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），训练损失函数通常作用于网络的最终输出，仅对网络参数施加一些正则化约束。然而，随着网络层数增加，损失函数对网络前端层的影响逐渐减弱，网络参数易陷入局部优化。同时，研究发现训练后的网络在各阶段特征中存在显著的信息冗余，降低了各阶段特征映射的有效性，不利于网络后续参数朝最优方向调整。因此，通过设计约束前端特征并消除其信息冗余的损失函数，可能使网络获得更优的解，并进一步提高网络分类精度。本文针对CNN提出了一种多阶段特征去相关损失（MFD Loss），通过对各阶段特征的相关性进行约束，细化有效特征并消除信息冗余。考虑到CNN中层级较多，通过实验对比分析，MFD Loss作用于CNN的多个前端层，约束每一层和每一通道的输出特征，并在网络训练过程中与分类损失函数联合进行监督训练。与单一Softmax Loss监督学习相比，在多个典型CNN上对若干常用数据集的实验证明，Softmax Loss+MFD Loss的分类性能显著更优。同时，MFD Loss与若干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。