuracy: 0.7766
0 Train accuracy: 0.86 Test accuracy: 0.7778
0 Train accuracy: 0.8 Test accuracy: 0.7799
0 Train accuracy: 0.78 Test accuracy: 0.7792
0 Train accuracy: 0.84 Test accuracy: 0.7782
0 Train accuracy: 0.76 Test accuracy: 0.7777
0 Train accuracy: 0.7 Test accuracy: 0.7787
0 Train accuracy: 0.76 Test accuracy: 0.7801
0 Train accuracy: 0.78 Test accuracy: 0.7804
0 Train accuracy: 0.84 Test accuracy: 0.7828
0 Train accuracy: 0.84 Test accuracy: 0.7829
0 Train accuracy: 0.74 Test accuracy: 0.7809
0 Train accuracy: 0.76 Test accuracy: 0.7849
0 Train accuracy: 0.8 Test accuracy: 0.7854
0 Train accuracy: 0.76 Test accuracy: 0.7871
0 Train accuracy: 0.86 Test accuracy: 0.7866
0 Train accuracy: 0.78 Test accuracy: 0.7845
0 Train accuracy: 0.66 Test accuracy: 0.7844
0 Train accuracy: 0.78 Test accuracy: 0.7878
0 Train accuracy: 0.66 Test accuracy: 0.7894
0 Train accuracy: 0.82 Test accuracy: 0.7899
0 Train accuracy: 0.88 Test accuracy: 0.7889
0 Train accuracy: 0.8 Test accuracy: 0.7949
0 Train accuracy: 0.86 Test accuracy: 0.7974
0 Train accuracy: 0.84 Test accuracy: 0.7956
0 Train accuracy: 0.86 Test accuracy: 0.7987
0 Train accuracy: 0.88 Test accuracy: 0.7978
0 Train accuracy: 0.84 Test accuracy: 0.7996
0 Train accuracy: 0.74 Test accuracy: 0.802
0 Train accuracy: 0.86 Test accuracy: 0.7982
0 Train accuracy: 0.84 Test accuracy: 0.8
0 Train accuracy: 0.8 Test accuracy: 0.8035
0 Train accuracy: 0.82 Test accuracy: 0.8018
0 Train accuracy: 0.8 Test accuracy: 0.8029
0 Train accuracy: 0.8 Test accuracy: 0.805
0 Train accuracy: 0.86 Test accuracy: 0.8068
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0 Train accuracy: 0.8 Test accuracy: 0.8077
0 Train accuracy: 0.82 Test accuracy: 0.8083
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0 Train accuracy: 0.82 Test accuracy: 0.8087
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0 Train accuracy: 0.88 Test accuracy: 0.8062
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0 Train accuracy: 0.82 Test accuracy: 0.8134
0 Train accuracy: 0.9 Test accuracy: 0.8165
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0 Train accuracy: 0.74 Test accuracy: 0.8191
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0 Train accuracy: 0.76 Test accuracy: 0.8201
0 Train accuracy: 0.88 Test accuracy: 0.8189
0 Train accuracy: 0.76 Test accuracy: 0.8231
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0 Train accuracy: 0.88 Test accuracy: 0.813
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0 Train accuracy: 0.74 Test accuracy: 0.8223
0 Train accuracy: 0.82 Test accuracy: 0.825
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0 Train accuracy: 0.78 Test accuracy: 0.8245
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0 Train accuracy: 0.8 Test accuracy: 0.8276
0 Train accuracy: 0.74 Test accuracy: 0.8294
0 Train accuracy: 0.84 Test accuracy: 0.829
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0 Train accuracy: 0.86 Test accuracy: 0.8296
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0 Train accuracy: 0.7 Test accuracy: 0.8318
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0 Train accuracy: 0.84 Test accuracy: 0.8349
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0 Train accuracy: 0.92 Test accuracy: 0.8347
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0 Train accuracy: 0.92 Test accuracy: 0.8365
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0 Train accuracy: 0.82 Test accuracy: 0.8404
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0 Train accuracy: 0.82 Test accuracy: 0.8406
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0 Train accuracy: 0.74 Test accuracy: 0.8432
0 Train accuracy: 0.82 Test accuracy: 0.8433
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0 Train accuracy: 0.84 Test accuracy: 0.8432
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0 Train accuracy: 0.9 Test accuracy: 0.8424
0 Train accuracy: 0.88 Test accuracy: 0.8415
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0 Train accuracy: 0.78 Test accuracy: 0.8406
0 Train accuracy: 0.86 Test accuracy: 0.8395
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0 Train accuracy: 0.82 Test accuracy: 0.8401
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0 Train accuracy: 0.76 Test accuracy: 0.8429
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0 Train accuracy: 0.92 Test accuracy: 0.8507
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0 Train accuracy: 0.86 Test accuracy: 0.8501
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0 Train accuracy: 0.82 Test accuracy: 0.851
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0 Train accuracy: 0.92 Test accuracy: 0.8516
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0 Train accuracy: 0.88 Test accuracy: 0.8521
0 Train accuracy: 0.82 Test accuracy: 0.8542
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0 Train accuracy: 0.9 Test accuracy: 0.8547
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0 Train accuracy: 0.78 Test accuracy: 0.8547
0 Train accuracy: 0.86 Test accuracy: 0.8575
0 Train accuracy: 0.82 Test accuracy: 0.8554
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0 Train accuracy: 0.86 Test accuracy: 0.8572
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0 Train accuracy: 0.86 Test accuracy: 0.854
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0 Train accuracy: 0.8 Test accuracy: 0.8571
0 Train accuracy: 0.92 Test accuracy: 0.8561
0 Train accuracy: 0.84 Test accuracy: 0.8582
0 Train accuracy: 0.96 Test accuracy: 0.8595
0 Train accuracy: 0.86 Test accuracy: 0.8591
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0 Train accuracy: 0.88 Test accuracy: 0.8586
0 Train accuracy: 0.84 Test accuracy: 0.8591
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0 Train accuracy: 0.96 Test accuracy: 0.8593
0 Train accuracy: 0.92 Test accuracy: 0.8601
0 Train accuracy: 0.84 Test accuracy: 0.8602
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0 Train accuracy: 0.86 Test accuracy: 0.8612
0 Train accuracy: 0.94 Test accuracy: 0.8621
0 Train accuracy: 0.92 Test accuracy: 0.8601
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0 Train accuracy: 0.96 Test accuracy: 0.862
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0 Train accuracy: 0.88 Test accuracy: 0.8615
0 Train accuracy: 0.92 Test accuracy: 0.8612
0 Train accuracy: 0.82 Test accuracy: 0.8616
0 Train accuracy: 0.84 Test accuracy: 0.8615
0 Train accuracy: 0.86 Test accuracy: 0.8615
0 Train accuracy: 0.92 Test accuracy: 0.8626
0 Train accuracy: 0.8 Test accuracy: 0.863
0 Train accuracy: 0.86 Test accuracy: 0.865
0 Train accuracy: 0.92 Test accuracy: 0.8639
0 Train accuracy: 0.92 Test accuracy: 0.8638
0 Train accuracy: 0.92 Test accuracy: 0.8589
0 Train accuracy: 0.86 Test accuracy: 0.8604
0 Train accuracy: 0.9 Test accuracy: 0.864
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0 Train accuracy: 0.92 Test accuracy: 0.8648
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0 Train accuracy: 0.88 Test accuracy: 0.8638
0 Train accuracy: 0.78 Test accuracy: 0.8672
0 Train accuracy: 0.86 Test accuracy: 0.8649
0 Train accuracy: 0.92 Test accuracy: 0.8647
0 Train accuracy: 0.9 Test accuracy: 0.8675
0 Train accuracy: 0.8 Test accuracy: 0.8676
0 Train accuracy: 0.96 Test accuracy: 0.8662
0 Train accuracy: 0.86 Test accuracy: 0.8654
0 Train accuracy: 0.86 Test accuracy: 0.8662
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0 Train accuracy: 0.92 Test accuracy: 0.8676
0 Train accuracy: 0.94 Test accuracy: 0.8672
0 Train accuracy: 0.84 Test accuracy: 0.8677
0 Train accuracy: 0.94 Test accuracy: 0.8665
0 Train accuracy: 0.86 Test accuracy: 0.8672
0 Train accuracy: 0.94 Test accuracy: 0.8668
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0 Train accuracy: 0.82 Test accuracy: 0.8672
0 Train accuracy: 0.9 Test accuracy: 0.8687
0 Train accuracy: 0.84 Test accuracy: 0.8681
0 Train accuracy: 0.9 Test accuracy: 0.8694
0 Train accuracy: 0.88 Test accuracy: 0.8697
0 Train accuracy: 0.92 Test accuracy: 0.8691
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0 Train accuracy: 0.94 Test accuracy: 0.8685
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0 Train accuracy: 0.9 Test accuracy: 0.8681
0 Train accuracy: 0.86 Test accuracy: 0.87
0 Train accuracy: 0.92 Test accuracy: 0.8708
0 Train accuracy: 0.92 Test accuracy: 0.8707
0 Train accuracy: 0.84 Test accuracy: 0.8693
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0 Train accuracy: 0.86 Test accuracy: 0.8706
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0 Train accuracy: 0.9 Test accuracy: 0.8674
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0 Train accuracy: 0.84 Test accuracy: 0.8688
0 Train accuracy: 0.7 Test accuracy: 0.8701
0 Train accuracy: 0.9 Test accuracy: 0.8723
0 Train accuracy: 0.88 Test accuracy: 0.8713
0 Train accuracy: 0.9 Test accuracy: 0.8743
0 Train accuracy: 0.88 Test accuracy: 0.8721
0 Train accuracy: 0.92 Test accuracy: 0.8714
0 Train accuracy: 0.86 Test accuracy: 0.869
0 Train accuracy: 0.72 Test accuracy: 0.8722
0 Train accuracy: 0.86 Test accuracy: 0.8727
0 Train accuracy: 0.9 Test accuracy: 0.873
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0 Train accuracy: 0.82 Test accuracy: 0.8736
0 Train accuracy: 0.92 Test accuracy: 0.8743
0 Train accuracy: 0.96 Test accuracy: 0.8747
0 Train accuracy: 0.86 Test accuracy: 0.8739
0 Train accuracy: 0.92 Test accuracy: 0.8747
0 Train accuracy: 0.9 Test accuracy: 0.8746
0 Train accuracy: 0.92 Test accuracy: 0.874
0 Train accuracy: 0.94 Test accuracy: 0.8759
0 Train accuracy: 0.92 Test accuracy: 0.8749
0 Train accuracy: 0.86 Test accuracy: 0.8739
0 Train accuracy: 0.84 Test accuracy: 0.8738
0 Train accuracy: 0.86 Test accuracy: 0.8747
0 Train accuracy: 0.86 Test accuracy: 0.8729
0 Train accuracy: 0.9 Test accuracy: 0.8737
0 Train accuracy: 0.86 Test accuracy: 0.8712
0 Train accuracy: 0.86 Test accuracy: 0.8742
0 Train accuracy: 0.88 Test accuracy: 0.8733
0 Train accuracy: 0.88 Test accuracy: 0.8734
0 Train accuracy: 0.88 Test accuracy: 0.8755
0 Train accuracy: 0.82 Test accuracy: 0.8747
0 Train accuracy: 0.82 Test accuracy: 0.872
0 Train accuracy: 0.92 Test accuracy: 0.8707
0 Train accuracy: 0.9 Test accuracy: 0.8725
0 Train accuracy: 0.94 Test accuracy: 0.873
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0 Train accuracy: 0.96 Test accuracy: 0.8786
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0 Train accuracy: 0.86 Test accuracy: 0.8793
0 Train accuracy: 0.88 Test accuracy: 0.8778
0 Train accuracy: 0.84 Test accuracy: 0.8789
0 Train accuracy: 0.94 Test accuracy: 0.8779
0 Train accuracy: 0.86 Test accuracy: 0.8783
0 Train accuracy: 0.92 Test accuracy: 0.8787
0 Train accuracy: 0.96 Test accuracy: 0.8762
0 Train accuracy: 0.88 Test accuracy: 0.8776
0 Train accuracy: 0.92 Test accuracy: 0.8778
0 Train accuracy: 0.84 Test accuracy: 0.8762
0 Train accuracy: 0.92 Test accuracy: 0.8761
