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.

翻译：针对用于模式分类的卷积神经网络（CNN），除对网络参数施加正则化约束外，训练损失函数通常仅作用于网络的最终输出层。然而，随着网络层数的增加，损失函数对网络浅层的影响逐渐减弱，网络参数易陷入局部最优。同时发现，训练后的网络在各阶段特征中存在显著的信息冗余，这不仅降低了各阶段的特征映射有效性，也不利于网络后续参数向最优方向调整。因此，通过设计约束浅层特征并消除其信息冗余的损失函数，有望获得更优的网络解，从而进一步提升网络分类精度。本文针对CNN提出一种多级特征去相关损失（MFD Loss），通过约束各阶段特征的相关性来提炼有效特征并消除信息冗余。考虑到CNN层数较多，通过实验对比分析，将MFD Loss作用于CNN的多个浅层，约束各层各通道的输出特征，在网络训练期间与分类损失函数联合进行监督训练。与单一的Softmax Loss监督学习相比，在多个典型CNN上使用多个常用数据集进行的实验证明，Softmax Loss+MFD Loss的分类性能显著更优。同时，MFD Loss与其他典型损失函数组合前后的对比实验验证了其良好的通用性。