A Simple Autoencoder

We'll start off by building a simple autoencoder to compress the MNIST dataset. With autoencoders, we pass input data through an encoder that makes a compressed representation of the input. Then, this representation is passed through a decoder to reconstruct the input data. Generally the encoder and decoder will be built with neural networks, then trained on example data.

In this notebook, we'll be build a simple network architecture for the encoder and decoder. Let's get started by importing our libraries and getting the dataset.



In [1]:

    
%matplotlib inline

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt



In [2]:

    
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets('MNIST_data', validation_size=0)









    



Successfully downloaded train-images-idx3-ubyte.gz 9912422 bytes.
Extracting MNIST_data/train-images-idx3-ubyte.gz
Successfully downloaded train-labels-idx1-ubyte.gz 28881 bytes.
Extracting MNIST_data/train-labels-idx1-ubyte.gz
Successfully downloaded t10k-images-idx3-ubyte.gz 1648877 bytes.
Extracting MNIST_data/t10k-images-idx3-ubyte.gz
Successfully downloaded t10k-labels-idx1-ubyte.gz 4542 bytes.
Extracting MNIST_data/t10k-labels-idx1-ubyte.gz

Below I'm plotting an example image from the MNIST dataset. These are 28x28 grayscale images of handwritten digits.



In [3]:

    
img = mnist.train.images[2]
plt.imshow(img.reshape((28, 28)), cmap='Greys_r')









    Out[3]:





<matplotlib.image.AxesImage at 0x7faa65b2feb8>

We'll train an autoencoder with these images by flattening them into 784 length vectors. The images from this dataset are already normalized such that the values are between 0 and 1. Let's start by building basically the simplest autoencoder with a single ReLU hidden layer. This layer will be used as the compressed representation. Then, the encoder is the input layer and the hidden layer. The decoder is the hidden layer and the output layer. Since the images are normalized between 0 and 1, we need to use a sigmoid activation on the output layer to get values matching the input.

Exercise: Build the graph for the autoencoder in the cell below. The input images will be flattened into 784 length vectors. The targets are the same as the inputs. And there should be one hidden layer with a ReLU activation and an output layer with a sigmoid activation. Feel free to use TensorFlow's higher level API, tf.layers. For instance, you would use tf.layers.dense(inputs, units, activation=tf.nn.relu) to create a fully connected layer with a ReLU activation. The loss should be calculated with the cross-entropy loss, there is a convenient TensorFlow function for this tf.nn.sigmoid_cross_entropy_with_logits (documentation). You should note that tf.nn.sigmoid_cross_entropy_with_logits takes the logits, but to get the reconstructed images you'll need to pass the logits through the sigmoid function.



In [5]:

    
# Size of the encoding layer (the hidden layer)
encoding_dim = 32 # feel free to change this value

image_size = mnist.train.images.shape[1]

# Input and target placeholders
inputs_ = tf.placeholder(tf.float32, (None, image_size), name='inputs')
targets_ = tf.placeholder(tf.float32, (None, image_size), name='targets')

# Output of hidden layer, single fully connected layer here with ReLU activation
encoded = tf.layers.dense(inputs_, encoding_dim, activation=tf.nn.relu)

# Output layer logits, fully connected layer with no activation
logits = tf.layers.dense(inputs_, image_size, activation=None)
# Sigmoid output from logits
decoded = tf.nn.sigmoid(logits, name='output')

# Sigmoid cross-entropy loss
loss = tf.nn.sigmoid_cross_entropy_with_logits(labels=targets_, logits=logits)
# Mean of the loss
cost = tf.reduce_mean(loss)

# Adam optimizer
learning_rate = 0.001
opt = tf.train.AdamOptimizer(learning_rate).minimize(cost)

Training



In [6]:

    
# Create the session
sess = tf.Session()

Here I'll write a bit of code to train the network. I'm not too interested in validation here, so I'll just monitor the training loss.

Calling mnist.train.next_batch(batch_size) will return a tuple of (images, labels). We're not concerned with the labels here, we just need the images. Otherwise this is pretty straightfoward training with TensorFlow. We initialize the variables with sess.run(tf.global_variables_initializer()). Then, run the optimizer and get the loss with batch_cost, _ = sess.run([cost, opt], feed_dict=feed).



In [7]:

    
epochs = 20
batch_size = 200
sess.run(tf.global_variables_initializer())
for e in range(epochs):
    for ii in range(mnist.train.num_examples//batch_size):
        batch = mnist.train.next_batch(batch_size)
        feed = {inputs_: batch[0], targets_: batch[0]}
        batch_cost, _ = sess.run([cost, opt], feed_dict=feed)

        print("Epoch: {}/{}...".format(e+1, epochs),
              "Training loss: {:.4f}".format(batch_cost))









    