0 Train accuracy: 0.92 Test accuracy: 0.8762
0 Train accuracy: 0.82 Test accuracy: 0.878
0 Train accuracy: 0.94 Test accuracy: 0.8793
0 Train accuracy: 0.88 Test accuracy: 0.8769
0 Train accuracy: 0.9 Test accuracy: 0.8773
0 Train accuracy: 0.94 Test accuracy: 0.8804
0 Train accuracy: 0.88 Test accuracy: 0.8806
0 Train accuracy: 0.86 Test accuracy: 0.882
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0 Train accuracy: 0.86 Test accuracy: 0.8785
0 Train accuracy: 0.92 Test accuracy: 0.8768
0 Train accuracy: 0.9 Test accuracy: 0.8771
0 Train accuracy: 0.88 Test accuracy: 0.8786
0 Train accuracy: 0.82 Test accuracy: 0.8796
0 Train accuracy: 0.86 Test accuracy: 0.8804
0 Train accuracy: 0.82 Test accuracy: 0.8801
0 Train accuracy: 0.82 Test accuracy: 0.8784
0 Train accuracy: 0.84 Test accuracy: 0.8787
0 Train accuracy: 0.88 Test accuracy: 0.8799
0 Train accuracy: 0.86 Test accuracy: 0.881
0 Train accuracy: 0.92 Test accuracy: 0.8798
0 Train accuracy: 0.94 Test accuracy: 0.879
0 Train accuracy: 0.88 Test accuracy: 0.8782
0 Train accuracy: 0.86 Test accuracy: 0.8789
0 Train accuracy: 0.88 Test accuracy: 0.8788
0 Train accuracy: 0.88 Test accuracy: 0.8795
0 Train accuracy: 0.92 Test accuracy: 0.8814
0 Train accuracy: 0.9 Test accuracy: 0.8819
0 Train accuracy: 0.96 Test accuracy: 0.8825
0 Train accuracy: 0.88 Test accuracy: 0.8824
0 Train accuracy: 0.96 Test accuracy: 0.8832
0 Train accuracy: 0.86 Test accuracy: 0.8836
0 Train accuracy: 0.9 Test accuracy: 0.8844
0 Train accuracy: 0.88 Test accuracy: 0.8815
0 Train accuracy: 0.88 Test accuracy: 0.8825
0 Train accuracy: 0.94 Test accuracy: 0.8829
0 Train accuracy: 0.92 Test accuracy: 0.8815
0 Train accuracy: 0.88 Test accuracy: 0.8817
0 Train accuracy: 0.92 Test accuracy: 0.8821
0 Train accuracy: 0.94 Test accuracy: 0.8811
0 Train accuracy: 0.92 Test accuracy: 0.883
0 Train accuracy: 0.94 Test accuracy: 0.8815
0 Train accuracy: 0.92 Test accuracy: 0.8826
0 Train accuracy: 0.88 Test accuracy: 0.88
0 Train accuracy: 0.94 Test accuracy: 0.8792
0 Train accuracy: 0.92 Test accuracy: 0.8779
0 Train accuracy: 0.86 Test accuracy: 0.8793
0 Train accuracy: 0.98 Test accuracy: 0.881
0 Train accuracy: 0.86 Test accuracy: 0.8827
0 Train accuracy: 0.96 Test accuracy: 0.8838
0 Train accuracy: 0.9 Test accuracy: 0.884
0 Train accuracy: 0.96 Test accuracy: 0.8856
0 Train accuracy: 0.94 Test accuracy: 0.8835
0 Train accuracy: 0.92 Test accuracy: 0.8832
0 Train accuracy: 0.92 Test accuracy: 0.8836
0 Train accuracy: 0.92 Test accuracy: 0.8831
0 Train accuracy: 0.84 Test accuracy: 0.8826
0 Train accuracy: 0.96 Test accuracy: 0.8801
0 Train accuracy: 0.86 Test accuracy: 0.8816
0 Train accuracy: 0.84 Test accuracy: 0.884
0 Train accuracy: 0.9 Test accuracy: 0.8841
0 Train accuracy: 0.86 Test accuracy: 0.8842
0 Train accuracy: 0.9 Test accuracy: 0.8854
0 Train accuracy: 0.86 Test accuracy: 0.8844
0 Train accuracy: 0.92 Test accuracy: 0.8855
0 Train accuracy: 0.88 Test accuracy: 0.8868
0 Train accuracy: 0.78 Test accuracy: 0.8855
0 Train accuracy: 0.84 Test accuracy: 0.885
0 Train accuracy: 0.9 Test accuracy: 0.8857
0 Train accuracy: 0.9 Test accuracy: 0.8839
0 Train accuracy: 0.84 Test accuracy: 0.8846
0 Train accuracy: 0.9 Test accuracy: 0.8833
0 Train accuracy: 0.86 Test accuracy: 0.8879
0 Train accuracy: 0.92 Test accuracy: 0.887
0 Train accuracy: 0.9 Test accuracy: 0.8865
0 Train accuracy: 0.88 Test accuracy: 0.8838
0 Train accuracy: 0.84 Test accuracy: 0.8879
0 Train accuracy: 0.88 Test accuracy: 0.8872
0 Train accuracy: 0.86 Test accuracy: 0.8885
0 Train accuracy: 0.94 Test accuracy: 0.8879
0 Train accuracy: 0.86 Test accuracy: 0.887
0 Train accuracy: 0.88 Test accuracy: 0.8866
0 Train accuracy: 0.98 Test accuracy: 0.8877
0 Train accuracy: 0.86 Test accuracy: 0.8867
0 Train accuracy: 0.78 Test accuracy: 0.887
0 Train accuracy: 0.88 Test accuracy: 0.8875
0 Train accuracy: 0.9 Test accuracy: 0.8872
0 Train accuracy: 0.94 Test accuracy: 0.8872
0 Train accuracy: 0.96 Test accuracy: 0.8869
0 Train accuracy: 0.86 Test accuracy: 0.887
0 Train accuracy: 0.84 Test accuracy: 0.8885
0 Train accuracy: 0.96 Test accuracy: 0.8871
0 Train accuracy: 0.92 Test accuracy: 0.8868
0 Train accuracy: 0.9 Test accuracy: 0.8875
0 Train accuracy: 0.86 Test accuracy: 0.8878
0 Train accuracy: 0.88 Test accuracy: 0.8882
0 Train accuracy: 0.92 Test accuracy: 0.8878
0 Train accuracy: 0.9 Test accuracy: 0.8877
0 Train accuracy: 0.88 Test accuracy: 0.8892
0 Train accuracy: 0.92 Test accuracy: 0.8883
0 Train accuracy: 0.98 Test accuracy: 0.8891
0 Train accuracy: 0.94 Test accuracy: 0.8869
0 Train accuracy: 0.94 Test accuracy: 0.8878
0 Train accuracy: 0.88 Test accuracy: 0.8846
0 Train accuracy: 0.9 Test accuracy: 0.8863
0 Train accuracy: 0.92 Test accuracy: 0.8874
0 Train accuracy: 0.9 Test accuracy: 0.887
0 Train accuracy: 0.92 Test accuracy: 0.8855
0 Train accuracy: 0.88 Test accuracy: 0.8845
0 Train accuracy: 0.86 Test accuracy: 0.8888
0 Train accuracy: 0.9 Test accuracy: 0.8878
0 Train accuracy: 0.86 Test accuracy: 0.8877
0 Train accuracy: 0.9 Test accuracy: 0.8889
0 Train accuracy: 0.86 Test accuracy: 0.8861
0 Train accuracy: 0.94 Test accuracy: 0.8856
0 Train accuracy: 0.92 Test accuracy: 0.8854
0 Train accuracy: 0.78 Test accuracy: 0.8896
0 Train accuracy: 0.92 Test accuracy: 0.8875
0 Train accuracy: 0.96 Test accuracy: 0.8901
0 Train accuracy: 0.9 Test accuracy: 0.8904
0 Train accuracy: 0.9 Test accuracy: 0.8908
0 Train accuracy: 0.88 Test accuracy: 0.8884
0 Train accuracy: 0.84 Test accuracy: 0.8893
0 Train accuracy: 0.9 Test accuracy: 0.8907
0 Train accuracy: 0.88 Test accuracy: 0.8895
0 Train accuracy: 0.8 Test accuracy: 0.8897
0 Train accuracy: 0.84 Test accuracy: 0.8893
0 Train accuracy: 0.88 Test accuracy: 0.8906
0 Train accuracy: 0.78 Test accuracy: 0.8918
0 Train accuracy: 0.88 Test accuracy: 0.8885
0 Train accuracy: 0.96 Test accuracy: 0.8903
0 Train accuracy: 0.86 Test accuracy: 0.8908
0 Train accuracy: 0.86 Test accuracy: 0.891
0 Train accuracy: 0.94 Test accuracy: 0.8916
0 Train accuracy: 0.88 Test accuracy: 0.8907
0 Train accuracy: 0.96 Test accuracy: 0.8903
0 Train accuracy: 0.96 Test accuracy: 0.8901
0 Train accuracy: 0.92 Test accuracy: 0.8901
0 Train accuracy: 0.86 Test accuracy: 0.8896
0 Train accuracy: 0.9 Test accuracy: 0.8904
0 Train accuracy: 0.9 Test accuracy: 0.8894
0 Train accuracy: 0.88 Test accuracy: 0.8907
0 Train accuracy: 0.96 Test accuracy: 0.8916
0 Train accuracy: 0.9 Test accuracy: 0.8922
0 Train accuracy: 0.88 Test accuracy: 0.8927
0 Train accuracy: 0.86 Test accuracy: 0.8937
0 Train accuracy: 0.9 Test accuracy: 0.8934
0 Train accuracy: 0.92 Test accuracy: 0.8928
0 Train accuracy: 0.86 Test accuracy: 0.8922
0 Train accuracy: 0.9 Test accuracy: 0.8922
0 Train accuracy: 0.94 Test accuracy: 0.8919
0 Train accuracy: 0.88 Test accuracy: 0.8912
0 Train accuracy: 0.94 Test accuracy: 0.8923
0 Train accuracy: 0.92 Test accuracy: 0.8921
0 Train accuracy: 0.9 Test accuracy: 0.8939
0 Train accuracy: 0.92 Test accuracy: 0.8937
0 Train accuracy: 0.86 Test accuracy: 0.8933
0 Train accuracy: 0.88 Test accuracy: 0.8922
0 Train accuracy: 0.98 Test accuracy: 0.8914
0 Train accuracy: 0.88 Test accuracy: 0.8908
0 Train accuracy: 0.94 Test accuracy: 0.8927
0 Train accuracy: 0.96 Test accuracy: 0.8932
0 Train accuracy: 0.82 Test accuracy: 0.8908
0 Train accuracy: 0.98 Test accuracy: 0.8905
0 Train accuracy: 0.9 Test accuracy: 0.8907
0 Train accuracy: 0.92 Test accuracy: 0.8903
0 Train accuracy: 0.96 Test accuracy: 0.8924
0 Train accuracy: 0.88 Test accuracy: 0.8922
0 Train accuracy: 0.88 Test accuracy: 0.8919
0 Train accuracy: 0.9 Test accuracy: 0.8934
0 Train accuracy: 0.86 Test accuracy: 0.8924
0 Train accuracy: 0.92 Test accuracy: 0.8933
0 Train accuracy: 0.82 Test accuracy: 0.8918
0 Train accuracy: 0.88 Test accuracy: 0.8904
0 Train accuracy: 0.84 Test accuracy: 0.8912
0 Train accuracy: 0.92 Test accuracy: 0.8923
0 Train accuracy: 0.86 Test accuracy: 0.8935
0 Train accuracy: 0.84 Test accuracy: 0.8941
0 Train accuracy: 0.92 Test accuracy: 0.8921
0 Train accuracy: 0.98 Test accuracy: 0.8936
0 Train accuracy: 0.92 Test accuracy: 0.8928
0 Train accuracy: 0.96 Test accuracy: 0.893
0 Train accuracy: 0.92 Test accuracy: 0.8939
0 Train accuracy: 0.9 Test accuracy: 0.8919
0 Train accuracy: 0.96 Test accuracy: 0.893
0 Train accuracy: 0.96 Test accuracy: 0.8915
0 Train accuracy: 0.9 Test accuracy: 0.8917
0 Train accuracy: 0.88 Test accuracy: 0.8932
0 Train accuracy: 0.9 Test accuracy: 0.8939
0 Train accuracy: 0.96 Test accuracy: 0.8929
0 Train accuracy: 0.92 Test accuracy: 0.8921
0 Train accuracy: 0.9 Test accuracy: 0.8921
0 Train accuracy: 0.8 Test accuracy: 0.8939
0 Train accuracy: 0.88 Test accuracy: 0.895
0 Train accuracy: 0.9 Test accuracy: 0.895
0 Train accuracy: 0.88 Test accuracy: 0.8947
0 Train accuracy: 0.88 Test accuracy: 0.8938
0 Train accuracy: 0.88 Test accuracy: 0.895
0 Train accuracy: 0.76 Test accuracy: 0.8937
0 Train accuracy: 0.94 Test accuracy: 0.8954
0 Train accuracy: 0.88 Test accuracy: 0.8949
0 Train accuracy: 0.94 Test accuracy: 0.8929
0 Train accuracy: 0.96 Test accuracy: 0.8918
0 Train accuracy: 0.94 Test accuracy: 0.8943
0 Train accuracy: 0.94 Test accuracy: 0.8939
0 Train accuracy: 0.92 Test accuracy: 0.8937
0 Train accuracy: 0.92 Test accuracy: 0.8924
0 Train accuracy: 0.92 Test accuracy: 0.8941
0 Train accuracy: 0.8 Test accuracy: 0.8959
0 Train accuracy: 0.92 Test accuracy: 0.8954
0 Train accuracy: 0.88 Test accuracy: 0.8955
0 Train accuracy: 0.9 Test accuracy: 0.8942
0 Train accuracy: 0.86 Test accuracy: 0.8953
0 Train accuracy: 0.94 Test accuracy: 0.8955
0 Train accuracy: 0.92 Test accuracy: 0.8942
0 Train accuracy: 0.9 Test accuracy: 0.8931
0 Train accuracy: 0.92 Test accuracy: 0.8934
0 Train accuracy: 0.9 Test accuracy: 0.8919
0 Train accuracy: 0.8 Test accuracy: 0.8941
0 Train accuracy: 0.92 Test accuracy: 0.8937
0 Train accuracy: 0.84 Test accuracy: 0.8948
0 Train accuracy: 0.88 Test accuracy: 0.893
0 Train accuracy: 0.88 Test accuracy: 0.8942
0 Train accuracy: 0.94 Test accuracy: 0.8946
0 Train accuracy: 0.98 Test accuracy: 0.8927
0 Train accuracy: 0.86 Test accuracy: 0.8937
0 Train accuracy: 0.96 Test accuracy: 0.8922
0 Train accuracy: 0.84 Test accuracy: 0.8919
0 Train accuracy: 0.9 Test accuracy: 0.893
0 Train accuracy: 0.88 Test accuracy: 0.8927
0 Train accuracy: 0.88 Test accuracy: 0.8954
0 Train accuracy: 0.92 Test accuracy: 0.8935
0 Train accuracy: 0.94 Test accuracy: 0.8959
0 Train accuracy: 0.9 Test accuracy: 0.8965
0 Train accuracy: 0.96 Test accuracy: 0.8973
0 Train accuracy: 0.88 Test accuracy: 0.8974
0 Train accuracy: 0.86 Test accuracy: 0.8966
0 Train accuracy: 0.92 Test accuracy: 0.8963
0 Train accuracy: 0.82 Test accuracy: 0.8965
0 Train accuracy: 0.82 Test accuracy: 0.8958
0 Train accuracy: 0.88 Test accuracy: 0.8971
0 Train accuracy: 0.84 Test accuracy: 0.8972
0 Train accuracy: 0.94 Test accuracy: 0.8956
