  In convolutional neural networks (CNNs), pooling operations play important
roles such as dimensionality reduction and deformation compensation. In
general, max pooling, which is the most widely used operation for local
pooling, is performed independently for each kernel. However, the deformation
may be spatially smooth over the neighboring kernels. This means that max
pooling is too flexible to compensate for actual deformations. In other words,
its excessive flexibility risks canceling the essential spatial differences
between classes. In this paper, we propose regularized pooling, which enables
the value selection direction in the pooling operation to be spatially smooth
across adjacent kernels so as to compensate only for actual deformations. The
results of experiments on handwritten character images and texture images
showed that regularized pooling not only improves recognition accuracy but also
accelerates the convergence of learning compared with conventional pooling
operations.
