title: Keras autoencoder simple example has a strange output
body: <p>I am trying to run a simple autoencoder, all the training input is the same. The training data features are equal to 3, and the hidden layer has 3 nodes in it. I train the autoencoder with that input, then I try to predict it (encode/decode) again (so if the autoencoder passes everything as is without any changes it should work)</p>
  
  <p>Anyway, that's not the case, and I am a sturggling a bit to understand why. I am not sure if it's something wrong in my code, or in my understanding of the autoencdoer implementation. Here is the code for reference.</p>
  
  <p>P.S. I played around with the number of epoches, number of examples in the training set, the batch size, made the training data values between 0-1, and kept track of the loss value, but that didn't help either.</p>
  
  <p>`</p>
  
  <pre><code>from keras.layers import Input, Dense
  from keras.models import Model
  import numpy as np 
  # this is the size of our encoded representations
  encoding_dim = 3
  
  x_train=np.array([[1,2,3],[1,2,3],[1,2,3],[1,2,3],[1,2,3],[1,2,3],[1,2,3],[1,2,3],[1,2,3]])
  in= Input(shape=(3,))
  encoded = Dense(encoding_dim, activation='relu')(in)
  decoded = Dense(3, activation='sigmoid')(encoded)
  
  # this model maps an input to its reconstruction
  autoencoder = Model(in, decoded)
  autoencoder.compile(optimizer='adadelta', loss='mse')
  
  autoencoder.fit(x_train, x_train,
                  epochs=100,
                  batch_size=4)
  autoencoder.predict(x_train)
  </code></pre>
  
  <p>`</p>
  
  <p>The output I get should be the same as the input (or at least close) but I get this instead)</p>
  
  <pre><code>`Out[180]: 
  array([[ 0.80265796,  0.89038897,  0.9100889 ],
         [ 0.80265796,  0.89038897,  0.9100889 ],
         [ 0.80265796,  0.89038897,  0.9100889 ],
         ..., 
         [ 0.80265796,  0.89038897,  0.9100889 ],
         [ 0.80265796,  0.89038897,  0.9100889 ],
         [ 0.80265796,  0.89038897,  0.9100889 ]], dtype=float32)`
  </code></pre>
  
  <p>Any help would be appreciated, most likely I understood something wrong so hopefully this question is not that hard to answer. </p>