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

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... ntial 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.