We present an efficient alternative to the convolutional layer using cheap spatial transformations. This construction exploits an inherent spatial redundancy of the learned convolutional filters to enable a much greater parameter efficiency, while maintaining the top-end accuracy of their dense counter-parts. Training these networks is modelled as a generalised pruning problem, whereby the pruned filters are replaced with cheap transformations from the set of non-pruned filters. We provide an efficient implementation of the proposed layer, followed by two natural extensions to avoid excessive feature compression and to improve the expressivity of the transformed features. We show that these networks can achieve comparable or improved performance to state-of-the-art pruning models across both the CIFAR-10 and ImageNet-1K datasets.

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