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Epoch: 4/20... Training loss: 0.0998
Epoch: 4/20... Training loss: 0.1018
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Epoch: 4/20... Training loss: 0.0992
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Epoch: 4/20... Training loss: 0.0997
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Epoch: 4/20... Training loss: 0.1048
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Epoch: 4/20... Training loss: 0.1039
Epoch: 4/20... Training loss: 0.0992
Epoch: 4/20... Training loss: 0.0996
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Epoch: 4/20... Training loss: 0.0999
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Epoch: 4/20... Training loss: 0.0995
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Epoch: 4/20... Training loss: 0.0994
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Epoch: 4/20... Training loss: 0.1001
Epoch: 4/20... Training loss: 0.0988
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Epoch: 4/20... Training loss: 0.1011
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Epoch: 4/20... Training loss: 0.0992
Epoch: 4/20... Training loss: 0.0989
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Epoch: 4/20... Training loss: 0.0998
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Epoch: 4/20... Training loss: 0.0999
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Epoch: 4/20... Training loss: 0.0992
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Epoch: 4/20... Training loss: 0.0993
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Epoch: 5/20... Training loss: 0.0981
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Epoch: 5/20... Training loss: 0.1008
Epoch: 5/20... Training loss: 0.0996
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Epoch: 5/20... Training loss: 0.0996
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Epoch: 5/20... Training loss: 0.0993
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Epoch: 5/20... Training loss: 0.0993
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Epoch: 5/20... Training loss: 0.0995
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Epoch: 5/20... Training loss: 0.0957
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Epoch: 5/20... Training loss: 0.0934
Epoch: 5/20... Training loss: 0.0948
Epoch: 5/20... Training loss: 0.0956
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Epoch: 5/20... Training loss: 0.0946
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Epoch: 5/20... Training loss: 0.0934
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Epoch: 6/20... Training loss: 0.0937
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Epoch: 6/20... Training loss: 0.0929
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Epoch: 6/20... Training loss: 0.0907
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Epoch: 6/20... Training loss: 0.0917
Epoch: 6/20... Training loss: 0.0934
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Epoch: 6/20... Training loss: 0.0934
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Epoch: 6/20... Training loss: 0.0907
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Epoch: 6/20... Training loss: 0.0929
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Epoch: 6/20... Training loss: 0.0931
Epoch: 6/20... Training loss: 0.0930
Epoch: 6/20... Training loss: 0.0902
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Epoch: 6/20... Training loss: 0.0926
Epoch: 6/20... Training loss: 0.0949
Epoch: 6/20... Training loss: 0.0932
Epoch: 6/20... Training loss: 0.0913
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Epoch: 6/20... Training loss: 0.0912
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Epoch: 6/20... Training loss: 0.0889
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Epoch: 6/20... Training loss: 0.0912
Epoch: 6/20... Training loss: 0.0917
Epoch: 6/20... Training loss: 0.0889
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Epoch: 6/20... Training loss: 0.0907
Epoch: 6/20... Training loss: 0.0929
Epoch: 6/20... Training loss: 0.0916
Epoch: 6/20... Training loss: 0.0937
Epoch: 6/20... Training loss: 0.0915
Epoch: 6/20... Training loss: 0.0927
Epoch: 6/20... Training loss: 0.0928
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Epoch: 6/20... Training loss: 0.0897
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Epoch: 6/20... Training loss: 0.0948
Epoch: 6/20... Training loss: 0.0887
Epoch: 6/20... Training loss: 0.0927
Epoch: 6/20... Training loss: 0.0929
Epoch: 6/20... Training loss: 0.0938
Epoch: 6/20... Training loss: 0.0926
Epoch: 6/20... Training loss: 0.0882
Epoch: 6/20... Training loss: 0.0930
Epoch: 6/20... Training loss: 0.0911
Epoch: 6/20... Training loss: 0.0926
Epoch: 6/20... Training loss: 0.0937
Epoch: 6/20... Training loss: 0.0888
Epoch: 6/20... Training loss: 0.0917
Epoch: 6/20... Training loss: 0.0935
Epoch: 6/20... Training loss: 0.0943
Epoch: 6/20... Training loss: 0.0935
Epoch: 6/20... Training loss: 0.0912
Epoch: 6/20... Training loss: 0.0934
Epoch: 6/20... Training loss: 0.0912
Epoch: 6/20... Training loss: 0.0916
Epoch: 6/20... Training loss: 0.0920
Epoch: 6/20... Training loss: 0.0914
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Epoch: 6/20... Training loss: 0.0907
Epoch: 6/20... Training loss: 0.0934
Epoch: 6/20... Training loss: 0.0914
Epoch: 6/20... Training loss: 0.0907
Epoch: 6/20... Training loss: 0.0898
Epoch: 6/20... Training loss: 0.0916
Epoch: 6/20... Training loss: 0.0894
Epoch: 6/20... Training loss: 0.0886
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Epoch: 6/20... Training loss: 0.0913
Epoch: 6/20... Training loss: 0.0914
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Epoch: 6/20... Training loss: 0.0893
Epoch: 6/20... Training loss: 0.0919
Epoch: 6/20... Training loss: 0.0904
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Epoch: 6/20... Training loss: 0.0937
Epoch: 6/20... Training loss: 0.0932
Epoch: 6/20... Training loss: 0.0905
Epoch: 6/20... Training loss: 0.0930
Epoch: 6/20... Training loss: 0.0906
Epoch: 6/20... Training loss: 0.0890
Epoch: 6/20... Training loss: 0.0907
Epoch: 6/20... Training loss: 0.0907
Epoch: 6/20... Training loss: 0.0927
Epoch: 6/20... Training loss: 0.0948
Epoch: 6/20... Training loss: 0.0892
Epoch: 6/20... Training loss: 0.0942
Epoch: 6/20... Training loss: 0.0898
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Epoch: 6/20... Training loss: 0.0922
Epoch: 6/20... Training loss: 0.0880
Epoch: 6/20... Training loss: 0.0899
Epoch: 6/20... Training loss: 0.0920
Epoch: 6/20... Training loss: 0.0925
Epoch: 6/20... Training loss: 0.0914