0 Train accuracy: 0.94 Test accuracy: 0.8959
0 Train accuracy: 0.9 Test accuracy: 0.8965
0 Train accuracy: 0.96 Test accuracy: 0.8979
0 Train accuracy: 0.88 Test accuracy: 0.8982
0 Train accuracy: 0.92 Test accuracy: 0.8982
0 Train accuracy: 0.92 Test accuracy: 0.8978
0 Train accuracy: 0.9 Test accuracy: 0.8972
0 Train accuracy: 0.9 Test accuracy: 0.8965
0 Train accuracy: 0.94 Test accuracy: 0.8981
0 Train accuracy: 0.88 Test accuracy: 0.8983
0 Train accuracy: 0.86 Test accuracy: 0.8938
0 Train accuracy: 0.94 Test accuracy: 0.8975
0 Train accuracy: 0.88 Test accuracy: 0.8966
0 Train accuracy: 0.9 Test accuracy: 0.8965
0 Train accuracy: 0.9 Test accuracy: 0.8984
0 Train accuracy: 0.88 Test accuracy: 0.8962
0 Train accuracy: 0.9 Test accuracy: 0.8981
0 Train accuracy: 0.94 Test accuracy: 0.897
0 Train accuracy: 0.86 Test accuracy: 0.8972
0 Train accuracy: 0.92 Test accuracy: 0.8989
0 Train accuracy: 0.86 Test accuracy: 0.8971
0 Train accuracy: 0.9 Test accuracy: 0.8973
0 Train accuracy: 0.9 Test accuracy: 0.8997
0 Train accuracy: 0.92 Test accuracy: 0.9004
0 Train accuracy: 0.92 Test accuracy: 0.8999
0 Train accuracy: 0.9 Test accuracy: 0.9
0 Train accuracy: 0.88 Test accuracy: 0.8994
0 Train accuracy: 0.92 Test accuracy: 0.8981
0 Train accuracy: 0.94 Test accuracy: 0.8975
0 Train accuracy: 0.9 Test accuracy: 0.8979
0 Train accuracy: 0.86 Test accuracy: 0.8983
0 Train accuracy: 0.9 Test accuracy: 0.8967
0 Train accuracy: 0.96 Test accuracy: 0.8971
0 Train accuracy: 0.88 Test accuracy: 0.8982
0 Train accuracy: 0.94 Test accuracy: 0.8988
0 Train accuracy: 0.94 Test accuracy: 0.8981
0 Train accuracy: 0.96 Test accuracy: 0.8974
0 Train accuracy: 0.86 Test accuracy: 0.8971
0 Train accuracy: 0.98 Test accuracy: 0.8976
0 Train accuracy: 0.92 Test accuracy: 0.8982
0 Train accuracy: 0.84 Test accuracy: 0.8967
0 Train accuracy: 0.94 Test accuracy: 0.8974
0 Train accuracy: 0.82 Test accuracy: 0.8973
0 Train accuracy: 0.9 Test accuracy: 0.8987
0 Train accuracy: 0.94 Test accuracy: 0.8976
0 Train accuracy: 0.88 Test accuracy: 0.8969
0 Train accuracy: 0.86 Test accuracy: 0.8974
0 Train accuracy: 0.88 Test accuracy: 0.8994
0 Train accuracy: 0.9 Test accuracy: 0.9003
0 Train accuracy: 0.98 Test accuracy: 0.899
0 Train accuracy: 0.88 Test accuracy: 0.8995
0 Train accuracy: 0.9 Test accuracy: 0.9002
0 Train accuracy: 0.9 Test accuracy: 0.8984
0 Train accuracy: 0.94 Test accuracy: 0.8993
0 Train accuracy: 0.96 Test accuracy: 0.8989
0 Train accuracy: 0.82 Test accuracy: 0.8975
0 Train accuracy: 0.9 Test accuracy: 0.8978
0 Train accuracy: 0.9 Test accuracy: 0.8965
0 Train accuracy: 0.9 Test accuracy: 0.8974
0 Train accuracy: 0.92 Test accuracy: 0.8969
0 Train accuracy: 0.86 Test accuracy: 0.8964
0 Train accuracy: 0.94 Test accuracy: 0.8994
0 Train accuracy: 0.86 Test accuracy: 0.8994
0 Train accuracy: 0.94 Test accuracy: 0.9008
0 Train accuracy: 0.96 Test accuracy: 0.8995
0 Train accuracy: 0.9 Test accuracy: 0.9
0 Train accuracy: 0.94 Test accuracy: 0.8991
0 Train accuracy: 0.88 Test accuracy: 0.9006
0 Train accuracy: 0.92 Test accuracy: 0.8997
0 Train accuracy: 0.9 Test accuracy: 0.8982
0 Train accuracy: 0.9 Test accuracy: 0.8998
0 Train accuracy: 0.8 Test accuracy: 0.9005
0 Train accuracy: 0.92 Test accuracy: 0.8995
0 Train accuracy: 0.96 Test accuracy: 0.8965
0 Train accuracy: 0.9 Test accuracy: 0.9005
0 Train accuracy: 0.92 Test accuracy: 0.9006
0 Train accuracy: 0.96 Test accuracy: 0.9016
0 Train accuracy: 0.92 Test accuracy: 0.901
0 Train accuracy: 0.96 Test accuracy: 0.9016
0 Train accuracy: 0.9 Test accuracy: 0.9018
0 Train accuracy: 0.9 Test accuracy: 0.9013
0 Train accuracy: 0.9 Test accuracy: 0.9003
0 Train accuracy: 0.86 Test accuracy: 0.8997
0 Train accuracy: 0.92 Test accuracy: 0.9
0 Train accuracy: 0.94 Test accuracy: 0.8998
0 Train accuracy: 0.9 Test accuracy: 0.8991
0 Train accuracy: 0.9 Test accuracy: 0.8994
0 Train accuracy: 0.76 Test accuracy: 0.8998
0 Train accuracy: 0.94 Test accuracy: 0.9
0 Train accuracy: 0.94 Test accuracy: 0.8994
0 Train accuracy: 0.9 Test accuracy: 0.8995
0 Train accuracy: 0.92 Test accuracy: 0.9002
0 Train accuracy: 0.82 Test accuracy: 0.9
0 Train accuracy: 0.98 Test accuracy: 0.8999
0 Train accuracy: 0.9 Test accuracy: 0.8991
0 Train accuracy: 0.92 Test accuracy: 0.8985
0 Train accuracy: 0.92 Test accuracy: 0.8996
0 Train accuracy: 0.9 Test accuracy: 0.8978
0 Train accuracy: 0.92 Test accuracy: 0.898
0 Train accuracy: 0.94 Test accuracy: 0.898
0 Train accuracy: 0.9 Test accuracy: 0.8978
0 Train accuracy: 0.86 Test accuracy: 0.8986
0 Train accuracy: 0.88 Test accuracy: 0.8977
0 Train accuracy: 0.92 Test accuracy: 0.8969
0 Train accuracy: 0.9 Test accuracy: 0.8978
0 Train accuracy: 0.96 Test accuracy: 0.8977
0 Train accuracy: 0.92 Test accuracy: 0.8981
0 Train accuracy: 0.84 Test accuracy: 0.8966
0 Train accuracy: 0.88 Test accuracy: 0.8964
0 Train accuracy: 0.88 Test accuracy: 0.8977
0 Train accuracy: 0.84 Test accuracy: 0.8975
0 Train accuracy: 0.9 Test accuracy: 0.8973
0 Train accuracy: 0.86 Test accuracy: 0.897
0 Train accuracy: 0.92 Test accuracy: 0.8983
0 Train accuracy: 0.88 Test accuracy: 0.899
0 Train accuracy: 0.9 Test accuracy: 0.8985
0 Train accuracy: 0.86 Test accuracy: 0.8952
0 Train accuracy: 0.96 Test accuracy: 0.8961
0 Train accuracy: 0.88 Test accuracy: 0.8953
0 Train accuracy: 0.9 Test accuracy: 0.8998
0 Train accuracy: 0.94 Test accuracy: 0.9007
0 Train accuracy: 0.88 Test accuracy: 0.9016
0 Train accuracy: 0.96 Test accuracy: 0.9026
0 Train accuracy: 0.96 Test accuracy: 0.902
0 Train accuracy: 0.9 Test accuracy: 0.9024
0 Train accuracy: 0.96 Test accuracy: 0.9032
0 Train accuracy: 0.92 Test accuracy: 0.9033
0 Train accuracy: 0.96 Test accuracy: 0.9036
0 Train accuracy: 0.82 Test accuracy: 0.9033
0 Train accuracy: 0.92 Test accuracy: 0.903
0 Train accuracy: 0.94 Test accuracy: 0.9033
0 Train accuracy: 0.86 Test accuracy: 0.9019
0 Train accuracy: 0.96 Test accuracy: 0.901
0 Train accuracy: 0.88 Test accuracy: 0.9014
0 Train accuracy: 0.92 Test accuracy: 0.9018
0 Train accuracy: 0.84 Test accuracy: 0.9022
0 Train accuracy: 0.96 Test accuracy: 0.9017
0 Train accuracy: 0.96 Test accuracy: 0.9025
0 Train accuracy: 0.96 Test accuracy: 0.9017
0 Train accuracy: 0.92 Test accuracy: 0.9022
0 Train accuracy: 0.86 Test accuracy: 0.9004
0 Train accuracy: 0.92 Test accuracy: 0.9008
0 Train accuracy: 0.86 Test accuracy: 0.9014
0 Train accuracy: 0.82 Test accuracy: 0.9042
0 Train accuracy: 0.88 Test accuracy: 0.904
0 Train accuracy: 0.92 Test accuracy: 0.9036
0 Train accuracy: 1.0 Test accuracy: 0.9032
0 Train accuracy: 0.92 Test accuracy: 0.9036
0 Train accuracy: 0.88 Test accuracy: 0.9036
0 Train accuracy: 0.94 Test accuracy: 0.9053
0 Train accuracy: 0.92 Test accuracy: 0.9052
0 Train accuracy: 0.96 Test accuracy: 0.9049
0 Train accuracy: 0.96 Test accuracy: 0.905
0 Train accuracy: 0.92 Test accuracy: 0.9041
0 Train accuracy: 0.88 Test accuracy: 0.9039
0 Train accuracy: 0.92 Test accuracy: 0.9027
0 Train accuracy: 0.96 Test accuracy: 0.9031
0 Train accuracy: 0.98 Test accuracy: 0.903
0 Train accuracy: 0.92 Test accuracy: 0.9037
0 Train accuracy: 0.82 Test accuracy: 0.9023
0 Train accuracy: 0.96 Test accuracy: 0.9036
0 Train accuracy: 0.9 Test accuracy: 0.9036
0 Train accuracy: 0.88 Test accuracy: 0.9036
0 Train accuracy: 0.94 Test accuracy: 0.9038
0 Train accuracy: 0.92 Test accuracy: 0.9035
0 Train accuracy: 0.92 Test accuracy: 0.904
0 Train accuracy: 0.86 Test accuracy: 0.9047
0 Train accuracy: 0.98 Test accuracy: 0.904
0 Train accuracy: 0.88 Test accuracy: 0.9029
0 Train accuracy: 0.94 Test accuracy: 0.9038
0 Train accuracy: 0.96 Test accuracy: 0.9025
0 Train accuracy: 0.96 Test accuracy: 0.9038
0 Train accuracy: 0.92 Test accuracy: 0.9019
0 Train accuracy: 0.92 Test accuracy: 0.9012
0 Train accuracy: 0.88 Test accuracy: 0.9023
0 Train accuracy: 0.9 Test accuracy: 0.9018
0 Train accuracy: 0.9 Test accuracy: 0.9014
0 Train accuracy: 0.94 Test accuracy: 0.9018
0 Train accuracy: 0.92 Test accuracy: 0.9033
0 Train accuracy: 0.98 Test accuracy: 0.9028
0 Train accuracy: 0.9 Test accuracy: 0.9037
0 Train accuracy: 0.88 Test accuracy: 0.9037
0 Train accuracy: 0.84 Test accuracy: 0.9027
0 Train accuracy: 0.96 Test accuracy: 0.9025
0 Train accuracy: 0.92 Test accuracy: 0.9043
0 Train accuracy: 0.92 Test accuracy: 0.9049
0 Train accuracy: 0.94 Test accuracy: 0.903
0 Train accuracy: 0.94 Test accuracy: 0.9041
0 Train accuracy: 0.9 Test accuracy: 0.9039
0 Train accuracy: 0.92 Test accuracy: 0.9022
0 Train accuracy: 0.88 Test accuracy: 0.9022
0 Train accuracy: 0.9 Test accuracy: 0.9051
0 Train accuracy: 0.88 Test accuracy: 0.9053
0 Train accuracy: 0.96 Test accuracy: 0.9036
0 Train accuracy: 0.92 Test accuracy: 0.9041
0 Train accuracy: 0.86 Test accuracy: 0.9035
0 Train accuracy: 0.92 Test accuracy: 0.9035
0 Train accuracy: 0.94 Test accuracy: 0.9026
0 Train accuracy: 0.92 Test accuracy: 0.9027
0 Train accuracy: 0.88 Test accuracy: 0.9035
0 Train accuracy: 0.94 Test accuracy: 0.9019
0 Train accuracy: 0.84 Test accuracy: 0.9034
0 Train accuracy: 0.9 Test accuracy: 0.9043
0 Train accuracy: 0.86 Test accuracy: 0.9022
0 Train accuracy: 0.88 Test accuracy: 0.9017
0 Train accuracy: 0.84 Test accuracy: 0.9032
0 Train accuracy: 0.9 Test accuracy: 0.9033
0 Train accuracy: 0.88 Test accuracy: 0.9028
0 Train accuracy: 0.92 Test accuracy: 0.9023
0 Train accuracy: 0.9 Test accuracy: 0.9024
0 Train accuracy: 0.96 Test accuracy: 0.9029
0 Train accuracy: 0.88 Test accuracy: 0.9036
0 Train accuracy: 0.96 Test accuracy: 0.9037
0 Train accuracy: 0.9 Test accuracy: 0.9028
0 Train accuracy: 0.96 Test accuracy: 0.9031
0 Train accuracy: 0.84 Test accuracy: 0.9042
0 Train accuracy: 0.92 Test accuracy: 0.9052
0 Train accuracy: 0.96 Test accuracy: 0.9056
0 Train accuracy: 0.94 Test accuracy: 0.9061
0 Train accuracy: 0.88 Test accuracy: 0.9058
0 Train accuracy: 1.0 Test accuracy: 0.9058
0 Train accuracy: 0.92 Test accuracy: 0.9065
0 Train accuracy: 0.88 Test accuracy: 0.9072
0 Train accuracy: 0.86 Test accuracy: 0.9066
0 Train accuracy: 0.96 Test accuracy: 0.9069
0 Train accuracy: 0.86 Test accuracy: 0.9072
0 Train accuracy: 0.92 Test accuracy: 0.9077
0 Train accuracy: 0.92 Test accuracy: 0.9069
0 Train accuracy: 0.94 Test accuracy: 0.9062
0 Train accuracy: 0.96 Test accuracy: 0.9079
0 Train accuracy: 0.94 Test accuracy: 0.9056
0 Train accuracy: 0.84 Test accuracy: 0.9054
0 Train accuracy: 0.96 Test accuracy: 0.9059
0 Train accuracy: 0.94 Test accuracy: 0.9055
0 Train accuracy: 0.92 Test accuracy: 0.9048
0 Train accuracy: 0.92 Test accuracy: 0.9041
0 Train accuracy: 0.9 Test accuracy: 0.9054
0 Train accuracy: 0.84 Test accuracy: 0.9051
0 Train accuracy: 0.92 Test accuracy: 0.9053
0 Train accuracy: 0.88 Test accuracy: 0.9049
0 Train accuracy: 1.0 Test accuracy: 0.9037
0 Train accuracy: 0.86 Test accuracy: 0.905
0 Train accuracy: 0.94 Test accuracy: 0.9054
0 Train accuracy: 0.86 Test accuracy: 0.9047
