聯合損失函數的多輸出Keras模型訓練

Question

我正在用Keras編寫兩個聯合解碼器，一個公共輸入，兩個獨立輸出以及一個將兩個輸出都考慮在內的損失函數。 我的問題是損失函數。

這是最小的Keras代碼，您可以重現該錯誤：

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
                )

我得到的錯誤是：

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}}]]

在第二次嘗試中，我嘗試編寫兩個損失函數並使用損失權重進行組合。

# 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')

但是我收到了

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

在這種情況下，問題實際上可能出在模型本身。 這是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
__________________________________________________________________________________________________

如果您認為模型有問題，請檢查“模型” 。 這個問題不同於在損失中僅使用一個輸出的問題 。 這也是Tensorflow中編寫的類似模型的損失函數：

# -- 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)

---

編輯：我嘗試使用實際數據集回答問題中的代碼，損失函數顯示的行為與代碼的Tensorflow實現不同。 答案中建議的損失函數迅速收斂並變為nan。 我同意回答output_1應該是絕對的。 基於此，我編寫了以下損失函數，該函數的收斂速度仍然不如Tensorflow之一快，但絕對不會崩潰：

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

您的代碼中有兩個問題：

首先是Lambda內部的K.dot操作必須為K.batch_dot

我用了：

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)

實際上，這有助於Keras計算輸出尺寸。 這是檢查代碼的簡便方法。 為了對其進行調試，我首先用現存損耗（ mse ）替換了自定義損耗，這很容易檢測。

第二個問題是自定義損失函數采用一對目標/輸出而不是列表。 損失函數的參數不是您在初始和編輯中都假定的張量列表。 所以我將損失函數定義為

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

並用作

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])

---

編輯：我最初誤讀了output2的自定義損失，因為它要求fcn_loss_1的值，但事實並非如此，您可以這樣寫：

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

並將其用作：

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

我假設output_1的損失是categorical_crossentropy 。 但是，即使您需要更改它，最簡單的方法是具有2個獨立的損失函數。 當然，您也可以選擇定義一個損失函數，該函數返回0並返回全部成本...但是將'loss（output1）+ 2 * loss（output2）'分為兩個損失加上重量，恕我直言。

完整的筆記本： https ： //colab.research.google.com/drive/1NG3uIiesg-VIt-W9254Sea2XXUYPoVH5