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We present a novel and compact architecture for deep Convolutional NeuralNetworks (CNNs) in this paper, termed $3$D-FilterMap Convolutional NeuralNetworks ($3$D-FM-CNNs). The convolution layer of $3$D-FM-CNN learns a compactrepresentation of the filters, named $3$D-FilterMap, instead of a set ofindependent filters in the conventional convolution layer. The filters areextracted from the $3$D-FilterMap as overlapping $3$D submatrics with weightsharing among nearby filters, and these filters are convolved with the input togenerate the output of the convolution layer for $3$D-FM-CNN. Due to the weightsharing scheme, the parameter size of the $3$D-FilterMap is much smaller thanthat of the filters to be learned in the conventional convolution layer when$3$D-FilterMap generates the same number of filters. Our work is fundamentallydifferent from the network compression literature that reduces the size of alearned large network in the sense that a small network is directly learnedfrom scratch. Experimental results demonstrate that $3$D-FM-CNN enjoys a smallparameter space by learning compact $3$D-FilterMaps, while achievingperformance compared to that of the baseline CNNs which learn the same numberof filters as that generated by the corresponding $3$D-FilterMap.

Learning $3$D-FilterMap for Deep Convolutional Neural Networks