Epoch: 6/20... Training loss: 0.0889
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Epoch: 6/20... Training loss: 0.0895
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Epoch: 6/20... Training loss: 0.0891
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Epoch: 6/20... Training loss: 0.0914
Epoch: 6/20... Training loss: 0.0921
Epoch: 6/20... Training loss: 0.0910
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Epoch: 6/20... Training loss: 0.0891
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Epoch: 6/20... Training loss: 0.0931
Epoch: 6/20... Training loss: 0.0888
Epoch: 6/20... Training loss: 0.0906
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Epoch: 6/20... Training loss: 0.0921
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Epoch: 6/20... Training loss: 0.0914
Epoch: 6/20... Training loss: 0.0890
Epoch: 6/20... Training loss: 0.0936
Epoch: 6/20... Training loss: 0.0905
Epoch: 6/20... Training loss: 0.0920
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Epoch: 6/20... Training loss: 0.0919
Epoch: 6/20... Training loss: 0.0910
Epoch: 6/20... Training loss: 0.0920
Epoch: 6/20... Training loss: 0.0917
Epoch: 6/20... Training loss: 0.0890
Epoch: 6/20... Training loss: 0.0899
Epoch: 6/20... Training loss: 0.0914
Epoch: 6/20... Training loss: 0.0886
Epoch: 6/20... Training loss: 0.0895
Epoch: 6/20... Training loss: 0.0908
Epoch: 6/20... Training loss: 0.0920
Epoch: 6/20... Training loss: 0.0910
Epoch: 6/20... Training loss: 0.0925
Epoch: 6/20... Training loss: 0.0891
Epoch: 6/20... Training loss: 0.0899
Epoch: 6/20... Training loss: 0.0872
Epoch: 6/20... Training loss: 0.0911
Epoch: 6/20... Training loss: 0.0942
Epoch: 6/20... Training loss: 0.0891
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Epoch: 6/20... Training loss: 0.0910
Epoch: 6/20... Training loss: 0.0931
Epoch: 6/20... Training loss: 0.0921
Epoch: 6/20... Training loss: 0.0918
Epoch: 6/20... Training loss: 0.0889
Epoch: 6/20... Training loss: 0.0898
Epoch: 6/20... Training loss: 0.0888
Epoch: 6/20... Training loss: 0.0902
Epoch: 6/20... Training loss: 0.0880
Epoch: 6/20... Training loss: 0.0897
Epoch: 6/20... Training loss: 0.0915
Epoch: 6/20... Training loss: 0.0876
Epoch: 6/20... Training loss: 0.0910
Epoch: 6/20... Training loss: 0.0872
Epoch: 6/20... Training loss: 0.0887
Epoch: 6/20... Training loss: 0.0895
Epoch: 6/20... Training loss: 0.0893
Epoch: 6/20... Training loss: 0.0897
Epoch: 6/20... Training loss: 0.0902
Epoch: 6/20... Training loss: 0.0905
Epoch: 6/20... Training loss: 0.0888
Epoch: 6/20... Training loss: 0.0917
Epoch: 6/20... Training loss: 0.0890
Epoch: 6/20... Training loss: 0.0911
Epoch: 6/20... Training loss: 0.0890
Epoch: 6/20... Training loss: 0.0888
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Epoch: 6/20... Training loss: 0.0907
Epoch: 6/20... Training loss: 0.0897
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Epoch: 6/20... Training loss: 0.0870
Epoch: 6/20... Training loss: 0.0895
Epoch: 6/20... Training loss: 0.0914
Epoch: 6/20... Training loss: 0.0875
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Epoch: 6/20... Training loss: 0.0891
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Epoch: 6/20... Training loss: 0.0884
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Epoch: 6/20... Training loss: 0.0888
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Epoch: 6/20... Training loss: 0.0898
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Epoch: 6/20... Training loss: 0.0902
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Epoch: 6/20... Training loss: 0.0878
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Epoch: 6/20... Training loss: 0.0891
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Epoch: 6/20... Training loss: 0.0902
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Epoch: 6/20... Training loss: 0.0911
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Epoch: 6/20... Training loss: 0.0916
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Epoch: 6/20... Training loss: 0.0886
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Epoch: 6/20... Training loss: 0.0888
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Epoch: 6/20... Training loss: 0.0872
Epoch: 6/20... Training loss: 0.0902
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Epoch: 6/20... Training loss: 0.0903
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Epoch: 6/20... Training loss: 0.0884
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Epoch: 6/20... Training loss: 0.0883
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Epoch: 6/20... Training loss: 0.0902
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Epoch: 7/20... Training loss: 0.0861
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Epoch: 7/20... Training loss: 0.0882
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Epoch: 7/20... Training loss: 0.0874
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Epoch: 7/20... Training loss: 0.0846
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Epoch: 7/20... Training loss: 0.0843
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Epoch: 7/20... Training loss: 0.0881
Epoch: 7/20... Training loss: 0.0844
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Epoch: 7/20... Training loss: 0.0846
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Epoch: 7/20... Training loss: 0.0881
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Epoch: 7/20... Training loss: 0.0856
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Epoch: 7/20... Training loss: 0.0861
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Epoch: 7/20... Training loss: 0.0846
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Epoch: 7/20... Training loss: 0.0888
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Epoch: 7/20... Training loss: 0.0855
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Epoch: 7/20... Training loss: 0.0857
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Epoch: 7/20... Training loss: 0.0888
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Epoch: 7/20... Training loss: 0.0863
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Epoch: 7/20... Training loss: 0.0847
Epoch: 7/20... Training loss: 0.0930
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Epoch: 7/20... Training loss: 0.0858
Epoch: 7/20... Training loss: 0.0842
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Epoch: 7/20... Training loss: 0.0847
Epoch: 7/20... Training loss: 0.0843
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Epoch: 7/20... Training loss: 0.0851
