Advanced Deep Learning with Keras

Disentangled Representation GANs
( )
StackedGAN ( D)
L =−E
log D f −E
log 1 −D G f , z
L
( ) + ( ( + ))
i fi~ pdata i fi 1~ pdata , zi
i 1 i
( G)
= −E
∼
( ( f z ))
log D G ,
adv
i fi+ 1 pdata , zi
i+
1 i
6.2.1
6.2.2
L
( G)
( G ( ))
cond
|| , , ||
i
= E
fi 1 pdata , z
f
i i 1
zi f
+ ∼
+ i+
1 2
6.2.3
L
( G)
( G ( ))
= || E f , z , z ||
ent
i fi+ 1 , zi
i+
1 i i 2
6.2.4
( G) ( G) ( G) ( G)
L = λ L + λ L + λ L
adv cond ent
i 1 i 2 i 3 i
6.2.5
where λ1 , λ2, andλ are weights and
3
i = Encoder and GAN id
Table 6.2.1: A comparison between the loss functions of GAN and StackedGAN.
~p data means sampling from the corresponding encoder data (input, feature or output).
Given the Encoder inputs (x r
) intermediate features (f 1r
) and labels (y r
), each GAN
is trained in the usual discriminator–adversarial manner. The loss functions are
given by Equation 6.2.1 to 6.2.5 in Table 6.2.1. Equations 6.2.1 and 6.2.2 are the usual
loss functions of the generic GAN. StackedGAN has two additional loss functions,
Conditional and Entropy.
( ) cond
G
The conditional loss function, L
i in Equation 6.2.3, ensures that the generator does
not ignore the input, f i+1
, when synthesizing the output, f i
, from input noise code
z i
. The encoder, Encoder i
, must be able to recover the generator input by inverting
the process of the generator, Generator i
. The difference between the generator input
and the recovered input using the encoder is measured by L2 or Euclidean distance
Mean Squared Error (MSE). Figure 6.2.4 shows the network elements involved in
( G)
cond
the computation of L :
0
[ 184 ]