  Considering the use of Fully Connected (FC) layer limits the performance of
Convolutional Neural Networks (CNNs), this paper develops a method to improve
the coupling between the convolution layer and the FC layer by reducing the
noise in Feature Maps (FMs). Our approach is divided into three steps. Firstly,
we separate all the FMs into n blocks equally. Then, the weighted summation of
FMs at the same position in all blocks constitutes a new block of FMs. Finally,
we replicate this new block into n copies and concatenate them as the input to
the FC layer. This sharing of FMs could reduce the noise in them apparently and
avert the impact by a particular FM on the specific part weight of hidden
layers, hence preventing the network from overfitting to some extent. Using the
Fermat Lemma, we prove that this method could make the global minima value
range of the loss function wider, by which makes it easier for neural networks
to converge and accelerates the convergence process. This method does not
significantly increase the amounts of network parameters (only a few more
coefficients added), and the experiments demonstrate that this method could
increase the convergence speed and improve the classification performance of
neural networks.