0 Train accuracy: 0.94 Test accuracy: 0.9046
0 Train accuracy: 0.96 Test accuracy: 0.9048
0 Train accuracy: 0.92 Test accuracy: 0.9053
0 Train accuracy: 0.96 Test accuracy: 0.9046
0 Train accuracy: 0.92 Test accuracy: 0.9056
0 Train accuracy: 0.92 Test accuracy: 0.9049
0 Train accuracy: 0.94 Test accuracy: 0.9053
0 Train accuracy: 0.88 Test accuracy: 0.9036
0 Train accuracy: 0.88 Test accuracy: 0.9035
0 Train accuracy: 0.94 Test accuracy: 0.9038
0 Train accuracy: 0.9 Test accuracy: 0.9042
0 Train accuracy: 0.9 Test accuracy: 0.9049
0 Train accuracy: 0.88 Test accuracy: 0.9038
0 Train accuracy: 0.92 Test accuracy: 0.9045
0 Train accuracy: 0.9 Test accuracy: 0.9042
0 Train accuracy: 0.96 Test accuracy: 0.9051
0 Train accuracy: 0.86 Test accuracy: 0.9034
0 Train accuracy: 0.94 Test accuracy: 0.9028
0 Train accuracy: 0.92 Test accuracy: 0.9026
0 Train accuracy: 0.82 Test accuracy: 0.8996
0 Train accuracy: 0.9 Test accuracy: 0.9016
0 Train accuracy: 0.9 Test accuracy: 0.901
0 Train accuracy: 0.92 Test accuracy: 0.9023
0 Train accuracy: 0.92 Test accuracy: 0.9055
0 Train accuracy: 0.88 Test accuracy: 0.9053
0 Train accuracy: 0.94 Test accuracy: 0.9053
0 Train accuracy: 0.92 Test accuracy: 0.9056
0 Train accuracy: 0.94 Test accuracy: 0.9053
0 Train accuracy: 0.92 Test accuracy: 0.906
0 Train accuracy: 0.94 Test accuracy: 0.9049
0 Train accuracy: 0.94 Test accuracy: 0.9052
0 Train accuracy: 0.96 Test accuracy: 0.9055
0 Train accuracy: 0.92 Test accuracy: 0.9054
0 Train accuracy: 0.9 Test accuracy: 0.9057
0 Train accuracy: 0.9 Test accuracy: 0.908
0 Train accuracy: 0.86 Test accuracy: 0.9079
0 Train accuracy: 0.94 Test accuracy: 0.9087
0 Train accuracy: 0.88 Test accuracy: 0.9087
0 Train accuracy: 0.88 Test accuracy: 0.909
0 Train accuracy: 0.94 Test accuracy: 0.9084
0 Train accuracy: 0.94 Test accuracy: 0.908
0 Train accuracy: 0.84 Test accuracy: 0.9065
0 Train accuracy: 0.98 Test accuracy: 0.9062
0 Train accuracy: 0.92 Test accuracy: 0.9075
0 Train accuracy: 0.96 Test accuracy: 0.9066
0 Train accuracy: 0.96 Test accuracy: 0.9074
0 Train accuracy: 0.98 Test accuracy: 0.9078
0 Train accuracy: 0.98 Test accuracy: 0.9079
0 Train accuracy: 0.88 Test accuracy: 0.9089
0 Train accuracy: 0.82 Test accuracy: 0.91
0 Train accuracy: 0.88 Test accuracy: 0.9077
0 Train accuracy: 0.88 Test accuracy: 0.9066
0 Train accuracy: 0.86 Test accuracy: 0.9067
0 Train accuracy: 0.92 Test accuracy: 0.9075
0 Train accuracy: 0.94 Test accuracy: 0.9072
0 Train accuracy: 0.94 Test accuracy: 0.9073
0 Train accuracy: 0.86 Test accuracy: 0.908
0 Train accuracy: 0.94 Test accuracy: 0.9078
0 Train accuracy: 0.82 Test accuracy: 0.9073
0 Train accuracy: 0.86 Test accuracy: 0.9066
0 Train accuracy: 0.96 Test accuracy: 0.9091
0 Train accuracy: 0.92 Test accuracy: 0.9098
0 Train accuracy: 0.94 Test accuracy: 0.9096
0 Train accuracy: 0.94 Test accuracy: 0.9091
0 Train accuracy: 0.92 Test accuracy: 0.91
0 Train accuracy: 0.9 Test accuracy: 0.9099
0 Train accuracy: 0.86 Test accuracy: 0.9097
0 Train accuracy: 1.0 Test accuracy: 0.9101
0 Train accuracy: 0.92 Test accuracy: 0.9101
0 Train accuracy: 0.96 Test accuracy: 0.91
0 Train accuracy: 0.92 Test accuracy: 0.9095
0 Train accuracy: 0.92 Test accuracy: 0.9101
0 Train accuracy: 0.96 Test accuracy: 0.9096
0 Train accuracy: 0.88 Test accuracy: 0.9098
0 Train accuracy: 0.94 Test accuracy: 0.9109
0 Train accuracy: 0.84 Test accuracy: 0.9105
0 Train accuracy: 0.92 Test accuracy: 0.9097
0 Train accuracy: 0.92 Test accuracy: 0.9099
0 Train accuracy: 0.96 Test accuracy: 0.9105
0 Train accuracy: 0.9 Test accuracy: 0.9088
0 Train accuracy: 0.94 Test accuracy: 0.9083
0 Train accuracy: 0.94 Test accuracy: 0.9087
0 Train accuracy: 0.84 Test accuracy: 0.909
0 Train accuracy: 0.9 Test accuracy: 0.9077
0 Train accuracy: 0.94 Test accuracy: 0.9084
0 Train accuracy: 0.96 Test accuracy: 0.9088
0 Train accuracy: 0.88 Test accuracy: 0.9103
0 Train accuracy: 0.94 Test accuracy: 0.9086
0 Train accuracy: 0.94 Test accuracy: 0.9093
0 Train accuracy: 0.92 Test accuracy: 0.9078
0 Train accuracy: 0.96 Test accuracy: 0.9083
0 Train accuracy: 0.9 Test accuracy: 0.9086
0 Train accuracy: 0.94 Test accuracy: 0.9088
0 Train accuracy: 0.96 Test accuracy: 0.9104
0 Train accuracy: 0.94 Test accuracy: 0.9095
0 Train accuracy: 0.92 Test accuracy: 0.9092
0 Train accuracy: 0.94 Test accuracy: 0.9073
0 Train accuracy: 0.94 Test accuracy: 0.9068
0 Train accuracy: 0.94 Test accuracy: 0.9091
0 Train accuracy: 0.96 Test accuracy: 0.9082
0 Train accuracy: 0.88 Test accuracy: 0.9094
0 Train accuracy: 1.0 Test accuracy: 0.9085
0 Train accuracy: 0.94 Test accuracy: 0.9098
0 Train accuracy: 0.92 Test accuracy: 0.9097
0 Train accuracy: 0.9 Test accuracy: 0.9092
0 Train accuracy: 0.92 Test accuracy: 0.9101
0 Train accuracy: 0.94 Test accuracy: 0.9106
0 Train accuracy: 0.94 Test accuracy: 0.9104
0 Train accuracy: 0.96 Test accuracy: 0.9106
0 Train accuracy: 0.92 Test accuracy: 0.9096
0 Train accuracy: 0.92 Test accuracy: 0.9098
0 Train accuracy: 0.92 Test accuracy: 0.9101
0 Train accuracy: 0.8 Test accuracy: 0.91
0 Train accuracy: 0.9 Test accuracy: 0.9103
0 Train accuracy: 0.96 Test accuracy: 0.9108
0 Train accuracy: 0.86 Test accuracy: 0.9113
0 Train accuracy: 0.86 Test accuracy: 0.9106
0 Train accuracy: 0.9 Test accuracy: 0.9102
0 Train accuracy: 0.96 Test accuracy: 0.9089
0 Train accuracy: 0.94 Test accuracy: 0.9071
0 Train accuracy: 0.9 Test accuracy: 0.9092
0 Train accuracy: 0.94 Test accuracy: 0.9086
0 Train accuracy: 0.86 Test accuracy: 0.9082
0 Train accuracy: 0.92 Test accuracy: 0.9081
0 Train accuracy: 0.9 Test accuracy: 0.9091
0 Train accuracy: 0.9 Test accuracy: 0.9083
0 Train accuracy: 0.98 Test accuracy: 0.908
0 Train accuracy: 0.94 Test accuracy: 0.9086
0 Train accuracy: 0.84 Test accuracy: 0.91
0 Train accuracy: 0.94 Test accuracy: 0.9089
0 Train accuracy: 0.94 Test accuracy: 0.9091
0 Train accuracy: 0.8 Test accuracy: 0.9106
0 Train accuracy: 0.92 Test accuracy: 0.9104
0 Train accuracy: 0.86 Test accuracy: 0.9113
0 Train accuracy: 0.82 Test accuracy: 0.9106
0 Train accuracy: 0.9 Test accuracy: 0.9105
0 Train accuracy: 0.94 Test accuracy: 0.91
0 Train accuracy: 0.94 Test accuracy: 0.9109
0 Train accuracy: 0.94 Test accuracy: 0.9125
0 Train accuracy: 0.92 Test accuracy: 0.9113
0 Train accuracy: 0.86 Test accuracy: 0.9117
0 Train accuracy: 0.94 Test accuracy: 0.9121
0 Train accuracy: 0.96 Test accuracy: 0.9118
0 Train accuracy: 0.96 Test accuracy: 0.912
0 Train accuracy: 0.9 Test accuracy: 0.911
0 Train accuracy: 0.94 Test accuracy: 0.9113
0 Train accuracy: 0.96 Test accuracy: 0.912
0 Train accuracy: 0.92 Test accuracy: 0.9101
0 Train accuracy: 0.84 Test accuracy: 0.9094
0 Train accuracy: 0.94 Test accuracy: 0.9092
0 Train accuracy: 0.88 Test accuracy: 0.9082
0 Train accuracy: 0.98 Test accuracy: 0.9075
0 Train accuracy: 0.92 Test accuracy: 0.9091
0 Train accuracy: 0.94 Test accuracy: 0.9102
0 Train accuracy: 0.9 Test accuracy: 0.9107
0 Train accuracy: 0.96 Test accuracy: 0.9096
0 Train accuracy: 0.96 Test accuracy: 0.9101
0 Train accuracy: 0.9 Test accuracy: 0.9093
0 Train accuracy: 0.86 Test accuracy: 0.9097
0 Train accuracy: 0.96 Test accuracy: 0.9093
0 Train accuracy: 0.94 Test accuracy: 0.9099
0 Train accuracy: 0.86 Test accuracy: 0.9069
0 Train accuracy: 0.88 Test accuracy: 0.9075
0 Train accuracy: 0.96 Test accuracy: 0.9099
0 Train accuracy: 0.96 Test accuracy: 0.9108
0 Train accuracy: 0.9 Test accuracy: 0.9108
0 Train accuracy: 0.88 Test accuracy: 0.9094
0 Train accuracy: 0.9 Test accuracy: 0.9104
0 Train accuracy: 0.88 Test accuracy: 0.9108
0 Train accuracy: 1.0 Test accuracy: 0.9105
0 Train accuracy: 0.96 Test accuracy: 0.9103
0 Train accuracy: 0.92 Test accuracy: 0.9109
0 Train accuracy: 0.92 Test accuracy: 0.91
0 Train accuracy: 0.9 Test accuracy: 0.9113
0 Train accuracy: 0.94 Test accuracy: 0.911
0 Train accuracy: 0.92 Test accuracy: 0.9113
0 Train accuracy: 0.86 Test accuracy: 0.9119
0 Train accuracy: 0.92 Test accuracy: 0.9128
0 Train accuracy: 0.84 Test accuracy: 0.9111
0 Train accuracy: 0.96 Test accuracy: 0.9127
0 Train accuracy: 0.94 Test accuracy: 0.911
0 Train accuracy: 0.86 Test accuracy: 0.9117
0 Train accuracy: 0.84 Test accuracy: 0.914
0 Train accuracy: 0.94 Test accuracy: 0.9129
0 Train accuracy: 0.88 Test accuracy: 0.9134
0 Train accuracy: 0.94 Test accuracy: 0.9127
0 Train accuracy: 0.88 Test accuracy: 0.9119
0 Train accuracy: 0.86 Test accuracy: 0.9119
0 Train accuracy: 0.98 Test accuracy: 0.9125
0 Train accuracy: 0.96 Test accuracy: 0.9131
0 Train accuracy: 0.92 Test accuracy: 0.9124
0 Train accuracy: 0.92 Test accuracy: 0.9114
0 Train accuracy: 0.94 Test accuracy: 0.9114
0 Train accuracy: 0.94 Test accuracy: 0.911
0 Train accuracy: 0.96 Test accuracy: 0.9121
0 Train accuracy: 0.92 Test accuracy: 0.9133
0 Train accuracy: 0.88 Test accuracy: 0.9133
0 Train accuracy: 0.96 Test accuracy: 0.9129
0 Train accuracy: 0.92 Test accuracy: 0.9138
0 Train accuracy: 0.9 Test accuracy: 0.9115
0 Train accuracy: 0.86 Test accuracy: 0.9136
0 Train accuracy: 0.88 Test accuracy: 0.913
0 Train accuracy: 0.92 Test accuracy: 0.9134
0 Train accuracy: 0.94 Test accuracy: 0.9126
0 Train accuracy: 0.86 Test accuracy: 0.9125
0 Train accuracy: 0.86 Test accuracy: 0.9124
1 Train accuracy: 0.94 Test accuracy: 0.9117
1 Train accuracy: 0.84 Test accuracy: 0.9113
1 Train accuracy: 0.9 Test accuracy: 0.9128
1 Train accuracy: 0.94 Test accuracy: 0.9125
1 Train accuracy: 0.94 Test accuracy: 0.9104
1 Train accuracy: 1.0 Test accuracy: 0.9126
1 Train accuracy: 0.88 Test accuracy: 0.9141
1 Train accuracy: 0.94 Test accuracy: 0.9136
1 Train accuracy: 0.96 Test accuracy: 0.9139
1 Train accuracy: 0.88 Test accuracy: 0.913
1 Train accuracy: 0.88 Test accuracy: 0.9143
1 Train accuracy: 0.96 Test accuracy: 0.9136
1 Train accuracy: 0.94 Test accuracy: 0.9127
1 Train accuracy: 0.92 Test accuracy: 0.9125
1 Train accuracy: 0.96 Test accuracy: 0.912
1 Train accuracy: 0.92 Test accuracy: 0.9113
1 Train accuracy: 0.88 Test accuracy: 0.9137
1 Train accuracy: 1.0 Test accuracy: 0.9134
1 Train accuracy: 0.86 Test accuracy: 0.9135
1 Train accuracy: 0.88 Test accuracy: 0.9146
1 Train accuracy: 0.9 Test accuracy: 0.9128
1 Train accuracy: 0.92 Test accuracy: 0.9131
1 Train accuracy: 0.86 Test accuracy: 0.9122
1 Train accuracy: 0.96 Test accuracy: 0.9116
1 Train accuracy: 0.78 Test accuracy: 0.9108
1 Train accuracy: 0.92 Test accuracy: 0.9119
1 Train accuracy: 0.92 Test accuracy: 0.9118
1 Train accuracy: 0.94 Test accuracy: 0.9129
1 Train accuracy: 1.0 Test accuracy: 0.9138
1 Train accuracy: 0.86 Test accuracy: 0.912
1 Train accuracy: 0.96 Test accuracy: 0.9146
1 Train accuracy: 0.94 Test accuracy: 0.9135
1 Train accuracy: 0.98 Test accuracy: 0.9127
1 Train accuracy: 0.9 Test accuracy: 0.9136
1 Train accuracy: 0.92 Test accuracy: 0.9132
1 Train accuracy: 0.9 Test accuracy: 0.9133
1 Train accuracy: 0.86 Test accuracy: 0.9135
1 Train accuracy: 0.94 Test accuracy: 0.9135
