Keras using Tensorflow backend— masking on loss fu

Question

I am trying to implement a sequence-to-sequence task using LSTM by Keras with Tensorflow backend. The inputs are English sentences with variable lengths. To construct a dataset with 2-D shape [batch_number, max_sentence_length], I add EOF at the end of line and pad each sentence with enough placeholders, e.g. "#". And then each character in sentence is transformed to one-hot vector, now the dataset has 3-D shape [batch_number, max_sentence_length, character_number]. After LSTM encoder and decoder layers, softmax cross entropy between output and target is computed.

To eliminate the padding effect in model training, masking could be used on input and loss function. Mask input in Keras can be done by using "layers.core.Masking". In Tensorflow, masking on loss function can be done as follows: custom masked loss function in Tensorflow

However, I don't find a way to realize it in Keras, since a used-defined loss function in keras only accepts parameters y_true and y_pred. So how to input true sequence_lengths to loss function and mask?

Besides, I find a function "_weighted_masked_objective(fn)" in \keras\engine\training.py. Its definition is "Adds support for masking and sample-weighting to an objective function.” But it seems that the function can only accept fn(y_true, y_pred). Is there a way to use this function to solve my problem?

To be specific, I modify the example of Yu-Yang.

from keras.models import Model
from keras.layers import Input, Masking, LSTM, Dense, RepeatVector, TimeDistributed, Activation
import numpy as np
from numpy.random import seed as random_seed
random_seed(123)

max_sentence_length = 5
character_number = 3 # valid character 'a, b' and placeholder '#'

input_tensor = Input(shape=(max_sentence_length, character_number))
masked_input = Masking(mask_value=0)(input_tensor)
encoder_output = LSTM(10, return_sequences=False)(masked_input)
repeat_output = RepeatVector(max_sentence_length)(encoder_output)
decoder_output = LSTM(10, return_sequences=True)(repeat_output)
output = Dense(3, activation='softmax')(decoder_output)

model = Model(input_tensor, output)
model.compile(loss='categorical_crossentropy', optimizer='adam')
model.summary()

X = np.array([[[0, 0, 0], [0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0]],
          [[0, 0, 0], [0, 1, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0]]])
y_true = np.array([[[0, 0, 1], [0, 0, 1], [1, 0, 0], [0, 1, 0], [0, 1, 0]], # the batch is ['##abb','#babb'], padding '#'
          [[0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 1, 0], [0, 1, 0]]])

y_pred = model.predict(X)
print('y_pred:', y_pred)
print('y_true:', y_true)
print('model.evaluate:', model.evaluate(X, y_true))
# See if the loss computed by model.evaluate() is equal to the masked loss
import tensorflow as tf
logits=tf.constant(y_pred, dtype=tf.float32)
target=tf.constant(y_true, dtype=tf.float32)
cross_entropy = tf.reduce_mean(-tf.reduce_sum(target * tf.log(logits),axis=2))
losses = -tf.reduce_sum(target * tf.log(logits),axis=2)
sequence_lengths=tf.constant([3,4])
mask = tf.reverse(tf.sequence_mask(sequence_lengths,maxlen=max_sentence_length),[0,1])
losses = tf.boolean_mask(losses, mask)
masked_loss = tf.reduce_mean(losses)
with tf.Session() as sess:
    c_e = sess.run(cross_entropy)
    m_c_e=sess.run(masked_loss)
    print("tf unmasked_loss:", c_e)
    print("tf masked_loss:", m_c_e)

The output in Keras and Tensorflow are compared as follows:

As shown above, masking is disabled after some kinds of layers. So how to mask loss function in keras when those layers are added?

Answer 1

If you're not using masks as in Yu-Yang's answer, you can try this.

If you have your target data Y with length and padded with the mask value, you can:

import keras.backend as K
def custom_loss(yTrue,yPred):

    #find which values in yTrue (target) are the mask value
    isMask = K.equal(yTrue, maskValue) #true for all mask values

    #since y is shaped as (batch, length, features), we need all features to be mask values
    isMask = K.all(isMask, axis=-1) #the entire output vector must be true
        #this second line is only necessary if the output features are more than 1

    #transform to float (0 or 1) and invert
    isMask = K.cast(isMask, dtype=K.floatx())
    isMask = 1 - isMask #now mask values are zero, and others are 1

    #multiply this by the inputs:
       #maybe you might need K.expand_dims(isMask) to add the extra dimension removed by K.all
     yTrue = yTrue * isMask   
     yPred = yPred * isMask

     return someLossFunction(yTrue,yPred)

---

If you have padding only for the input data, or if Y has no length, you can have your own mask outside the function:

masks = [
   [1,1,1,1,1,1,0,0,0],
   [1,1,1,1,0,0,0,0,0],
   [1,1,1,1,1,1,1,1,0]
]
 #shape (samples, length). If it fails, make it (samples, length, 1). 

import keras.backend as K

masks = K.constant(masks)

Since masks depend on your input data, you can use your mask value to know where to put zeros, such as:

masks = np.array((X_train == maskValue).all(), dtype='float64')    
masks = 1 - masks

#here too, if you have a problem with dimensions in the multiplications below
#expand masks dimensions by adding a last dimension = 1.

