CNN 仅针对 binary_crossentropy 损失 function 收敛并在测试数据集上失败

Question

The problem consists in training a CNN with a data set containing an input of (n,n) shape matrices of numbers between 0 and 1000. The output should represent the very same (n,n) shape matrices having the 0 values patched with other values between 1 and 1000. (Similar with denoising images)

Example:
Input:             Output: 
135 0   283 4      135 75  283 4
25  38  43  0      25  38  43  815
0   99  820 481    533 99  820 481
728 331 3   28     728 331 3   28

The outputs were generated by running the inputs through a genetic algorithm for optimizing an external cost function. (this function is quite complex and computed in an external dedicated program) The entire data set contains 3000 Inputs and Outputs, each having a (10,10) shape.

As the problem resembles similarities with image processing neural networks, I decided to use a CNN. X_data contains the values of each input matrix and Y_data contains binary encodings (10 decimal long) of the output patched data. (worked out this encoding in order to reduce output size and improve convergence speed)

Example:
X_data:            Y_data:
135 0   283 4      0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1...
25  38  43  0
0   99  820 481
728 331 3   28

The network is converging only when using the 'binary_crossentropy' loss function, but when I compare the performance of the trained CNN over new inputs, there is no improvement. (I measure this by comparing the CNN output with the genetic algorithm optimized output over the same external cost function)

The questions: Are the training input and output data sets compatible with this kind of problem? Is the data set large enough to obtain proper results or should provide more training data? Is the encoding of the output data a good approach, or is it the problem that`s making the trained CNN not work? If there are any other approach flaws, please help me work them out!

inshape = (dim,dim,1)
outshape = (dim*dim*10)

model = Sequential()     
inp = Input(inshape) 
x = BatchNormalization()(inp)
x = Conv2D(1000, kernel_size=3,padding='same')(x)
x = Activation('relu')(x)    
x = Reshape((100,100,-1))(x)
x = MaxPooling2D(pool_size=(5,5))(x)
x = SpatialDropout2D(rate = 0.5)(x, training=True)    
x = Conv2D(250, kernel_size=3,padding='same')(x)
x = Activation('relu')(x)
x = MaxPooling2D(pool_size=(4,4))(x)    
x = SpatialDropout2D(rate = 0.3)(x, training=True)
x = Conv2D(400, kernel_size=3,padding='same')(x) 
x = Activation('sigmoid')(x)
x = MaxPooling2D(pool_size=(2,2))(x) 
x = Conv2D(2500, kernel_size=3,padding='same')(x) 
x = Activation('sigmoid')(x)
x = MaxPooling2D(pool_size=(2,2))(x)  
x = BatchNormalization()(x)
x = Flatten()(x)
out = Dense(outshape, activation='sigmoid',name='out')(x)
model = Model(inputs=inp,outputs=(out)) 
model.compile(optimizer=Adadelta(lr=1.0),
              loss = ['binary_crossentropy'], metrics =['accuracy'])

Answer 1

First of all, do you really need a CNN, or just fully connected layers? To answer this question, ask yourself if there is a spatial relationship between the values of your input data, like in images. Now for your questions:

Are the training input and output data sets compatible with this kind of problem?

Yes it is. What you need is called a denoizing autoencoder (CNN or fully connected, it depends on your data). Autoencoders are applying successively two functions on x, such that f(g(x)) = x', and x and x' have the same size. To stop the autoencoder from learning the identity matrix, layers in the middle are significantly smaller. Denoizing is a variant, because zeros in the input array are considered as noise, and you want to reconstruct the missing information in the output layer.

Is the data set large enough to obtain proper results or do I need more data?

It depends on the complexity of the function that relates predictors to outcomes, as well as the entropy of your data. Try to modify the width and depth of your layers to see if it helps.

Is the encoding of the output data a good approach, or is it the problem that`s making the trained CNN not work?

One-hot encoding is useful when you are dealing with a classification task, and not a regression task. From what I understand what you have here is a regression task, even if you're trying to output integers. You could simply try to reconstruct the input x on the output layer with a matrix of real numbers, and eventually round them for computing your loss, which could be a simple RMSE (binary cross entropy is for classification tasks).

Now, making neural networks to work is complex, there is a lot of different factors, and knowledge alone is not enough. You also need experience, trials and errors, etc. I recommend you to start simple, get satisfactory results, and then try to improve your prediction accuracy step by step.