1 Train accuracy: 0.98 Test accuracy: 0.9133
1 Train accuracy: 0.92 Test accuracy: 0.9145
1 Train accuracy: 0.96 Test accuracy: 0.9146
1 Train accuracy: 0.84 Test accuracy: 0.914
1 Train accuracy: 0.9 Test accuracy: 0.916
1 Train accuracy: 0.88 Test accuracy: 0.9154
1 Train accuracy: 0.86 Test accuracy: 0.9153
1 Train accuracy: 0.88 Test accuracy: 0.9147
1 Train accuracy: 0.86 Test accuracy: 0.9156
1 Train accuracy: 0.92 Test accuracy: 0.9141
1 Train accuracy: 0.88 Test accuracy: 0.9155
1 Train accuracy: 0.98 Test accuracy: 0.914
1 Train accuracy: 0.9 Test accuracy: 0.913
1 Train accuracy: 0.86 Test accuracy: 0.9115
1 Train accuracy: 0.94 Test accuracy: 0.9127
1 Train accuracy: 0.92 Test accuracy: 0.9131
1 Train accuracy: 0.96 Test accuracy: 0.9134
1 Train accuracy: 0.9 Test accuracy: 0.9128
1 Train accuracy: 0.98 Test accuracy: 0.9132
1 Train accuracy: 0.92 Test accuracy: 0.9133
1 Train accuracy: 0.9 Test accuracy: 0.9139
1 Train accuracy: 0.94 Test accuracy: 0.9128
1 Train accuracy: 0.96 Test accuracy: 0.9138
1 Train accuracy: 0.92 Test accuracy: 0.914
1 Train accuracy: 0.9 Test accuracy: 0.9138
1 Train accuracy: 0.92 Test accuracy: 0.9136
1 Train accuracy: 0.92 Test accuracy: 0.9132
1 Train accuracy: 0.96 Test accuracy: 0.9146
1 Train accuracy: 0.9 Test accuracy: 0.9138
1 Train accuracy: 0.92 Test accuracy: 0.9141
1 Train accuracy: 0.92 Test accuracy: 0.9146
1 Train accuracy: 0.9 Test accuracy: 0.9146
1 Train accuracy: 0.88 Test accuracy: 0.9147
1 Train accuracy: 0.86 Test accuracy: 0.9146
1 Train accuracy: 0.94 Test accuracy: 0.9145
1 Train accuracy: 0.92 Test accuracy: 0.9143
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1 Train accuracy: 0.94 Test accuracy: 0.9149
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1 Train accuracy: 0.88 Test accuracy: 0.9197
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1 Train accuracy: 0.94 Test accuracy: 0.9187
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1 Train accuracy: 0.94 Test accuracy: 0.9197
1 Train accuracy: 0.96 Test accuracy: 0.922
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1 Train accuracy: 0.94 Test accuracy: 0.9206
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1 Train accuracy: 0.88 Test accuracy: 0.9197
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1 Train accuracy: 0.98 Test accuracy: 0.9203
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1 Train accuracy: 0.88 Test accuracy: 0.9204
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1 Train accuracy: 0.92 Test accuracy: 0.9194
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1 Train accuracy: 0.96 Test accuracy: 0.9225
1 Train accuracy: 0.94 Test accuracy: 0.9228
1 Train accuracy: 0.92 Test accuracy: 0.9236
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1 Train accuracy: 0.96 Test accuracy: 0.922
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1 Train accuracy: 0.96 Test accuracy: 0.9219
1 Train accuracy: 0.9 Test accuracy: 0.9226
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1 Train accuracy: 0.92 Test accuracy: 0.9228
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1 Train accuracy: 0.98 Test accuracy: 0.9228
1 Train accuracy: 0.94 Test accuracy: 0.9201
1 Train accuracy: 0.9 Test accuracy: 0.9187
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1 Train accuracy: 0.9 Test accuracy: 0.9209
1 Train accuracy: 0.96 Test accuracy: 0.9216
1 Train accuracy: 0.88 Test accuracy: 0.922
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1 Train accuracy: 0.88 Test accuracy: 0.9221
1 Train accuracy: 0.94 Test accuracy: 0.9216
1 Train accuracy: 0.92 Test accuracy: 0.9221
1 Train accuracy: 1.0 Test accuracy: 0.9218
1 Train accuracy: 0.92 Test accuracy: 0.9215
1 Train accuracy: 0.94 Test accuracy: 0.9207
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1 Train accuracy: 0.9 Test accuracy: 0.9208
1 Train accuracy: 0.94 Test accuracy: 0.9214
1 Train accuracy: 0.92 Test accuracy: 0.9206
1 Train accuracy: 0.94 Test accuracy: 0.9199
1 Train accuracy: 0.9 Test accuracy: 0.9203
1 Train accuracy: 0.82 Test accuracy: 0.9204
1 Train accuracy: 0.88 Test accuracy: 0.921
1 Train accuracy: 0.94 Test accuracy: 0.9212
1 Train accuracy: 0.98 Test accuracy: 0.9221
1 Train accuracy: 0.92 Test accuracy: 0.922
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1 Train accuracy: 0.96 Test accuracy: 0.9221
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1 Train accuracy: 0.92 Test accuracy: 0.9231
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1 Train accuracy: 0.96 Test accuracy: 0.9232
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1 Train accuracy: 0.92 Test accuracy: 0.9237
1 Train accuracy: 0.94 Test accuracy: 0.9233
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1 Train accuracy: 1.0 Test accuracy: 0.9221
1 Train accuracy: 0.96 Test accuracy: 0.9231
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1 Train accuracy: 0.9 Test accuracy: 0.9229
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1 Train accuracy: 1.0 Test accuracy: 0.9229
1 Train accuracy: 0.92 Test accuracy: 0.9222
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1 Train accuracy: 0.98 Test accuracy: 0.9221
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1 Train accuracy: 0.92 Test accuracy: 0.9207
1 Train accuracy: 0.9 Test accuracy: 0.9198
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1 Train accuracy: 0.92 Test accuracy: 0.9213
1 Train accuracy: 0.92 Test accuracy: 0.9209
1 Train accuracy: 0.96 Test accuracy: 0.9221
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1 Train accuracy: 0.94 Test accuracy: 0.922
1 Train accuracy: 0.98 Test accuracy: 0.9223
1 Train accuracy: 0.86 Test accuracy: 0.9209
1 Train accuracy: 0.96 Test accuracy: 0.9199
1 Train accuracy: 0.96 Test accuracy: 0.9178
1 Train accuracy: 0.9 Test accuracy: 0.9193
1 Train accuracy: 0.9 Test accuracy: 0.9197
1 Train accuracy: 0.9 Test accuracy: 0.9202
1 Train accuracy: 0.92 Test accuracy: 0.9206
1 Train accuracy: 0.84 Test accuracy: 0.9204
1 Train accuracy: 0.96 Test accuracy: 0.9203
1 Train accuracy: 0.94 Test accuracy: 0.92
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1 Train accuracy: 0.88 Test accuracy: 0.9224
1 Train accuracy: 1.0 Test accuracy: 0.9236
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1 Train accuracy: 0.94 Test accuracy: 0.9223
1 Train accuracy: 0.96 Test accuracy: 0.9214
1 Train accuracy: 0.94 Test accuracy: 0.9231
1 Train accuracy: 0.94 Test accuracy: 0.9235
1 Train accuracy: 0.94 Test accuracy: 0.9229
1 Train accuracy: 0.96 Test accuracy: 0.923
1 Train accuracy: 0.8 Test accuracy: 0.9241
1 Train accuracy: 0.98 Test accuracy: 0.9242
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1 Train accuracy: 0.86 Test accuracy: 0.9231
1 Train accuracy: 0.92 Test accuracy: 0.9232
1 Train accuracy: 0.98 Test accuracy: 0.9237
1 Train accuracy: 0.86 Test accuracy: 0.9236
1 Train accuracy: 0.94 Test accuracy: 0.9248
1 Train accuracy: 0.98 Test accuracy: 0.9251
1 Train accuracy: 0.9 Test accuracy: 0.9227
1 Train accuracy: 0.94 Test accuracy: 0.9239
1 Train accuracy: 0.94 Test accuracy: 0.9236
1 Train accuracy: 0.84 Test accuracy: 0.9244
1 Train accuracy: 0.94 Test accuracy: 0.9246
1 Train accuracy: 0.94 Test accuracy: 0.9251
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1 Train accuracy: 0.92 Test accuracy: 0.9237
1 Train accuracy: 0.98 Test accuracy: 0.9246
1 Train accuracy: 0.94 Test accuracy: 0.9246
1 Train accuracy: 0.98 Test accuracy: 0.9244
1 Train accuracy: 0.94 Test accuracy: 0.9244
1 Train accuracy: 0.9 Test accuracy: 0.923
1 Train accuracy: 0.96 Test accuracy: 0.9232
1 Train accuracy: 0.9 Test accuracy: 0.9236
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1 Train accuracy: 0.92 Test accuracy: 0.9245
1 Train accuracy: 0.96 Test accuracy: 0.9233
1 Train accuracy: 0.92 Test accuracy: 0.9236
1 Train accuracy: 0.98 Test accuracy: 0.9243
1 Train accuracy: 0.92 Test accuracy: 0.9229
1 Train accuracy: 0.98 Test accuracy: 0.923
1 Train accuracy: 0.96 Test accuracy: 0.9234
1 Train accuracy: 0.9 Test accuracy: 0.9244
1 Train accuracy: 0.92 Test accuracy: 0.9245
1 Train accuracy: 0.9 Test accuracy: 0.924
1 Train accuracy: 0.88 Test accuracy: 0.9236
1 Train accuracy: 0.92 Test accuracy: 0.9241
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1 Train accuracy: 0.9 Test accuracy: 0.9248
1 Train accuracy: 0.94 Test accuracy: 0.9235
1 Train accuracy: 0.96 Test accuracy: 0.924
1 Train accuracy: 0.92 Test accuracy: 0.9238
1 Train accuracy: 0.94 Test accuracy: 0.9229
1 Train accuracy: 0.96 Test accuracy: 0.922
1 Train accuracy: 0.98 Test accuracy: 0.9232
1 Train accuracy: 0.9 Test accuracy: 0.9222
1 Train accuracy: 0.98 Test accuracy: 0.9231
1 Train accuracy: 0.98 Test accuracy: 0.923
1 Train accuracy: 0.96 Test accuracy: 0.9239
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1 Train accuracy: 1.0 Test accuracy: 0.9231
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1 Train accuracy: 0.92 Test accuracy: 0.9297
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1 Train accuracy: 0.96 Test accuracy: 0.9321
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1 Train accuracy: 0.92 Test accuracy: 0.9323
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1 Train accuracy: 0.94 Test accuracy: 0.9295
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1 Train accuracy: 0.92 Test accuracy: 0.9304
1 Train accuracy: 0.98 Test accuracy: 0.9303
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1 Train accuracy: 0.88 Test accuracy: 0.9298
1 Train accuracy: 0.92 Test accuracy: 0.93
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1 Train accuracy: 0.94 Test accuracy: 0.9301
1 Train accuracy: 0.96 Test accuracy: 0.9307
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1 Train accuracy: 0.86 Test accuracy: 0.9319
1 Train accuracy: 0.96 Test accuracy: 0.9314
1 Train accuracy: 0.94 Test accuracy: 0.931
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1 Train accuracy: 0.96 Test accuracy: 0.9319
1 Train accuracy: 0.88 Test accuracy: 0.9312
1 Train accuracy: 0.88 Test accuracy: 0.9306
1 Train accuracy: 0.96 Test accuracy: 0.9303
1 Train accuracy: 0.98 Test accuracy: 0.9296
1 Train accuracy: 0.9 Test accuracy: 0.9297
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1 Train accuracy: 0.96 Test accuracy: 0.9323
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5 Train accuracy: 0.92 Test accuracy: 0.9517
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5 Train accuracy: 0.94 Test accuracy: 0.9517
5 Train accuracy: 0.92 Test accuracy: 0.9519
5 Train accuracy: 0.96 Test accuracy: 0.9515
5 Train accuracy: 0.9 Test accuracy: 0.9517
5 Train accuracy: 0.98 Test accuracy: 0.9523
5 Train accuracy: 0.96 Test accuracy: 0.9528
5 Train accuracy: 0.98 Test accuracy: 0.9526
5 Train accuracy: 0.96 Test accuracy: 0.9521
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5 Train accuracy: 0.96 Test accuracy: 0.9522
