Training of multi-output Keras model on a joint loss function

Question

I'm writing two joint decoders in Keras, with one common input, two separate outputs, and a loss function that takes both outputs into account. The problem that I have is with the loss function.

Here is the minimal Keras code that you can reproduce the error:

import tensorflow as tf
from scat import *

from keras.layers import Input, Reshape, Permute, Lambda, Flatten
from keras.layers.core import Dense
from keras.layers.advanced_activations import LeakyReLU
from keras.models import Model
from keras import backend as K

def identity(x):
    return K.identity(x)

# custom loss function
def custom_loss():
    def my_loss(y_dummy, pred):
        fcn_loss_1 = tf.nn.softmax_cross_entropy_with_logits(labels=y_dummy[0], logits=pred[0])
        fcn_loss_2 = tf.nn.softmax_cross_entropy_with_logits(labels=y_dummy[1], logits=pred[1])
        fcn_loss_2 = tf.matrix_band_part(fcn_loss_2, 0, -1) - tf.matrix_band_part(fcn_loss_2, 0, 0)

        fcn_loss = tf.reduce_mean(fcn_loss_1) + 2 * tf.reduce_mean(fcn_loss_2)

        return fcn_loss
    return my_loss

def keras_version():
    input = Input(shape=(135,), name='feature_input')
    out1 = Dense(128, kernel_initializer='glorot_normal', activation='linear')(input)
    out1 = LeakyReLU(alpha=.2)(out1)
    out1 = Dense(256, kernel_initializer='glorot_normal', activation='linear')(out1)
    out1 = LeakyReLU(alpha=.2)(out1)
    out1 = Dense(512, kernel_initializer='glorot_normal', activation='linear')(out1)
    out1 = LeakyReLU(alpha=.2)(out1)
    out1 = Dense(45, kernel_initializer='glorot_normal', activation='linear')(out1)
    out1 = LeakyReLU(alpha=.2)(out1)
    out1 = Reshape((9, 5))(out1)

    out2 = Dense(128, kernel_initializer='glorot_normal', activation='linear')(input)
    out2 = LeakyReLU(alpha=.2)(out2)
    out2 = Dense(256, kernel_initializer='glorot_normal', activation='linear')(out2)
    out2 = LeakyReLU(alpha=.2)(out2)
    out2 = Dense(512, kernel_initializer='glorot_normal', activation='linear')(out2)
    out2 = LeakyReLU(alpha=.2)(out2)
    out2 = Dense(540, kernel_initializer='glorot_normal', activation='linear')(out2)
    out2 = LeakyReLU(alpha=.2)(out2)
    out2 = Reshape((9, 4, 15))(out2)
    out2 = Lambda(lambda x: K.dot(K.permute_dimensions(x, (0, 2, 1, 3)),
                                  K.permute_dimensions(x, (0, 2, 3, 1))), output_shape=(4,9,9))(out2)
    out2 = Flatten()(out2)
    out2 = Dense(324, kernel_initializer='glorot_normal', activation='linear')(out2)
    out2 = LeakyReLU(alpha=.2)(out2)
    out2 = Reshape((4, 9, 9))(out2)
    out2 = Lambda(lambda x: K.permute_dimensions(x, (0, 2, 3, 1)))(out2)

    out1 = Lambda(identity, name='output_1')(out1)
    out2 = Lambda(identity, name='output_2')(out2)

    return Model(input, [out1, out2])

model = keras_version()
model.compile(loss=custom_loss(), optimizer='adam')

model.summary()

feature_final = np.random.normal(0,1,[5000, 9, 15])
train_features_array = np.random.normal(0,1,[5000, 9, 5])
train_adj_array = np.random.normal(0,1,[5000, 9, 9, 4])

feature_final = feature_final.reshape(-1, 135)
model.fit(feature_final, [train_features_array, train_adj_array],
                batch_size=50,
                epochs=10
                )

The error I get is:

File "...", line 135, in <module>
    epochs=10
File ".../keras/engine/training.py", line 1039, in fit
    validation_steps=validation_steps)
File ".../keras/backend/tensorflow_backend.py", line 2675, in _call
    fetched = self._callable_fn(*array_vals)
File ".../tensorflow/python/client/session.py", line 1458, in __call__
    run_metadata_ptr)
tensorflow.python.framework.errors_impl.InvalidArgumentError: input must be at least 2-dim, received shape: [9]
     [[{{node loss/output_1_loss/MatrixBandPart_1}}]]

On a second attempt, I tried writing two loss functions and using loss weights to combine them.