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Epoch: 8/20... Training loss: 0.0849
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Epoch: 8/20... Training loss: 0.0852
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Epoch: 8/20... Training loss: 0.0839
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Epoch: 8/20... Training loss: 0.0863
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Epoch: 8/20... Training loss: 0.0855
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Epoch: 8/20... Training loss: 0.0832
Epoch: 8/20... Training loss: 0.0871
Epoch: 8/20... Training loss: 0.0838
Epoch: 8/20... Training loss: 0.0888
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Epoch: 8/20... Training loss: 0.0833
Epoch: 8/20... Training loss: 0.0832
Epoch: 8/20... Training loss: 0.0839
Epoch: 8/20... Training loss: 0.0843
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Epoch: 8/20... Training loss: 0.0793
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Epoch: 8/20... Training loss: 0.0839
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Epoch: 8/20... Training loss: 0.0843
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Epoch: 8/20... Training loss: 0.0831
Epoch: 8/20... Training loss: 0.0854
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Epoch: 8/20... Training loss: 0.0837
Epoch: 8/20... Training loss: 0.0871
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Epoch: 8/20... Training loss: 0.0849
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Epoch: 8/20... Training loss: 0.0853
Epoch: 8/20... Training loss: 0.0838
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Epoch: 8/20... Training loss: 0.0833
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Epoch: 8/20... Training loss: 0.0842
Epoch: 8/20... Training loss: 0.0834
Epoch: 8/20... Training loss: 0.0844
Epoch: 8/20... Training loss: 0.0851
Epoch: 8/20... Training loss: 0.0843
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Epoch: 8/20... Training loss: 0.0832
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Epoch: 8/20... Training loss: 0.0849
Epoch: 8/20... Training loss: 0.0853
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Epoch: 8/20... Training loss: 0.0839
Epoch: 8/20... Training loss: 0.0834
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Epoch: 8/20... Training loss: 0.0844
Epoch: 8/20... Training loss: 0.0851
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Epoch: 9/20... Training loss: 0.0796
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Epoch: 9/20... Training loss: 0.0794
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Epoch: 9/20... Training loss: 0.0796
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Epoch: 9/20... Training loss: 0.0773
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Epoch: 9/20... Training loss: 0.0812
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Epoch: 9/20... Training loss: 0.0832
Epoch: 9/20... Training loss: 0.0798
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Epoch: 9/20... Training loss: 0.0827
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Epoch: 9/20... Training loss: 0.0797
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Epoch: 9/20... Training loss: 0.0794
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Epoch: 9/20... Training loss: 0.0818
Epoch: 9/20... Training loss: 0.0798
Epoch: 9/20... Training loss: 0.0808
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Epoch: 9/20... Training loss: 0.0808
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Epoch: 9/20... Training loss: 0.0798
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Epoch: 9/20... Training loss: 0.0811
Epoch: 9/20... Training loss: 0.0797
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Epoch: 9/20... Training loss: 0.0782
Epoch: 9/20... Training loss: 0.0813
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Epoch: 9/20... Training loss: 0.0804
Epoch: 9/20... Training loss: 0.0794
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Epoch: 9/20... Training loss: 0.0788
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Epoch: 9/20... Training loss: 0.0799
Epoch: 9/20... Training loss: 0.0815
Epoch: 9/20... Training loss: 0.0786
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Epoch: 9/20... Training loss: 0.0818
Epoch: 9/20... Training loss: 0.0798
Epoch: 9/20... Training loss: 0.0790
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Epoch: 9/20... Training loss: 0.0813
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Epoch: 9/20... Training loss: 0.0798
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Epoch: 9/20... Training loss: 0.0776
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Epoch: 9/20... Training loss: 0.0794
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Epoch: 9/20... Training loss: 0.0814
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Epoch: 9/20... Training loss: 0.0774
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Epoch: 9/20... Training loss: 0.0796
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Epoch: 10/20... Training loss: 0.0776
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Epoch: 10/20... Training loss: 0.0765
Epoch: 10/20... Training loss: 0.0790
Epoch: 10/20... Training loss: 0.0792
Epoch: 10/20... Training loss: 0.0779
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Epoch: 10/20... Training loss: 0.0786
Epoch: 10/20... Training loss: 0.0804
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Epoch: 10/20... Training loss: 0.0796
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Epoch: 10/20... Training loss: 0.0753
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Epoch: 10/20... Training loss: 0.0793
Epoch: 10/20... Training loss: 0.0788
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Epoch: 10/20... Training loss: 0.0792
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Epoch: 10/20... Training loss: 0.0825
Epoch: 10/20... Training loss: 0.0776
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Epoch: 10/20... Training loss: 0.0790
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Epoch: 10/20... Training loss: 0.0774
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Epoch: 10/20... Training loss: 0.0763
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Epoch: 10/20... Training loss: 0.0774
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Epoch: 10/20... Training loss: 0.0751
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Epoch: 11/20... Training loss: 0.0767
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Epoch: 11/20... Training loss: 0.0763
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Epoch: 11/20... Training loss: 0.0779
