Custom loss function in Keras that penalizes output from intermediate layer

Question

Imagine I have a convolutional neural network to classify MNIST digits, such as this Keras example. This is purely for experimentation so I don't have a clear reason or justification as to why I'm doing this, but let's say I would like to regularize or penalize the output of an intermediate layer. I realize that the visualization below does not correspond to the MNIST CNN example and instead just has several fully connected layers. However, to help visualize what I mean let's say I want to impose a penalty on the node values in layer 4 (either pre or post activation is fine with me). In addition to having a categorical cross entropy loss term which is typical for multi-class classification, I would like to add another term to the loss function that minimizes the squared sum of the output at a given layer. This is somewhat similar in concept to l2 regularization, except that l2 regularization is penalizing the squared sum of all weights in the network. Instead, I am purely interested in the values of a given layer (e.g. layer 4) and not all the weights in the network.

I realize that this requires writing a custom loss function using keras backend to combine categorical crossentropy and the penalty term, but I am not sure how to use an intermediate layer for the penalty term in the loss function. I would greatly appreciate help on how to do this. Thanks!

Answer 1

Actually, what you are interested in is regularization and in Keras there are two different kinds of built-in regularization approach available for most of the layers (e.g. Dense, Conv1D, Conv2D, etc.):

• Weight regularization, which penalizes the weights of a layer. Usually, you can use kernel_regularizer and bias_regularizer arguments when constructing a layer to enable it. For example:

   l1_l2 = tf.keras.regularizers.l1_l2(l1=1.0, l2=0.01)
   x = tf.keras.layers.Dense(..., kernel_regularizer=l1_l2, bias_regularizer=l1_l2)
  

• Activity regularization, which penalizes the output (i.e. activation) of a layer. To enable this, you can use activity_regularizer argument when constructing a layer:

   l1_l2 = tf.keras.regularizers.l1_l2(l1=1.0, l2=0.01)
   x = tf.keras.layers.Dense(..., activity_regularizer=l1_l2)
  

  Note that you can set activity regularization through activity_regularizer argument for all the layers, even custom layers.

In both cases, the penalties are summed into the model's loss function, and the result would be the final loss value which would be optimized by the optimizer during training.

Further, besides the built-in regularization methods (i.e. L1 and L2), you can define your own custom regularizer method (see Developing new regularizers). As always, the documentation provides additional information which might be helpful as well.