'''This script demonstrates how to build a variational autoencoder with Keras.

Reference: "Auto-Encoding Variational Bayes" https://arxiv.org/abs/1312.6114
'''
import numpy as np
import matplotlib.pyplot as plt

from keras.layers import Input, Dense, Lambda
from keras.models import Model
from keras import backend as K
from keras import objectives
from keras.datasets import mnist

batch_size = 16
original_dim = 784
latent_dim = 2
intermediate_dim = 128
epsilon_std = 0.01
nb_epoch = 40

x = Input(batch_shape=(batch_size, original_dim))
h = Dense(intermediate_dim, activation='relu')(x)
z_mean = Dense(latent_dim)(h)
z_log_std = Dense(latent_dim)(h)

def sampling(args):
    z_mean, z_log_std = args
    epsilon = K.random_normal(shape=(batch_size, latent_dim),
                              mean=0., std=epsilon_std)
    return z_mean + K.exp(z_log_std) * epsilon

# note that "output_shape" isn't necessary with the TensorFlow backend
# so you could write `Lambda(sampling)([z_mean, z_log_std])`
z = Lambda(sampling, output_shape=(latent_dim,))([z_mean, z_log_std])

# we instantiate these layers separately so as to reuse them later
decoder_h = Dense(intermediate_dim, activation='relu')
decoder_mean = Dense(original_dim, activation='sigmoid')
h_decoded = decoder_h(z)
x_decoded_mean = decoder_mean(h_decoded)

def vae_loss(x, x_decoded_mean):
    xent_loss = objectives.binary_crossentropy(x, x_decoded_mean)
    kl_loss = - 0.5 * K.mean(1 + z_log_std - K.square(z_mean) - K.exp(z_log_std), axis=-1)
    return xent_loss + kl_loss

vae = Model(x, x_decoded_mean)
vae.compile(optimizer='rmsprop', loss=vae_loss)

# train the VAE on MNIST digits
(x_train, y_train), (x_test, y_test) = mnist.load_data()

x_train = x_train.astype('float32') / 255.
x_test = x_test.astype('float32') / 255.
x_train = x_train.reshape((len(x_train), np.prod(x_train.shape[1:])))
x_test = x_test.reshape((len(x_test), np.prod(x_test.shape[1:])))

vae.fit(x_train, x_train,
        shuffle=True,
        nb_epoch=nb_epoch,
        batch_size=batch_size,
        validation_data=(x_test, x_test))

# build a model to project inputs on the latent space
encoder = Model(x, z_mean)

# display a 2D plot of the digit classes in the latent space
x_test_encoded = encoder.predict(x_test, batch_size=batch_size)
plt.figure(figsize=(6, 6))
plt.scatter(x_test_encoded[:, 0], x_test_encoded[:, 1], c=y_test)
plt.colorbar()
plt.show()

# build a digit generator that can sample from the learned distribution
decoder_input = Input(shape=(latent_dim,))
_h_decoded = decoder_h(decoder_input)
_x_decoded_mean = decoder_mean(_h_decoded)
generator = Model(decoder_input, _x_decoded_mean)

# display a 2D manifold of the digits
n = 15  # figure with 15x15 digits
digit_size = 28
figure = np.zeros((digit_size * n, digit_size * n))
# we will sample n points within [-15, 15] standard deviations
grid_x = np.linspace(-15, 15, n)
grid_y = np.linspace(-15, 15, n)

for i, yi in enumerate(grid_x):
    for j, xi in enumerate(grid_y):
        z_sample = np.array([[xi, yi]]) * epsilon_std
        x_decoded = generator.predict(z_sample)
        digit = x_decoded[0].reshape(digit_size, digit_size)
        figure[i * digit_size: (i + 1) * digit_size,
               j * digit_size: (j + 1) * digit_size] = digit

plt.figure(figsize=(10, 10))
plt.imshow(figure)
plt.show()

@@ -245,22 +245,21 @@
  Dense, 
-Lambda
+merge
 %0Afrom ke
@@ -390,17 +390,18 @@
 size = 1
-6
+00
 %0Aorigina
@@ -450,30 +450,11 @@
 m = 
-128%0Aepsilon_std = 0.01
+500
 %0Anb_
@@ -461,17 +461,18 @@
 epoch = 
-4
+10
 0%0A%0Ax = I
@@ -602,19 +602,19 @@
 )%0Az_log_
-std
+var
  = Dense
@@ -668,19 +668,19 @@
 , z_log_
-std
+var
  = args%0A
@@ -744,63 +744,16 @@
 im),
-%0A                              mean=0., std=epsilon_std
+ mean=0.
 )%0A  
@@ -782,19 +782,21 @@
 p(z_log_
-std
+var/2
 ) * epsi
@@ -875,80 +875,44 @@
 end%0A
-# so you could write %60Lambda(sampling)(%5Bz_mean, z_log_std%5D)%60%0Az = Lambda(
+z = merge(%5Bz_mean, z_log_var%5D, mode=
 samp
@@ -948,29 +948,8 @@
 m,))
-(%5Bz_mean, z_log_std%5D)
 %0A%0A# 
@@ -1240,16 +1240,31 @@
 t_loss =
+ original_dim *
  objecti
@@ -1330,20 +1330,19 @@
 0.5 * K.
-mean
+sum
 (1 + z_l
@@ -1344,19 +1344,19 @@
 + z_log_
-std
+var
  - K.squ
@@ -1381,19 +1381,19 @@
 p(z_log_
-std
+var
 ), axis=
@@ -2924,22 +2924,8 @@
 i%5D%5D)
- * epsilon_std
 %0A   

Fix VAE example (#3220)