  For the convolutional neural network (CNN) used for pattern classification,
the training loss function is usually applied to the final output of the
network, except for some regularization constraints on the network parameters.
However, with the increasing of the number of network layers, the influence of
the loss function on the network front layers gradually decreases, and the
network parameters tend to fall into local optimization. At the same time, it
is found that the trained network has significant information redundancy at all
stages of features, which reduces the effectiveness of feature mapping at all
stages and is not conducive to the change of the subsequent parameters of the
network in the direction of optimality. Therefore, it is possible to obtain a
more optimized solution of the network and further improve the classification
accuracy of the network by designing a loss function for restraining the front
stage features and eliminating the information redundancy of the front stage
features .For CNN, this article proposes a multi-stage feature decorrelation
loss (MFD Loss), which refines effective features and eliminates information
redundancy by constraining the correlation of features at all stages.
Considering that there are many layers in CNN, through experimental comparison
and analysis, MFD Loss acts on multiple front layers of CNN, constrains the
output features of each layer and each channel, and performs supervision
training jointly with classification loss function during network training.
Compared with the single Softmax Loss supervised learning, the experiments on
several commonly used datasets on several typical CNNs prove that the
classification performance of Softmax Loss+MFD Loss is significantly better.
Meanwhile, the comparison experiments before and after the combination of MFD
Loss and some other typical loss functions verify its good universality.
