Deep Symmetry Networks 论文

摘要

The chief difficulty in object recognition is that objects ’ classes are obscured by a large number of extraneous sources of variability, such as pose and part de-formation. These sources of variation can be represented by symmetry groups, sets of composable transformations that preserve object identity. Convolutional neural networks (convnets) achieve a degree of translational invariance by com-puting feature maps over the translation group, but cannot handle other groups. As a result, these groups ’ effects have to be approximated by small translations, which often requires augmenting datasets and leads to high sample complexity. In this paper, we introduce deep symmetry networks (symnets), a generalization of convnets that forms feature maps over arbitrary symmetry groups. Symnets use kernel-based interpolation to tractably tie parameters and pool over symmetry spaces of any dimension. Like convnets, they are trained with backpropagation. The composition of feature transformations through the layers of a symnet pro-vides a new approach to deep learning. Experiments on NORB and MNIST-rot show that symnets over the affine group greatly reduce sample complexity relative to convnets by better capturing the symmetries in the data. 1