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5 Train accuracy: 0.96 Test accuracy: 0.9527
5 Train accuracy: 0.88 Test accuracy: 0.9523
5 Train accuracy: 0.98 Test accuracy: 0.9528
5 Train accuracy: 0.92 Test accuracy: 0.9528
5 Train accuracy: 1.0 Test accuracy: 0.9533
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5 Train accuracy: 0.92 Test accuracy: 0.9528
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5 Train accuracy: 0.96 Test accuracy: 0.9525
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5 Train accuracy: 0.9 Test accuracy: 0.9526
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5 Train accuracy: 0.96 Test accuracy: 0.9512
5 Train accuracy: 1.0 Test accuracy: 0.9531
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5 Train accuracy: 0.96 Test accuracy: 0.9516
5 Train accuracy: 0.94 Test accuracy: 0.9499
5 Train accuracy: 0.94 Test accuracy: 0.9512
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5 Train accuracy: 0.96 Test accuracy: 0.9513
5 Train accuracy: 0.96 Test accuracy: 0.9525
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5 Train accuracy: 0.98 Test accuracy: 0.9518
5 Train accuracy: 0.98 Test accuracy: 0.9521
5 Train accuracy: 1.0 Test accuracy: 0.952
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5 Train accuracy: 0.92 Test accuracy: 0.9534
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5 Train accuracy: 0.98 Test accuracy: 0.9537
5 Train accuracy: 0.98 Test accuracy: 0.9532
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5 Train accuracy: 0.98 Test accuracy: 0.9535
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5 Train accuracy: 1.0 Test accuracy: 0.9538
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5 Train accuracy: 0.92 Test accuracy: 0.9504
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5 Train accuracy: 0.96 Test accuracy: 0.9509
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5 Train accuracy: 0.98 Test accuracy: 0.9522
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5 Train accuracy: 0.96 Test accuracy: 0.9513
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5 Train accuracy: 1.0 Test accuracy: 0.9519
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5 Train accuracy: 0.96 Test accuracy: 0.9516
5 Train accuracy: 0.98 Test accuracy: 0.9508
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5 Train accuracy: 1.0 Test accuracy: 0.9527
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5 Train accuracy: 0.92 Test accuracy: 0.9519
5 Train accuracy: 1.0 Test accuracy: 0.9523
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5 Train accuracy: 0.98 Test accuracy: 0.9526
5 Train accuracy: 0.9 Test accuracy: 0.9525
5 Train accuracy: 1.0 Test accuracy: 0.9522
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5 Train accuracy: 0.92 Test accuracy: 0.9534
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5 Train accuracy: 0.96 Test accuracy: 0.9516
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5 Train accuracy: 0.98 Test accuracy: 0.9526
5 Train accuracy: 0.94 Test accuracy: 0.9522
5 Train accuracy: 0.94 Test accuracy: 0.9521
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5 Train accuracy: 1.0 Test accuracy: 0.9524
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5 Train accuracy: 0.98 Test accuracy: 0.9521
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5 Train accuracy: 0.94 Test accuracy: 0.9525
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5 Train accuracy: 0.92 Test accuracy: 0.9522
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5 Train accuracy: 0.98 Test accuracy: 0.9514
5 Train accuracy: 1.0 Test accuracy: 0.9521
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5 Train accuracy: 0.96 Test accuracy: 0.9518
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5 Train accuracy: 1.0 Test accuracy: 0.9526
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5 Train accuracy: 0.9 Test accuracy: 0.9525
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5 Train accuracy: 0.96 Test accuracy: 0.9536
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5 Train accuracy: 1.0 Test accuracy: 0.9526
5 Train accuracy: 0.96 Test accuracy: 0.9534
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5 Train accuracy: 0.94 Test accuracy: 0.9537
5 Train accuracy: 0.98 Test accuracy: 0.9533
5 Train accuracy: 0.96 Test accuracy: 0.9531
5 Train accuracy: 0.92 Test accuracy: 0.9536
5 Train accuracy: 0.96 Test accuracy: 0.9535
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5 Train accuracy: 0.96 Test accuracy: 0.9532
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5 Train accuracy: 1.0 Test accuracy: 0.953
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5 Train accuracy: 0.94 Test accuracy: 0.9534
5 Train accuracy: 1.0 Test accuracy: 0.954
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5 Train accuracy: 0.96 Test accuracy: 0.9527
5 Train accuracy: 0.96 Test accuracy: 0.9523
5 Train accuracy: 1.0 Test accuracy: 0.9525
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5 Train accuracy: 0.94 Test accuracy: 0.9521
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5 Train accuracy: 0.96 Test accuracy: 0.9531
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5 Train accuracy: 0.96 Test accuracy: 0.9525
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5 Train accuracy: 0.92 Test accuracy: 0.9529
5 Train accuracy: 0.96 Test accuracy: 0.9522
5 Train accuracy: 0.98 Test accuracy: 0.9533
5 Train accuracy: 0.98 Test accuracy: 0.9536
5 Train accuracy: 0.94 Test accuracy: 0.9525
5 Train accuracy: 0.96 Test accuracy: 0.9522
5 Train accuracy: 0.98 Test accuracy: 0.9524
5 Train accuracy: 1.0 Test accuracy: 0.9518
5 Train accuracy: 0.96 Test accuracy: 0.9521
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5 Train accuracy: 0.92 Test accuracy: 0.953
5 Train accuracy: 0.98 Test accuracy: 0.9534
5 Train accuracy: 0.96 Test accuracy: 0.9525
5 Train accuracy: 0.98 Test accuracy: 0.9529
5 Train accuracy: 1.0 Test accuracy: 0.9523
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5 Train accuracy: 1.0 Test accuracy: 0.952
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5 Train accuracy: 0.96 Test accuracy: 0.9521
5 Train accuracy: 0.96 Test accuracy: 0.9516
5 Train accuracy: 0.94 Test accuracy: 0.9513
5 Train accuracy: 0.96 Test accuracy: 0.9518
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5 Train accuracy: 0.98 Test accuracy: 0.9528
5 Train accuracy: 1.0 Test accuracy: 0.9531
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5 Train accuracy: 0.96 Test accuracy: 0.9529
5 Train accuracy: 0.96 Test accuracy: 0.9523
5 Train accuracy: 0.98 Test accuracy: 0.9528
5 Train accuracy: 0.88 Test accuracy: 0.951
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5 Train accuracy: 0.94 Test accuracy: 0.9511
5 Train accuracy: 0.96 Test accuracy: 0.9524
5 Train accuracy: 0.94 Test accuracy: 0.9528
5 Train accuracy: 0.92 Test accuracy: 0.9528
5 Train accuracy: 1.0 Test accuracy: 0.9529
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5 Train accuracy: 0.98 Test accuracy: 0.9538
5 Train accuracy: 1.0 Test accuracy: 0.9539
5 Train accuracy: 0.98 Test accuracy: 0.9537
5 Train accuracy: 0.96 Test accuracy: 0.953
5 Train accuracy: 0.96 Test accuracy: 0.9535
5 Train accuracy: 0.92 Test accuracy: 0.9537
5 Train accuracy: 0.96 Test accuracy: 0.9542
5 Train accuracy: 1.0 Test accuracy: 0.9539
5 Train accuracy: 0.92 Test accuracy: 0.9531
5 Train accuracy: 0.98 Test accuracy: 0.9535
5 Train accuracy: 0.98 Test accuracy: 0.9544
5 Train accuracy: 0.94 Test accuracy: 0.9526
5 Train accuracy: 0.96 Test accuracy: 0.952
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5 Train accuracy: 1.0 Test accuracy: 0.9524
5 Train accuracy: 1.0 Test accuracy: 0.9524
5 Train accuracy: 0.92 Test accuracy: 0.9515
5 Train accuracy: 0.92 Test accuracy: 0.9519
5 Train accuracy: 0.98 Test accuracy: 0.9528
5 Train accuracy: 0.92 Test accuracy: 0.9531
5 Train accuracy: 0.96 Test accuracy: 0.9531
5 Train accuracy: 0.98 Test accuracy: 0.9532
5 Train accuracy: 0.98 Test accuracy: 0.9536
5 Train accuracy: 1.0 Test accuracy: 0.9536
5 Train accuracy: 0.98 Test accuracy: 0.9529
5 Train accuracy: 0.96 Test accuracy: 0.9522
5 Train accuracy: 0.96 Test accuracy: 0.9524
5 Train accuracy: 0.9 Test accuracy: 0.9522
5 Train accuracy: 0.96 Test accuracy: 0.9529
5 Train accuracy: 0.92 Test accuracy: 0.9526
5 Train accuracy: 0.98 Test accuracy: 0.9525
5 Train accuracy: 1.0 Test accuracy: 0.9526
5 Train accuracy: 0.96 Test accuracy: 0.9528
5 Train accuracy: 0.98 Test accuracy: 0.9528
5 Train accuracy: 0.92 Test accuracy: 0.9524
5 Train accuracy: 0.96 Test accuracy: 0.9536
5 Train accuracy: 0.94 Test accuracy: 0.9538
5 Train accuracy: 0.98 Test accuracy: 0.9525
5 Train accuracy: 0.92 Test accuracy: 0.9528
5 Train accuracy: 0.86 Test accuracy: 0.9537
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5 Train accuracy: 0.98 Test accuracy: 0.9528
5 Train accuracy: 0.96 Test accuracy: 0.9536
5 Train accuracy: 1.0 Test accuracy: 0.9537
5 Train accuracy: 0.96 Test accuracy: 0.954
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5 Train accuracy: 0.92 Test accuracy: 0.9544
5 Train accuracy: 0.98 Test accuracy: 0.9545
5 Train accuracy: 1.0 Test accuracy: 0.9541
5 Train accuracy: 0.98 Test accuracy: 0.9538
5 Train accuracy: 0.9 Test accuracy: 0.9534
5 Train accuracy: 1.0 Test accuracy: 0.9534
5 Train accuracy: 0.96 Test accuracy: 0.9526
5 Train accuracy: 0.94 Test accuracy: 0.9537
5 Train accuracy: 0.98 Test accuracy: 0.9534
5 Train accuracy: 0.98 Test accuracy: 0.954
5 Train accuracy: 0.92 Test accuracy: 0.9533
5 Train accuracy: 1.0 Test accuracy: 0.9533
5 Train accuracy: 1.0 Test accuracy: 0.9532
5 Train accuracy: 1.0 Test accuracy: 0.9532
5 Train accuracy: 0.92 Test accuracy: 0.953
5 Train accuracy: 1.0 Test accuracy: 0.9529
5 Train accuracy: 0.92 Test accuracy: 0.9531
5 Train accuracy: 1.0 Test accuracy: 0.9533
5 Train accuracy: 0.98 Test accuracy: 0.9533
5 Train accuracy: 0.92 Test accuracy: 0.9532
5 Train accuracy: 0.98 Test accuracy: 0.9524
5 Train accuracy: 0.96 Test accuracy: 0.9525
5 Train accuracy: 0.94 Test accuracy: 0.9529
5 Train accuracy: 0.98 Test accuracy: 0.9539
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5 Train accuracy: 0.98 Test accuracy: 0.9537
5 Train accuracy: 0.98 Test accuracy: 0.9531
5 Train accuracy: 0.94 Test accuracy: 0.9529
5 Train accuracy: 0.96 Test accuracy: 0.9527
5 Train accuracy: 0.98 Test accuracy: 0.9524
5 Train accuracy: 0.96 Test accuracy: 0.9521
5 Train accuracy: 0.94 Test accuracy: 0.9518
5 Train accuracy: 0.94 Test accuracy: 0.9527
5 Train accuracy: 0.94 Test accuracy: 0.9526
5 Train accuracy: 0.98 Test accuracy: 0.9523
5 Train accuracy: 0.94 Test accuracy: 0.9527
5 Train accuracy: 0.94 Test accuracy: 0.9532
5 Train accuracy: 0.96 Test accuracy: 0.9536
5 Train accuracy: 1.0 Test accuracy: 0.9535