And make your function taking masks from outside of it (you must recreate the loss function if you change the input data):

def customLoss(yTrue,yPred):

    yTrue = masks*yTrue
    yPred = masks*yPred

    return someLossFunction(yTrue,yPred)

---

Does anyone know if keras automatically masks the loss function?? Since it provides a Masking layer and says nothing about the outputs, maybe it does it automatically?

Answer 2

If there's a mask in your model, it'll be propagated layer-by-layer and eventually applied to the loss. So if you're padding and masking the sequences in a correct way, the loss on the padding placeholders would be ignored.

Some Details:

It's a bit involved to explain the whole process, so I'll just break it down to several steps:

1. In compile(), the mask is collected by calling compute_mask() and applied to the loss(es) (irrelevant lines are ignored for clarity).

weighted_losses = [_weighted_masked_objective(fn) for fn in loss_functions]

# Prepare output masks.
masks = self.compute_mask(self.inputs, mask=None)
if masks is None:
    masks = [None for _ in self.outputs]
if not isinstance(masks, list):
    masks = [masks]

# Compute total loss.
total_loss = None
with K.name_scope('loss'):
    for i in range(len(self.outputs)):
        y_true = self.targets[i]
        y_pred = self.outputs[i]
        weighted_loss = weighted_losses[i]
        sample_weight = sample_weights[i]
        mask = masks[i]
        with K.name_scope(self.output_names[i] + '_loss'):
            output_loss = weighted_loss(y_true, y_pred,
                                        sample_weight, mask)

2. Inside Model.compute_mask(), run_internal_graph() is called.
3. Inside run_internal_graph(), the masks in the model is propagated layer-by-layer from the model's inputs to outputs by calling Layer.compute_mask() for each layer iteratively.

So if you're using a Masking layer in your model, you shouldn't worry about the loss on the padding placeholders. The loss on those entries will be masked out as you've probably already seen inside _weighted_masked_objective().

A Small Example:

max_sentence_length = 5
character_number = 2

input_tensor = Input(shape=(max_sentence_length, character_number))
masked_input = Masking(mask_value=0)(input_tensor)
output = LSTM(3, return_sequences=True)(masked_input)
model = Model(input_tensor, output)
model.compile(loss='mae', optimizer='adam')

X = np.array([[[0, 0], [0, 0], [1, 0], [0, 1], [0, 1]],
              [[0, 0], [0, 1], [1, 0], [0, 1], [0, 1]]])
y_true = np.ones((2, max_sentence_length, 3))
y_pred = model.predict(X)
print(y_pred)
[[[ 0.          0.          0.        ]
  [ 0.          0.          0.        ]
  [-0.11980877  0.05803877  0.07880752]
  [-0.00429189  0.13382857  0.19167568]
  [ 0.06817091  0.19093043  0.26219055]]

 [[ 0.          0.          0.        ]
  [ 0.0651961   0.10283815  0.12413475]
  [-0.04420842  0.137494    0.13727818]
  [ 0.04479844  0.17440712  0.24715884]
  [ 0.11117355  0.21645413  0.30220413]]]

# See if the loss computed by model.evaluate() is equal to the masked loss
unmasked_loss = np.abs(1 - y_pred).mean()
masked_loss = np.abs(1 - y_pred[y_pred != 0]).mean()

print(model.evaluate(X, y_true))
0.881977558136

print(masked_loss)
0.881978

print(unmasked_loss)
0.917384

As can be seen from this example, the loss on the masked part (the zeroes in y_pred) is ignored, and the output of model.evaluate() is equal to masked_loss.

---

EDIT:

If there's a recurrent layer with return_sequences=False, the mask stop propagates (i.e., the returned mask is None). In RNN.compute_mask():

def compute_mask(self, inputs, mask):
    if isinstance(mask, list):
        mask = mask[0]
    output_mask = mask if self.return_sequences else None
    if self.return_state:
        state_mask = [None for _ in self.states]
        return [output_mask] + state_mask
    else:
        return output_mask

In your case, if I understand correctly, you want a mask that's based on y_true, and whenever the value of y_true is [0, 0, 1] (the one-hot encoding of "#") you want the loss to be masked. If so, you need to mask the loss values in a somewhat similar way to Daniel's answer.

The main difference is the final average. The average should be taken over the number of unmasked values, which is just K.sum(mask). And also, y_true can be compared to the one-hot encoded vector [0, 0, 1] directly.

def get_loss(mask_value):
    mask_value = K.variable(mask_value)
    def masked_categorical_crossentropy(y_true, y_pred):
        # find out which timesteps in `y_true` are not the padding character '#'
        mask = K.all(K.equal(y_true, mask_value), axis=-1)
        mask = 1 - K.cast(mask, K.floatx())

        # multiply categorical_crossentropy with the mask
        loss = K.categorical_crossentropy(y_true, y_pred) * mask

        # take average w.r.t. the number of unmasked entries
        return K.sum(loss) / K.sum(mask)
    return masked_categorical_crossentropy

masked_categorical_crossentropy = get_loss(np.array([0, 0, 1]))
model = Model(input_tensor, output)
model.compile(loss=masked_categorical_crossentropy, optimizer='adam')

The output of the above code then shows that the loss is computed only on the unmasked values:

model.evaluate: 1.08339476585
tf unmasked_loss: 1.08989
tf masked_loss: 1.08339

The value is different from yours because I've changed the axis argument in tf.reverse from [0,1] to [1].