  Deep convolutional neural networks have recently proven extremely competitive
in challenging image recognition tasks. This paper proposes the epitomic
convolution as a new building block for deep neural networks. An epitomic
convolution layer replaces a pair of consecutive convolution and max-pooling
layers found in standard deep convolutional neural networks. The main version
of the proposed model uses mini-epitomes in place of filters and computes
responses invariant to small translations by epitomic search instead of
max-pooling over image positions. The topographic version of the proposed model
uses large epitomes to learn filter maps organized in translational
topographies. We show that error back-propagation can successfully learn
multiple epitomic layers in a supervised fashion. The effectiveness of the
proposed method is assessed in image classification tasks on standard
benchmarks. Our experiments on Imagenet indicate improved recognition
performance compared to standard convolutional neural networks of similar
architecture. Our models pre-trained on Imagenet perform excellently on
Caltech-101. We also obtain competitive image classification results on the
small-image MNIST and CIFAR-10 datasets.