5 Train accuracy: 0.98 Test accuracy: 0.9535
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5 Train accuracy: 0.96 Test accuracy: 0.9538
5 Train accuracy: 0.98 Test accuracy: 0.9534
5 Train accuracy: 0.98 Test accuracy: 0.9535
5 Train accuracy: 0.92 Test accuracy: 0.9535
5 Train accuracy: 0.94 Test accuracy: 0.9525
5 Train accuracy: 0.96 Test accuracy: 0.9528
5 Train accuracy: 0.96 Test accuracy: 0.9527
5 Train accuracy: 1.0 Test accuracy: 0.9529
5 Train accuracy: 0.92 Test accuracy: 0.9527
5 Train accuracy: 0.96 Test accuracy: 0.9534
5 Train accuracy: 0.96 Test accuracy: 0.9541
5 Train accuracy: 0.98 Test accuracy: 0.9534
5 Train accuracy: 1.0 Test accuracy: 0.9538
5 Train accuracy: 0.96 Test accuracy: 0.9531
5 Train accuracy: 0.96 Test accuracy: 0.9534
5 Train accuracy: 1.0 Test accuracy: 0.953
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5 Train accuracy: 0.94 Test accuracy: 0.953
5 Train accuracy: 0.96 Test accuracy: 0.9531
5 Train accuracy: 0.96 Test accuracy: 0.9536
5 Train accuracy: 1.0 Test accuracy: 0.9541
5 Train accuracy: 0.98 Test accuracy: 0.9546
5 Train accuracy: 0.88 Test accuracy: 0.9535
5 Train accuracy: 0.96 Test accuracy: 0.9524
5 Train accuracy: 0.98 Test accuracy: 0.9521
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5 Train accuracy: 0.94 Test accuracy: 0.9531
5 Train accuracy: 0.96 Test accuracy: 0.9528
5 Train accuracy: 0.92 Test accuracy: 0.9528
5 Train accuracy: 0.94 Test accuracy: 0.9531
5 Train accuracy: 1.0 Test accuracy: 0.9529
5 Train accuracy: 0.94 Test accuracy: 0.9532
5 Train accuracy: 0.92 Test accuracy: 0.9527
5 Train accuracy: 0.94 Test accuracy: 0.9522
5 Train accuracy: 0.94 Test accuracy: 0.9525
5 Train accuracy: 0.94 Test accuracy: 0.9529
5 Train accuracy: 1.0 Test accuracy: 0.9524
5 Train accuracy: 0.98 Test accuracy: 0.9517
5 Train accuracy: 0.96 Test accuracy: 0.9528
5 Train accuracy: 0.94 Test accuracy: 0.9523
5 Train accuracy: 0.96 Test accuracy: 0.9527
5 Train accuracy: 0.92 Test accuracy: 0.9529
5 Train accuracy: 1.0 Test accuracy: 0.9516
5 Train accuracy: 0.94 Test accuracy: 0.9523
5 Train accuracy: 0.96 Test accuracy: 0.9527
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5 Train accuracy: 0.98 Test accuracy: 0.9524
5 Train accuracy: 0.96 Test accuracy: 0.9526
5 Train accuracy: 0.96 Test accuracy: 0.9531
5 Train accuracy: 0.94 Test accuracy: 0.9535
5 Train accuracy: 0.96 Test accuracy: 0.9536
5 Train accuracy: 0.92 Test accuracy: 0.9527
5 Train accuracy: 0.94 Test accuracy: 0.9526
5 Train accuracy: 0.94 Test accuracy: 0.9531
5 Train accuracy: 0.96 Test accuracy: 0.9525
5 Train accuracy: 0.94 Test accuracy: 0.9523
5 Train accuracy: 0.98 Test accuracy: 0.9529
5 Train accuracy: 0.96 Test accuracy: 0.954
5 Train accuracy: 1.0 Test accuracy: 0.9537
5 Train accuracy: 0.96 Test accuracy: 0.9536
5 Train accuracy: 1.0 Test accuracy: 0.9534
5 Train accuracy: 0.94 Test accuracy: 0.9534
5 Train accuracy: 0.88 Test accuracy: 0.953
5 Train accuracy: 0.9 Test accuracy: 0.9531
5 Train accuracy: 0.94 Test accuracy: 0.9531
5 Train accuracy: 0.98 Test accuracy: 0.9539
5 Train accuracy: 0.96 Test accuracy: 0.9538
5 Train accuracy: 0.92 Test accuracy: 0.9528
5 Train accuracy: 0.92 Test accuracy: 0.9537
5 Train accuracy: 0.96 Test accuracy: 0.9537
5 Train accuracy: 1.0 Test accuracy: 0.9537
5 Train accuracy: 0.92 Test accuracy: 0.9535
5 Train accuracy: 0.98 Test accuracy: 0.9537
5 Train accuracy: 0.96 Test accuracy: 0.9537
5 Train accuracy: 1.0 Test accuracy: 0.9539
5 Train accuracy: 0.96 Test accuracy: 0.9535
5 Train accuracy: 0.96 Test accuracy: 0.9535
5 Train accuracy: 0.94 Test accuracy: 0.9541
5 Train accuracy: 0.96 Test accuracy: 0.9538
5 Train accuracy: 0.94 Test accuracy: 0.9538
5 Train accuracy: 0.94 Test accuracy: 0.9538
5 Train accuracy: 0.96 Test accuracy: 0.9542
5 Train accuracy: 0.96 Test accuracy: 0.9531
5 Train accuracy: 0.96 Test accuracy: 0.9526
5 Train accuracy: 1.0 Test accuracy: 0.9533
5 Train accuracy: 0.9 Test accuracy: 0.9538
5 Train accuracy: 0.94 Test accuracy: 0.9515
5 Train accuracy: 1.0 Test accuracy: 0.952
5 Train accuracy: 0.94 Test accuracy: 0.9523
5 Train accuracy: 0.92 Test accuracy: 0.9532
5 Train accuracy: 0.96 Test accuracy: 0.9534
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9 Train accuracy: 0.98 Test accuracy: 0.9642
9 Train accuracy: 0.98 Test accuracy: 0.9633
9 Train accuracy: 1.0 Test accuracy: 0.9628
9 Train accuracy: 1.0 Test accuracy: 0.9626
9 Train accuracy: 0.98 Test accuracy: 0.9633
9 Train accuracy: 0.96 Test accuracy: 0.9628
9 Train accuracy: 1.0 Test accuracy: 0.9628
9 Train accuracy: 0.98 Test accuracy: 0.9628
9 Train accuracy: 1.0 Test accuracy: 0.9628
9 Train accuracy: 0.98 Test accuracy: 0.9634
9 Train accuracy: 0.96 Test accuracy: 0.9624
9 Train accuracy: 0.98 Test accuracy: 0.9633
9 Train accuracy: 0.98 Test accuracy: 0.9637
9 Train accuracy: 0.94 Test accuracy: 0.9622
9 Train accuracy: 0.96 Test accuracy: 0.963
9 Train accuracy: 0.96 Test accuracy: 0.9628
9 Train accuracy: 0.98 Test accuracy: 0.9643
9 Train accuracy: 1.0 Test accuracy: 0.9643
9 Train accuracy: 0.98 Test accuracy: 0.963
9 Train accuracy: 1.0 Test accuracy: 0.9633
9 Train accuracy: 1.0 Test accuracy: 0.9639
9 Train accuracy: 0.96 Test accuracy: 0.9636
9 Train accuracy: 0.96 Test accuracy: 0.964
9 Train accuracy: 0.98 Test accuracy: 0.9646
9 Train accuracy: 0.94 Test accuracy: 0.9637
9 Train accuracy: 0.98 Test accuracy: 0.9636
9 Train accuracy: 0.98 Test accuracy: 0.9635
9 Train accuracy: 0.96 Test accuracy: 0.9644
9 Train accuracy: 1.0 Test accuracy: 0.9645
9 Train accuracy: 1.0 Test accuracy: 0.9644
9 Train accuracy: 0.98 Test accuracy: 0.9636
9 Train accuracy: 0.98 Test accuracy: 0.9632
9 Train accuracy: 1.0 Test accuracy: 0.9636
9 Train accuracy: 1.0 Test accuracy: 0.9635
9 Train accuracy: 0.96 Test accuracy: 0.9634
9 Train accuracy: 0.98 Test accuracy: 0.9629
9 Train accuracy: 0.96 Test accuracy: 0.9629
9 Train accuracy: 0.94 Test accuracy: 0.963
9 Train accuracy: 0.98 Test accuracy: 0.9629
9 Train accuracy: 0.98 Test accuracy: 0.9624
9 Train accuracy: 0.98 Test accuracy: 0.9632
9 Train accuracy: 1.0 Test accuracy: 0.9631
9 Train accuracy: 1.0 Test accuracy: 0.9633
9 Train accuracy: 0.96 Test accuracy: 0.963
9 Train accuracy: 0.98 Test accuracy: 0.9642
9 Train accuracy: 0.92 Test accuracy: 0.9633
9 Train accuracy: 0.96 Test accuracy: 0.9639
9 Train accuracy: 0.98 Test accuracy: 0.9638
9 Train accuracy: 1.0 Test accuracy: 0.9637
9 Train accuracy: 1.0 Test accuracy: 0.9632
9 Train accuracy: 0.98 Test accuracy: 0.9637
9 Train accuracy: 1.0 Test accuracy: 0.9638
9 Train accuracy: 0.96 Test accuracy: 0.9637
9 Train accuracy: 0.96 Test accuracy: 0.9641
9 Train accuracy: 1.0 Test accuracy: 0.9642
9 Train accuracy: 1.0 Test accuracy: 0.9642
9 Train accuracy: 0.98 Test accuracy: 0.9644
9 Train accuracy: 1.0 Test accuracy: 0.9643
9 Train accuracy: 1.0 Test accuracy: 0.9648
9 Train accuracy: 0.98 Test accuracy: 0.9648
9 Train accuracy: 1.0 Test accuracy: 0.9642
9 Train accuracy: 1.0 Test accuracy: 0.9642
9 Train accuracy: 0.96 Test accuracy: 0.9641
9 Train accuracy: 1.0 Test accuracy: 0.9636
9 Train accuracy: 0.96 Test accuracy: 0.9641
9 Train accuracy: 0.98 Test accuracy: 0.9641
9 Train accuracy: 0.98 Test accuracy: 0.9641
9 Train accuracy: 1.0 Test accuracy: 0.9639
9 Train accuracy: 1.0 Test accuracy: 0.9641
9 Train accuracy: 0.94 Test accuracy: 0.9641
9 Train accuracy: 1.0 Test accuracy: 0.9642
9 Train accuracy: 0.98 Test accuracy: 0.964
9 Train accuracy: 1.0 Test accuracy: 0.964
9 Train accuracy: 1.0 Test accuracy: 0.9632
9 Train accuracy: 0.98 Test accuracy: 0.9636
9 Train accuracy: 0.98 Test accuracy: 0.9634
9 Train accuracy: 1.0 Test accuracy: 0.9636
9 Train accuracy: 1.0 Test accuracy: 0.9641
9 Train accuracy: 0.98 Test accuracy: 0.9634
9 Train accuracy: 0.98 Test accuracy: 0.9645
9 Train accuracy: 0.96 Test accuracy: 0.9639
9 Train accuracy: 0.94 Test accuracy: 0.9628
9 Train accuracy: 0.98 Test accuracy: 0.9626
9 Train accuracy: 0.98 Test accuracy: 0.9631
9 Train accuracy: 0.98 Test accuracy: 0.963
9 Train accuracy: 1.0 Test accuracy: 0.9628
9 Train accuracy: 0.96 Test accuracy: 0.9635
9 Train accuracy: 0.96 Test accuracy: 0.9629
9 Train accuracy: 0.96 Test accuracy: 0.9634
9 Train accuracy: 0.94 Test accuracy: 0.9635
9 Train accuracy: 0.98 Test accuracy: 0.9634
9 Train accuracy: 1.0 Test accuracy: 0.9636
9 Train accuracy: 0.96 Test accuracy: 0.9644
9 Train accuracy: 0.98 Test accuracy: 0.9638
9 Train accuracy: 0.98 Test accuracy: 0.9632
9 Train accuracy: 0.98 Test accuracy: 0.9636
9 Train accuracy: 1.0 Test accuracy: 0.9634
9 Train accuracy: 1.0 Test accuracy: 0.9625
9 Train accuracy: 0.94 Test accuracy: 0.963
9 Train accuracy: 1.0 Test accuracy: 0.9628
9 Train accuracy: 0.98 Test accuracy: 0.9624
9 Train accuracy: 0.98 Test accuracy: 0.9627
9 Train accuracy: 0.98 Test accuracy: 0.963
9 Train accuracy: 0.96 Test accuracy: 0.9639
9 Train accuracy: 0.98 Test accuracy: 0.9642
9 Train accuracy: 0.98 Test accuracy: 0.9638
9 Train accuracy: 0.98 Test accuracy: 0.964
9 Train accuracy: 0.98 Test accuracy: 0.9638
9 Train accuracy: 1.0 Test accuracy: 0.9643
9 Train accuracy: 0.98 Test accuracy: 0.9634
9 Train accuracy: 0.98 Test accuracy: 0.9635
9 Train accuracy: 0.98 Test accuracy: 0.9637
9 Train accuracy: 0.98 Test accuracy: 0.9632
9 Train accuracy: 0.9 Test accuracy: 0.9638
9 Train accuracy: 0.98 Test accuracy: 0.964
9 Train accuracy: 0.94 Test accuracy: 0.9634
9 Train accuracy: 1.0 Test accuracy: 0.9637
  1. Above code opens a TensorFlow session, and it runs the init node that initializes all the variables.
  2. Then it runs the main training loop:
  3. at each epoch, the code iterates through a number of mini-batches that corresponds to the training set size.
  4. Each mini-batch is fetched via the next_batch() method,
  5. then the code simply runs the training operation, feeding it the current mini-batch input data and targets.
  6. Next, at the end of each epoch, the code evaluates the model on the last mini-batch and on the full training set, and it prints out the result.
  7. Finally, the model parameters are saved to disk.
# Plan B: define our own shuffle function (python generator) n_epochs = 40 batch_size = 50 def shuffle_batch(X, y, batch_size): rnd_idx = np.random.permutation(len(X)) n_batches = len(X) // batch_size for batch_idx in np.array_split(rnd_idx, n_batches): X_batch, y_batch = X[batch_idx], y[batch_idx] yield X_batch, y_batch
# training using our generator with tf.Session() as sess: init.run() for epoch in range(n_epochs): for X_batch, y_batch in shuffle_batch(X_train, y_train, batch_size): sess.run(training_op, feed_dict={X: X_batch, y: y_batch}) acc_batch = accuracy.eval(feed_dict={X: X_batch, y: y_batch}) acc_val = accuracy.eval(feed_dict={X: X_valid, y: y_valid}) print(epoch, "Batch accuracy:", acc_batch, "Val accuracy:", acc_val) save_path = saver.save(sess, "./my_model_final.ckpt")