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Epoch: 11/20... Training loss: 0.0787
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Epoch: 11/20... Training loss: 0.0786
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Epoch: 11/20... Training loss: 0.0766
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Epoch: 11/20... Training loss: 0.0776
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Epoch: 11/20... Training loss: 0.0774
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Epoch: 11/20... Training loss: 0.0782
Epoch: 11/20... Training loss: 0.0766
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Epoch: 11/20... Training loss: 0.0787
Epoch: 11/20... Training loss: 0.0783
Epoch: 11/20... Training loss: 0.0744
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Epoch: 11/20... Training loss: 0.0763
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Epoch: 11/20... Training loss: 0.0761
Epoch: 11/20... Training loss: 0.0785
Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0787
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Epoch: 11/20... Training loss: 0.0742
Epoch: 11/20... Training loss: 0.0771
Epoch: 11/20... Training loss: 0.0772
Epoch: 11/20... Training loss: 0.0743
Epoch: 11/20... Training loss: 0.0756
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Epoch: 11/20... Training loss: 0.0746
Epoch: 11/20... Training loss: 0.0758
Epoch: 11/20... Training loss: 0.0773
Epoch: 11/20... Training loss: 0.0753
Epoch: 11/20... Training loss: 0.0755
Epoch: 11/20... Training loss: 0.0763
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Epoch: 11/20... Training loss: 0.0788
Epoch: 11/20... Training loss: 0.0774
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Epoch: 11/20... Training loss: 0.0766
Epoch: 11/20... Training loss: 0.0739
Epoch: 11/20... Training loss: 0.0761
Epoch: 11/20... Training loss: 0.0767
Epoch: 11/20... Training loss: 0.0763
Epoch: 11/20... Training loss: 0.0778
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Epoch: 11/20... Training loss: 0.0785
Epoch: 11/20... Training loss: 0.0771
Epoch: 11/20... Training loss: 0.0790
Epoch: 11/20... Training loss: 0.0788
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Epoch: 11/20... Training loss: 0.0778
Epoch: 11/20... Training loss: 0.0785
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Epoch: 11/20... Training loss: 0.0783
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Epoch: 11/20... Training loss: 0.0754
Epoch: 11/20... Training loss: 0.0789
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Epoch: 11/20... Training loss: 0.0781
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Epoch: 11/20... Training loss: 0.0786
Epoch: 11/20... Training loss: 0.0769
Epoch: 11/20... Training loss: 0.0776
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Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0790
Epoch: 11/20... Training loss: 0.0758
Epoch: 11/20... Training loss: 0.0785
Epoch: 11/20... Training loss: 0.0761
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Epoch: 11/20... Training loss: 0.0790
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Epoch: 11/20... Training loss: 0.0759
Epoch: 11/20... Training loss: 0.0789
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Epoch: 11/20... Training loss: 0.0769
Epoch: 11/20... Training loss: 0.0773
Epoch: 11/20... Training loss: 0.0769
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Epoch: 11/20... Training loss: 0.0762
Epoch: 11/20... Training loss: 0.0779
Epoch: 11/20... Training loss: 0.0798
Epoch: 11/20... Training loss: 0.0772
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Epoch: 11/20... Training loss: 0.0743
Epoch: 11/20... Training loss: 0.0794
Epoch: 11/20... Training loss: 0.0761
Epoch: 11/20... Training loss: 0.0797
Epoch: 11/20... Training loss: 0.0763
Epoch: 11/20... Training loss: 0.0770
Epoch: 11/20... Training loss: 0.0759
Epoch: 11/20... Training loss: 0.0757
Epoch: 11/20... Training loss: 0.0774
Epoch: 11/20... Training loss: 0.0773
Epoch: 11/20... Training loss: 0.0762
Epoch: 11/20... Training loss: 0.0730
Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0755
Epoch: 11/20... Training loss: 0.0766
Epoch: 11/20... Training loss: 0.0769
Epoch: 11/20... Training loss: 0.0763
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Epoch: 11/20... Training loss: 0.0761
Epoch: 11/20... Training loss: 0.0785
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Epoch: 11/20... Training loss: 0.0784
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Epoch: 11/20... Training loss: 0.0762
Epoch: 11/20... Training loss: 0.0783
Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0784
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Epoch: 11/20... Training loss: 0.0784
Epoch: 11/20... Training loss: 0.0756
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Epoch: 11/20... Training loss: 0.0757
Epoch: 11/20... Training loss: 0.0754
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Epoch: 11/20... Training loss: 0.0762
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Epoch: 11/20... Training loss: 0.0755
Epoch: 11/20... Training loss: 0.0748
Epoch: 11/20... Training loss: 0.0764
Epoch: 11/20... Training loss: 0.0786
Epoch: 11/20... Training loss: 0.0752
Epoch: 11/20... Training loss: 0.0771
Epoch: 11/20... Training loss: 0.0784
Epoch: 11/20... Training loss: 0.0769
Epoch: 11/20... Training loss: 0.0757
Epoch: 11/20... Training loss: 0.0757
Epoch: 11/20... Training loss: 0.0746
Epoch: 11/20... Training loss: 0.0789
Epoch: 11/20... Training loss: 0.0763
Epoch: 11/20... Training loss: 0.0786
Epoch: 11/20... Training loss: 0.0758
Epoch: 11/20... Training loss: 0.0754
Epoch: 11/20... Training loss: 0.0782
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Epoch: 11/20... Training loss: 0.0772
Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0766
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Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0763
Epoch: 11/20... Training loss: 0.0761
Epoch: 11/20... Training loss: 0.0779
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Epoch: 11/20... Training loss: 0.0742
Epoch: 11/20... Training loss: 0.0767
Epoch: 11/20... Training loss: 0.0775
Epoch: 11/20... Training loss: 0.0777
Epoch: 11/20... Training loss: 0.0751
Epoch: 11/20... Training loss: 0.0766
Epoch: 11/20... Training loss: 0.0771
Epoch: 11/20... Training loss: 0.0769
Epoch: 11/20... Training loss: 0.0756
Epoch: 11/20... Training loss: 0.0741
Epoch: 11/20... Training loss: 0.0770
Epoch: 11/20... Training loss: 0.0776
Epoch: 11/20... Training loss: 0.0757
