neural network - What is the purpose of the add_loss function in Keras?

Question

Currently I stumbled across variational autoencoders and tried to make them work on MNIST using keras. I found a tutorial on github.

My question concerns the following lines of code:

# Build model
vae = Model(x, x_decoded_mean)

# Calculate custom loss
xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
vae_loss = K.mean(xent_loss + kl_loss)

# Compile
vae.add_loss(vae_loss)
vae.compile(optimizer='rmsprop')

Why is add_loss used instead of specifying it as compile option? Something like vae.compile(optimizer='rmsprop', loss=vae_loss) does not seem to work and throws the following error:

ValueError: The model cannot be compiled because it has no loss to optimize.

What is the difference between this function and a custom loss function, that I can add as an argument for Model.fit()?

Thanks in advance!

P.S.: I know there are several issues concerning this on github, but most of them were open and uncommented. If this has been resolved already, please share the link!

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Edit 1

I removed the line which adds the loss to the model and used the loss argument of the compile function. It looks like this now:

# Build model
vae = Model(x, x_decoded_mean)

# Calculate custom loss
xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
vae_loss = K.mean(xent_loss + kl_loss)

# Compile
vae.compile(optimizer='rmsprop', loss=vae_loss)

This throws an TypeError:

TypeError: Using a 'tf.Tensor' as a Python 'bool' is not allowed. Use 'if t is not None:' instead of 'if t:' to test if a tensor is defined, and use TensorFlow ops such as tf.cond to execute subgraphs conditioned on the value of a tensor.

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Edit 2

Thanks to @MarioZ's efforts, I was able to figure out a workaround for this.

# Build model
vae = Model(x, x_decoded_mean)

# Calculate custom loss in separate function
def vae_loss(x, x_decoded_mean):
    xent_loss = original_dim * metrics.binary_crossentropy(x, x_decoded_mean)
    kl_loss = - 0.5 * K.sum(1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)
    vae_loss = K.mean(xent_loss + kl_loss)
    return vae_loss

# Compile
vae.compile(optimizer='rmsprop', loss=vae_loss)

...

vae.fit(x_train, 
    x_train,        # <-- did not need this previously
    shuffle=True,
    epochs=epochs,
    batch_size=batch_size,
    validation_data=(x_test, x_test))     # <-- worked with (x_test, None) before

For some strange reason, I had to explicitly specify y and y_test while fitting the model. Originally, I didn't need to do this. The produced samples seem reasonable to me.

Although I could resolve this, I still don't know what the differences and disadvantages of these two methods are (other than needing a different syntax). Can someone give me more insight?

Answer 1

I'll try to answer the original question of why model.add_loss() is being used instead of specifying a custom loss function to model.compile(loss=...).

All loss functions in Keras always take two parameters y_true and y_pred. Have a look at the definition of the various standard loss functions available in Keras, they all have these two parameters. They are the 'targets' (the Y variable in many textbooks) and the actual output of the model. Most standard loss functions can be written as an expression of these two tensors. But some more complex losses cannot be written in that way. For your VAE example this is the case because the loss function also depends on additional tensors, namely z_log_var and z_mean, which are not available to the loss functions. Using model.add_loss() has no such restriction and allows you to write much more complex losses that depend on many other tensors, but it has the inconvenience of being more dependent on the model, whereas the standard loss functions work with just any model.

(Note: The code proposed in other answers here are somewhat cheating in as much as they just use global variables to sneak in the additional required dependencies. This makes the loss function not a true function in the mathematical sense. I consider this to be much less clean code and I expect it to be more error-prone.)