Using the Neural Network

Now that the neural network is trained, you can use it to make predictions. To do that, you can reuse the same construction phase, but change the execution phase like this:

In [ ]:
with tf.Session() as sess:    
    saver.restore(sess, "./my_model_final.ckpt")    
    X_new_scaled = [...]  # some new images (scaled from 0 to 1)    
    Z = logits.eval(feed_dict={X: X_new_scaled})    
    y_pred = np.argmax(Z, axis=1) 
  1. First the code loads the model parameters from disk.
  2. Then it loads some new images that you want to classify. must apply same feature scaling as for the training data (in this case, scale it from 0 to 1).
  3. Then the code evaluates the logits node. If you wanted to know all the estimated class probabilities, you would need to apply the softmax() function to the logits, but if you just want to predict a class, you can simply pick the class that has the highest logit value (using the argmax() function does the trick).
In [ ]:
print("Predicted classes:", y_pred)
print("Actual classes:   ", y_test[:20])
In [ ]:
from tensorflow_graph_in_jupyter import show_graph
show_graph(tf.get_default_graph())

VI. Design & Optimization Strategy

Fine-Tuning Neural Network Hyperparameters

The flexibility of neural networks is also one of their main drawbacks: there are many hyperparameters to tweak.

For any task you can use any imaginable network topology (how neurons are interconnected), but even in a simple MLP you can change:

  • the number of layers,
  • the number of neurons per layer,
  • the type of activation function to use in each layer,
  • the weight initialization logic,
  • and much more.

How do you know what combination of hyperparameters is the best for your task?

Grid-search + Cross-validation?

  • many hyperparameters to tune,
  • and training a neural network on a large dataset takes a lot of time,
  • hence you will only be able to explore a tiny part of the hyperparameter space in a reasonable amount of time

Other ("better") options:

  • Randomized search - see chapter 2
  • Oscar or similar tool

Rules of thumb

  • Find in publications or class texts
  • Give an idea of what hyperparameter values are reasonable to restrict search space

Number of Hidden Layers

  • For many problems, you can just begin with a single hidden layer and you will get reasonable results.
  • universal approximator results caused researchers to not look into deeper networks for long time
  • But recent results show deep networks have a much higher parameter efficiency than shallow ones: they can model complex functions using exponentially fewer neurons than shallow nets, making them much faster to train.
  • hierarchical architecture perspective on deep networks
  • also generalize better to new problems/data; common low-level structures (edges, points) plus new high-level features

Start small

  • for many problems you can start with just one or two hidden layers and it will work just fine (e.g., you can easily reach above 97% accuracy on the MNIST dataset using just one hidden layer with a few hundred neurons, and above 98% accuracy using two hidden layers with the same total amount of neurons, in roughly the same amount of training time).
  • For more complex problems, you can gradually ramp up the number of hidden layers, until you start overfitting the training set. Very complex tasks, such as large image classification or speech recognition, typically require networks with dozens of layers (or even hundreds), and they need a huge amount of training data.
  • You will rarely have to train such networks from scratch: it is much more common to reuse parts of a pretrained state-of-the-art network that performs a similar task. Training will be a lot faster and require much less data

Number of Neurons per Hidden Layer

  • Number of neurons in the input and output layers is determined by the type of input and output your task requires. For example, the MNIST task requires 28 x 28 = 784 input neurons and 10 output neurons
  • For hidden layers, an older practice is to size them to form a funnel, with fewer and fewer neurons at each layer— the rationale being that many low-level features can coalesce into far fewer high-level features. For example, a typical neural network for MNIST may have two hidden layers, the first with 300 neurons and the second with 100.
  • this practice is not as common now, and you may simply use the same size for all hidden layers—for example, all hidden layers with 150 neurons: that’s just one hyperparameter to tune instead of one per layer.
  • Just like for the number of layers, you can try increasing the number of neurons gradually until the network starts overfitting.
  • In general you will get more bang for the buck by increasing the number of layers than the number of neurons per layer

"Stretch pants approach"

  • Simpler idea: pick a model with more layers and neurons than you actually need
  • use early stopping to prevent it from overfitting (also use other regularization techniques, especially dropout).
  • Dubbed the “stretch pants” approach (By Vincent Vanhoucke's Deep Learning class on Udacity.com)
  • Instead of wasting time looking for pants that perfectly match your size, just use large stretch pants that will shrink down to the right size.