Epoch: 11/20... Training loss: 0.0766
Epoch: 11/20... Training loss: 0.0784
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Epoch: 11/20... Training loss: 0.0750
Epoch: 11/20... Training loss: 0.0748
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Epoch: 11/20... Training loss: 0.0762
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Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0755
Epoch: 11/20... Training loss: 0.0780
Epoch: 11/20... Training loss: 0.0754
Epoch: 11/20... Training loss: 0.0758
Epoch: 11/20... Training loss: 0.0746
Epoch: 11/20... Training loss: 0.0753
Epoch: 11/20... Training loss: 0.0752
Epoch: 11/20... Training loss: 0.0755
Epoch: 11/20... Training loss: 0.0757
Epoch: 11/20... Training loss: 0.0773
Epoch: 11/20... Training loss: 0.0791
Epoch: 11/20... Training loss: 0.0761
Epoch: 11/20... Training loss: 0.0747
Epoch: 11/20... Training loss: 0.0761
Epoch: 11/20... Training loss: 0.0756
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Epoch: 11/20... Training loss: 0.0749
Epoch: 11/20... Training loss: 0.0754
Epoch: 11/20... Training loss: 0.0749
Epoch: 11/20... Training loss: 0.0754
Epoch: 11/20... Training loss: 0.0766
Epoch: 11/20... Training loss: 0.0768
Epoch: 11/20... Training loss: 0.0779
Epoch: 11/20... Training loss: 0.0744
Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0764
Epoch: 11/20... Training loss: 0.0750
Epoch: 11/20... Training loss: 0.0793
Epoch: 11/20... Training loss: 0.0768
Epoch: 11/20... Training loss: 0.0774
Epoch: 11/20... Training loss: 0.0761
Epoch: 11/20... Training loss: 0.0753
Epoch: 11/20... Training loss: 0.0756
Epoch: 11/20... Training loss: 0.0747
Epoch: 11/20... Training loss: 0.0737
Epoch: 11/20... Training loss: 0.0749
Epoch: 11/20... Training loss: 0.0737
Epoch: 11/20... Training loss: 0.0740
Epoch: 11/20... Training loss: 0.0765
Epoch: 11/20... Training loss: 0.0772
Epoch: 11/20... Training loss: 0.0748
Epoch: 11/20... Training loss: 0.0744
Epoch: 11/20... Training loss: 0.0770
Epoch: 11/20... Training loss: 0.0755
Epoch: 11/20... Training loss: 0.0772
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Epoch: 11/20... Training loss: 0.0766
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Epoch: 11/20... Training loss: 0.0744
Epoch: 11/20... Training loss: 0.0739
Epoch: 11/20... Training loss: 0.0745
Epoch: 11/20... Training loss: 0.0779
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Epoch: 11/20... Training loss: 0.0745
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Epoch: 11/20... Training loss: 0.0771
Epoch: 11/20... Training loss: 0.0766
Epoch: 11/20... Training loss: 0.0746
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Epoch: 11/20... Training loss: 0.0776
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Epoch: 11/20... Training loss: 0.0767
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Epoch: 11/20... Training loss: 0.0742
Epoch: 11/20... Training loss: 0.0767
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Epoch: 11/20... Training loss: 0.0747
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Epoch: 11/20... Training loss: 0.0749
Epoch: 11/20... Training loss: 0.0776
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Epoch: 11/20... Training loss: 0.0741
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Epoch: 11/20... Training loss: 0.0766
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Epoch: 11/20... Training loss: 0.0763
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Epoch: 11/20... Training loss: 0.0766
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Epoch: 11/20... Training loss: 0.0748
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Epoch: 12/20... Training loss: 0.0755
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Epoch: 12/20... Training loss: 0.0748
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Epoch: 12/20... Training loss: 0.0756
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Epoch: 12/20... Training loss: 0.0749
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Epoch: 12/20... Training loss: 0.0763
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Epoch: 12/20... Training loss: 0.0739
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Epoch: 12/20... Training loss: 0.0741
Epoch: 12/20... Training loss: 0.0765
Epoch: 12/20... Training loss: 0.0778
Epoch: 12/20... Training loss: 0.0756
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Epoch: 12/20... Training loss: 0.0746
Epoch: 12/20... Training loss: 0.0762
Epoch: 12/20... Training loss: 0.0739
Epoch: 12/20... Training loss: 0.0737
Epoch: 12/20... Training loss: 0.0748
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Epoch: 12/20... Training loss: 0.0745
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Epoch: 12/20... Training loss: 0.0756
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Epoch: 12/20... Training loss: 0.0766
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Epoch: 12/20... Training loss: 0.0741
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Epoch: 16/20... Training loss: 0.0709
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Epoch: 18/20... Training loss: 0.0690
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Epoch: 18/20... Training loss: 0.0695
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Epoch: 18/20... Training loss: 0.0691
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Epoch: 19/20... Training loss: 0.0655
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Epoch: 19/20... Training loss: 0.0684
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Epoch: 19/20... Training loss: 0.0662
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Epoch: 19/20... Training loss: 0.0676
Epoch: 19/20... Training loss: 0.0684
Epoch: 19/20... Training loss: 0.0678
Epoch: 19/20... Training loss: 0.0656
Epoch: 19/20... Training loss: 0.0685
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Epoch: 19/20... Training loss: 0.0681
Epoch: 19/20... Training loss: 0.0671
Epoch: 19/20... Training loss: 0.0686
Epoch: 19/20... Training loss: 0.0681
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Epoch: 19/20... Training loss: 0.0675
Epoch: 19/20... Training loss: 0.0677
Epoch: 19/20... Training loss: 0.0687
Epoch: 19/20... Training loss: 0.0679
Epoch: 19/20... Training loss: 0.0685
Epoch: 19/20... Training loss: 0.0673
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Epoch: 19/20... Training loss: 0.0690
Epoch: 19/20... Training loss: 0.0673
Epoch: 19/20... Training loss: 0.0686
Epoch: 19/20... Training loss: 0.0689
Epoch: 19/20... Training loss: 0.0679
Epoch: 19/20... Training loss: 0.0689