# custom loss function
def custom_loss_1():
    def my_loss_1(y_dummy, pred):
        fcn_loss_1 = tf.nn.softmax_cross_entropy_with_logits(labels=y_dummy[0], logits=pred[0])

        return tf.reduce_mean(fcn_loss_1)
    return my_loss_1

def custom_loss_2():
    def my_loss_2(y_dummy, pred):
        fcn_loss_2 = tf.nn.softmax_cross_entropy_with_logits(labels=y_dummy[1], logits=pred[1])
        fcn_loss_2 = tf.matrix_band_part(fcn_loss_2, 0, -1) - tf.matrix_band_part(fcn_loss_2, 0, 0)

        return tf.reduce_mean(fcn_loss_2)
    return my_loss_2

model.compile(loss={'output_1':custom_loss_1(), 'output_2':custom_loss_2()},
              loss_weights={'output_1':1.0, 'output_2':2.0}, optimizer='adam')

but I received

tensorflow.python.framework.errors_impl.InvalidArgumentError: Matrix size-incompatible: In[0]: [20,25920], In[1]: [324,324]
     [[{{node dense_9/BiasAdd}}]]

In that case, the problem might actually be from the model itself. Here is the model.summary :

__________________________________________________________________________________________________
Layer (type)                    Output Shape         Param #     Connected to                     
==================================================================================================
feature_input (InputLayer)      (None, 135)          0                                            
__________________________________________________________________________________________________
dense_5 (Dense)                 (None, 128)          17408       feature_input[0][0]              
__________________________________________________________________________________________________
leaky_re_lu_5 (LeakyReLU)       (None, 128)          0           dense_5[0][0]                    
__________________________________________________________________________________________________
dense_6 (Dense)                 (None, 256)          33024       leaky_re_lu_5[0][0]              
__________________________________________________________________________________________________
leaky_re_lu_6 (LeakyReLU)       (None, 256)          0           dense_6[0][0]                    
__________________________________________________________________________________________________
dense_7 (Dense)                 (None, 512)          131584      leaky_re_lu_6[0][0]              
__________________________________________________________________________________________________
leaky_re_lu_7 (LeakyReLU)       (None, 512)          0           dense_7[0][0]                    
__________________________________________________________________________________________________
dense_1 (Dense)                 (None, 128)          17408       feature_input[0][0]              
__________________________________________________________________________________________________
dense_8 (Dense)                 (None, 540)          277020      leaky_re_lu_7[0][0]              
__________________________________________________________________________________________________
leaky_re_lu_1 (LeakyReLU)       (None, 128)          0           dense_1[0][0]                    
__________________________________________________________________________________________________
leaky_re_lu_8 (LeakyReLU)       (None, 540)          0           dense_8[0][0]                    
__________________________________________________________________________________________________
dense_2 (Dense)                 (None, 256)          33024       leaky_re_lu_1[0][0]              
__________________________________________________________________________________________________
reshape_2 (Reshape)             (None, 9, 4, 15)     0           leaky_re_lu_8[0][0]              
__________________________________________________________________________________________________
leaky_re_lu_2 (LeakyReLU)       (None, 256)          0           dense_2[0][0]                    
__________________________________________________________________________________________________
lambda_1 (Lambda)               (None, 4, 9, 9)      0           reshape_2[0][0]                  
__________________________________________________________________________________________________
dense_3 (Dense)                 (None, 512)          131584      leaky_re_lu_2[0][0]              
__________________________________________________________________________________________________
flatten_1 (Flatten)             (None, 324)          0           lambda_1[0][0]                   
__________________________________________________________________________________________________
leaky_re_lu_3 (LeakyReLU)       (None, 512)          0           dense_3[0][0]                    
__________________________________________________________________________________________________
dense_9 (Dense)                 (None, 324)          105300      flatten_1[0][0]                  
__________________________________________________________________________________________________
dense_4 (Dense)                 (None, 45)           23085       leaky_re_lu_3[0][0]              
__________________________________________________________________________________________________
leaky_re_lu_9 (LeakyReLU)       (None, 324)          0           dense_9[0][0]                    
__________________________________________________________________________________________________
leaky_re_lu_4 (LeakyReLU)       (None, 45)           0           dense_4[0][0]                    
__________________________________________________________________________________________________
reshape_3 (Reshape)             (None, 4, 9, 9)      0           leaky_re_lu_9[0][0]              
__________________________________________________________________________________________________
reshape_1 (Reshape)             (None, 9, 5)         0           leaky_re_lu_4[0][0]              
__________________________________________________________________________________________________
lambda_2 (Lambda)               (None, 9, 9, 4)      0           reshape_3[0][0]                  
__________________________________________________________________________________________________
output_1 (Lambda)               (None, 9, 5)         0           reshape_1[0][0]                  
__________________________________________________________________________________________________
output_2 (Lambda)               (None, 9, 9, 4)      0           lambda_2[0][0]                   
==================================================================================================
Total params: 769,437
Trainable params: 769,437
Non-trainable params: 0
__________________________________________________________________________________________________

If you think the model has an issue, please check "model" . This question is different from this question which uses only one output in the loss. Here is also the loss function from a similar model that was written in Tensorflow:

# -- loss function
Y_1 = tf.placeholder(tf.float32, shape=[None, 9, 9, 4])
Y_2 = tf.placeholder(tf.float32, shape=[None, 9, 5])

loss_1 = tf.nn.softmax_cross_entropy_with_logits(labels=Y_2, logits=fcn(X)[0])
loss_2 = tf.nn.softmax_cross_entropy_with_logits(labels=Y_1, logits=fcn(X)[1])
loss_2 = tf.matrix_band_part(loss_2, 0, -1) - tf.matrix_band_part(loss_2, 0, 0)

loss = tf.reduce_mean(loss_1) + 2 * tf.reduce_mean(loss_2)

---

Edits: I tried the code in the answer with the actual dataset, and loss function shows a different behavior from Tensorflow implementation of the code. The loss function suggested in the answers converges quickly and becomes nan. I agree with the answer which says output_1 should be categorical. Based on this, I wrote the following loss function, which still does not converge as fast as Tensorflow one, but definitly does not blow up:

def custom_loss_1(model, output_1):
    """ This loss function is called for output2
        It needs to fetch model.output[0] and the output_1 predictions in
        order to calculate fcn_loss_1
    """
    def my_loss(y_true, y_pred):
        fcn_loss_1 = tf.nn.softmax_cross_entropy_with_logits(labels=model.targets[0], logits=output_1)

        return tf.reduce_mean(fcn_loss_1)

    return my_loss

def custom_loss_2():
    """ This loss function is called for output2
        It needs to fetch model.output[0] and the output_1 predictions in
        order to calculate fcn_loss_1
    """
    def my_loss(y_true, y_pred):
        fcn_loss_2 = tf.nn.softmax_cross_entropy_with_logits(labels=y_true, logits=y_pred)
        fcn_loss_2 = tf.matrix_band_part(fcn_loss_2, 0, -1) - tf.matrix_band_part(fcn_loss_2, 0, 0)
        return tf.reduce_mean(fcn_loss_2)

    return my_loss

output_layer_1 = [layer for layer in model.layers if layer.name == 'output_1'][0]
losses = {'output_1': custom_loss_1(model, output_layer_1.output), 'output_2': custom_loss_2()}
model.compile(loss=losses, optimizer='adam', loss_weights=[1.0, 2.0])

Answer 1

You had two issues in your code:

The first is that the K.dot operation inside the Lambda needed to be K.batch_dot

I used:

def output_mult(x):
    a = K.permute_dimensions(x, (0, 2, 1, 3))
    b = K.permute_dimensions(x, (0, 2, 3, 1))
    return K.batch_dot(a, b)


out2 = Lambda(output_mult)(out2)

It helps to actually let Keras compute the output dimensions. It is an easy way to check the code. In order to debug it, I first replaced the custom loss with an exists loss ( mse ) and this was easy to detect.

Second issue is that a custom loss function takes a single pair of target / output rather than a list. The arguments to a loss function are not a list of tensors as you assumed both initially and in your edit. So I defined your loss function as

def custom_loss(model, output_1):
    """ This loss function is called for output2
        It needs to fetch model.output[0] and the output_1 predictions in
        order to calculate fcn_loss_1
    """
    def my_loss(y_true, y_pred):
        fcn_loss_1 = tf.nn.softmax_cross_entropy_with_logits(labels=model.targets[0], logits=output_1)
        fcn_loss_2 = tf.nn.softmax_cross_entropy_with_logits(labels=y_true, logits=y_pred)
        fcn_loss_2 = tf.matrix_band_part(fcn_loss_2, 0, -1) - tf.matrix_band_part(fcn_loss_2, 0, 0)
        return tf.reduce_mean(fcn_loss_2)

    return my_loss

And used it as

output_layer_1 = [layer for layer in model.layers if layer.name == 'output_1'][0]
losses = {'output_1': 'categorical_crossentropy', 'output_2': custom_loss(model, output_layer_1.output)}
model.compile(loss=losses, optimizer='adam', loss_weights=[1.0, 2.0])

---

Edit: I initially misread the custom loss for output2 as requiring the value of fcn_loss_1 , this doesn't seem to be the case and you can just write this as:

def custom_loss():
    def my_loss(y_true, y_pred):
        fcn_loss_2 = tf.nn.softmax_cross_entropy_with_logits(labels=y_true, logits=y_pred)
        fcn_loss_2 = tf.matrix_band_part(fcn_loss_2, 0, -1) - tf.matrix_band_part(fcn_loss_2, 0, 0)
        return tf.reduce_mean(fcn_loss_2)

    return my_loss

And used it as:

losses = {'output_1': 'categorical_crossentropy', 'output_2': custom_loss()}
model.compile(loss=losses, optimizer='adam', loss_weights=[1.0, 2.0])

I'm making the assumption that the loss for output_1 is categorical_crossentropy . But even if you need to change it, the simplest way to do it is to have 2 independent loss functions. Of course you can also choose to define a loss function that returns 0 and one that returns the full cost... but it would be cleaner to split the 'loss(output1) + 2 * loss(output2)' in two loss plus the weights, imho.

Full notebook: https://colab.research.google.com/drive/1NG3uIiesg-VIt-W9254Sea2XXUYPoVH5