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Epoch: 19/20... Training loss: 0.0683
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Epoch: 19/20... Training loss: 0.0676
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Epoch: 19/20... Training loss: 0.0682
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Epoch: 19/20... Training loss: 0.0670
Epoch: 19/20... Training loss: 0.0669
Epoch: 19/20... Training loss: 0.0664
Epoch: 19/20... Training loss: 0.0686
Epoch: 19/20... Training loss: 0.0693
Epoch: 19/20... Training loss: 0.0674
Epoch: 19/20... Training loss: 0.0690
Epoch: 19/20... Training loss: 0.0673
Epoch: 19/20... Training loss: 0.0666
Epoch: 19/20... Training loss: 0.0683
Epoch: 19/20... Training loss: 0.0686
Epoch: 19/20... Training loss: 0.0683
Epoch: 19/20... Training loss: 0.0695
Epoch: 19/20... Training loss: 0.0681
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Epoch: 19/20... Training loss: 0.0689
Epoch: 19/20... Training loss: 0.0666
Epoch: 19/20... Training loss: 0.0659
Epoch: 19/20... Training loss: 0.0685
Epoch: 19/20... Training loss: 0.0668
Epoch: 19/20... Training loss: 0.0683
Epoch: 19/20... Training loss: 0.0668
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Epoch: 19/20... Training loss: 0.0683
Epoch: 19/20... Training loss: 0.0687
Epoch: 19/20... Training loss: 0.0666
Epoch: 19/20... Training loss: 0.0672
Epoch: 19/20... Training loss: 0.0661
Epoch: 19/20... Training loss: 0.0662
Epoch: 19/20... Training loss: 0.0673
Epoch: 19/20... Training loss: 0.0661
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Epoch: 19/20... Training loss: 0.0682
Epoch: 19/20... Training loss: 0.0683
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Epoch: 19/20... Training loss: 0.0689
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Epoch: 19/20... Training loss: 0.0685
Epoch: 19/20... Training loss: 0.0656
Epoch: 19/20... Training loss: 0.0682
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Epoch: 19/20... Training loss: 0.0667
Epoch: 19/20... Training loss: 0.0668
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Epoch: 19/20... Training loss: 0.0662
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Epoch: 19/20... Training loss: 0.0686
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Epoch: 19/20... Training loss: 0.0667
Epoch: 19/20... Training loss: 0.0675
Epoch: 19/20... Training loss: 0.0684
Epoch: 19/20... Training loss: 0.0696
Epoch: 19/20... Training loss: 0.0681
Epoch: 19/20... Training loss: 0.0686
Epoch: 19/20... Training loss: 0.0695
Epoch: 19/20... Training loss: 0.0693
Epoch: 19/20... Training loss: 0.0689
Epoch: 19/20... Training loss: 0.0667
Epoch: 19/20... Training loss: 0.0684
Epoch: 19/20... Training loss: 0.0693
Epoch: 19/20... Training loss: 0.0694
Epoch: 19/20... Training loss: 0.0685
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Epoch: 19/20... Training loss: 0.0656
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Epoch: 19/20... Training loss: 0.0685
Epoch: 19/20... Training loss: 0.0693
Epoch: 19/20... Training loss: 0.0679
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Epoch: 19/20... Training loss: 0.0679
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Epoch: 19/20... Training loss: 0.0688
Epoch: 19/20... Training loss: 0.0681
Epoch: 19/20... Training loss: 0.0685
Epoch: 19/20... Training loss: 0.0673
Epoch: 19/20... Training loss: 0.0679
Epoch: 19/20... Training loss: 0.0667
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Epoch: 19/20... Training loss: 0.0694
Epoch: 19/20... Training loss: 0.0693
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Epoch: 19/20... Training loss: 0.0683
Epoch: 19/20... Training loss: 0.0669
Epoch: 19/20... Training loss: 0.0673
Epoch: 19/20... Training loss: 0.0687
Epoch: 19/20... Training loss: 0.0666
Epoch: 19/20... Training loss: 0.0671
Epoch: 19/20... Training loss: 0.0674
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Epoch: 19/20... Training loss: 0.0664
Epoch: 19/20... Training loss: 0.0682
Epoch: 19/20... Training loss: 0.0677
Epoch: 19/20... Training loss: 0.0663
Epoch: 19/20... Training loss: 0.0669
Epoch: 19/20... Training loss: 0.0693
Epoch: 19/20... Training loss: 0.0683
Epoch: 19/20... Training loss: 0.0674
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Epoch: 19/20... Training loss: 0.0687
Epoch: 19/20... Training loss: 0.0685
Epoch: 19/20... Training loss: 0.0678
Epoch: 19/20... Training loss: 0.0680
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Epoch: 19/20... Training loss: 0.0684
Epoch: 19/20... Training loss: 0.0669
Epoch: 19/20... Training loss: 0.0671
Epoch: 19/20... Training loss: 0.0664
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Epoch: 20/20... Training loss: 0.0685
Epoch: 20/20... Training loss: 0.0655
Epoch: 20/20... Training loss: 0.0673
Epoch: 20/20... Training loss: 0.0667
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Epoch: 20/20... Training loss: 0.0678
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Epoch: 20/20... Training loss: 0.0664
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Epoch: 20/20... Training loss: 0.0663
Epoch: 20/20... Training loss: 0.0678
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Epoch: 20/20... Training loss: 0.0665
Epoch: 20/20... Training loss: 0.0682
Epoch: 20/20... Training loss: 0.0677
Epoch: 20/20... Training loss: 0.0681
Epoch: 20/20... Training loss: 0.0683
Epoch: 20/20... Training loss: 0.0669
Epoch: 20/20... Training loss: 0.0662
Epoch: 20/20... Training loss: 0.0684
Epoch: 20/20... Training loss: 0.0657
Epoch: 20/20... Training loss: 0.0664
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Epoch: 20/20... Training loss: 0.0654
Epoch: 20/20... Training loss: 0.0682
Epoch: 20/20... Training loss: 0.0660
Epoch: 20/20... Training loss: 0.0679
Epoch: 20/20... Training loss: 0.0673
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Epoch: 20/20... Training loss: 0.0671
Epoch: 20/20... Training loss: 0.0680
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Epoch: 20/20... Training loss: 0.0678
Epoch: 20/20... Training loss: 0.0673
Epoch: 20/20... Training loss: 0.0684
Epoch: 20/20... Training loss: 0.0674
Epoch: 20/20... Training loss: 0.0678
Epoch: 20/20... Training loss: 0.0669
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Epoch: 20/20... Training loss: 0.0677
Epoch: 20/20... Training loss: 0.0661
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Epoch: 20/20... Training loss: 0.0666
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Epoch: 20/20... Training loss: 0.0678
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Epoch: 20/20... Training loss: 0.0681
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Epoch: 20/20... Training loss: 0.0679
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Epoch: 20/20... Training loss: 0.0671
Epoch: 20/20... Training loss: 0.0680
Epoch: 20/20... Training loss: 0.0693
Epoch: 20/20... Training loss: 0.0695
Epoch: 20/20... Training loss: 0.0680
Epoch: 20/20... Training loss: 0.0683
Epoch: 20/20... Training loss: 0.0681
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Epoch: 20/20... Training loss: 0.0677
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Epoch: 20/20... Training loss: 0.0677
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Epoch: 20/20... Training loss: 0.0668
Epoch: 20/20... Training loss: 0.0666
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Epoch: 20/20... Training loss: 0.0664
Epoch: 20/20... Training loss: 0.0690
Epoch: 20/20... Training loss: 0.0682
Epoch: 20/20... Training loss: 0.0669
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Epoch: 20/20... Training loss: 0.0681
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Epoch: 20/20... Training loss: 0.0674
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Epoch: 20/20... Training loss: 0.0660
Epoch: 20/20... Training loss: 0.0673
Epoch: 20/20... Training loss: 0.0685
Epoch: 20/20... Training loss: 0.0682
Epoch: 20/20... Training loss: 0.0676
Epoch: 20/20... Training loss: 0.0671
Epoch: 20/20... Training loss: 0.0666
Epoch: 20/20... Training loss: 0.0688
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Epoch: 20/20... Training loss: 0.0687
Epoch: 20/20... Training loss: 0.0679
Epoch: 20/20... Training loss: 0.0690
Epoch: 20/20... Training loss: 0.0682
Epoch: 20/20... Training loss: 0.0659
Epoch: 20/20... Training loss: 0.0674
Epoch: 20/20... Training loss: 0.0693
Epoch: 20/20... Training loss: 0.0659
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Epoch: 20/20... Training loss: 0.0673
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Epoch: 20/20... Training loss: 0.0674
Epoch: 20/20... Training loss: 0.0686
Epoch: 20/20... Training loss: 0.0657
Epoch: 20/20... Training loss: 0.0677
Epoch: 20/20... Training loss: 0.0674
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Epoch: 20/20... Training loss: 0.0684
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Epoch: 20/20... Training loss: 0.0672
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Epoch: 20/20... Training loss: 0.0694
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Epoch: 20/20... Training loss: 0.0666
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Epoch: 20/20... Training loss: 0.0677
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Epoch: 20/20... Training loss: 0.0663
Epoch: 20/20... Training loss: 0.0659
Epoch: 20/20... Training loss: 0.0666
Epoch: 20/20... Training loss: 0.0683
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Epoch: 20/20... Training loss: 0.0651
Epoch: 20/20... Training loss: 0.0690
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Epoch: 20/20... Training loss: 0.0679
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Epoch: 20/20... Training loss: 0.0677
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Epoch: 20/20... Training loss: 0.0683
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Epoch: 20/20... Training loss: 0.0677
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Epoch: 20/20... Training loss: 0.0666
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Epoch: 20/20... Training loss: 0.0682
Epoch: 20/20... Training loss: 0.0663
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Epoch: 20/20... Training loss: 0.0681
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Epoch: 20/20... Training loss: 0.0693
Epoch: 20/20... Training loss: 0.0673
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Epoch: 20/20... Training loss: 0.0674
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Epoch: 20/20... Training loss: 0.0651
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Epoch: 20/20... Training loss: 0.0684
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Epoch: 20/20... Training loss: 0.0677
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Epoch: 20/20... Training loss: 0.0679
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Epoch: 20/20... Training loss: 0.0687
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Epoch: 20/20... Training loss: 0.0691
Epoch: 20/20... Training loss: 0.0657
Epoch: 20/20... Training loss: 0.0659
Epoch: 20/20... Training loss: 0.0663
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Epoch: 20/20... Training loss: 0.0663
Epoch: 20/20... Training loss: 0.0667
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Epoch: 20/20... Training loss: 0.0673
Epoch: 20/20... Training loss: 0.0661
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Epoch: 20/20... Training loss: 0.0679
Epoch: 20/20... Training loss: 0.0690
Epoch: 20/20... Training loss: 0.0659
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Epoch: 20/20... Training loss: 0.0688
Epoch: 20/20... Training loss: 0.0691
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Epoch: 20/20... Training loss: 0.0674
Epoch: 20/20... Training loss: 0.0673
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Epoch: 20/20... Training loss: 0.0688
Epoch: 20/20... Training loss: 0.0666
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Epoch: 20/20... Training loss: 0.0674
Epoch: 20/20... Training loss: 0.0671
Epoch: 20/20... Training loss: 0.0660
Epoch: 20/20... Training loss: 0.0651

Checking out the results

Below I've plotted some of the test images along with their reconstructions. For the most part these look pretty good except for some blurriness in some parts.



In [8]:

    
fig, axes = plt.subplots(nrows=2, ncols=10, sharex=True, sharey=True, figsize=(20,4))
in_imgs = mnist.test.images[:10]
reconstructed, compressed = sess.run([decoded, encoded], feed_dict={inputs_: in_imgs})

for images, row in zip([in_imgs, reconstructed], axes):
    for img, ax in zip(images, row):
        ax.imshow(img.reshape((28, 28)), cmap='Greys_r')
        ax.get_xaxis().set_visible(False)
        ax.get_yaxis().set_visible(False)

fig.tight_layout(pad=0.1)



In [9]:

    
sess.close()

Up Next

We're dealing with images here, so we can (usually) get better performance using convolution layers. So, next we'll build a better autoencoder with convolutional layers.

In practice, autoencoders aren't actually better at compression compared to typical methods like JPEGs and MP3s. But, they are being used for noise reduction, which you'll also build.



In [ ]: