Deformation Robust Roto-Scale-Translation Equivariant CNNs
Deformation Robust Roto-Scale-Translation Equivariant CNNs
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发表时间：
2021-11
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通讯作者：
Liyao (Mars) Gao;Guang Lin;Wei Zhu
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作者：
Liyao (Mars) Gao;Guang Lin;Wei Zhu
将群体对称性直接融入到学习过程中已被证明是模型设计的有效指导方针。群等变卷积神经网络(G-CNN)通过产生保证协变变换为输入的群体行为的特征，在具有内在对称性的学习任务中获得显著的泛化性能。对于平面图像，无论是在旋转变换下，还是在缩放变换下，G-CNN的一般理论和实际实现都得到了研究，但都是单独的。本文提出了一种旋转尺度平移等变CNN(RST-CNN)，它通过耦合群卷积保证在这三个群上共同实现等变。此外，由于现实中的对称变换很少是完美的，并且通常会受到输入变形的影响，我们给出了输入失真表示的等方差的稳定性分析，这促使了卷积滤波器在(预先固定的)低频空间模式下的截断展开。所得到的模型可证明实现了变形稳健的RST等价性，即当变换被讨厌的数据变形“污染”时，RST对称性仍被“近似”保留，这一特性对于不分布的概化特别重要。在MNIST、Fashion-MNIST和STL-10上的数值实验表明，所提出的模型比现有技术有显著的改进，特别是在数据中既存在旋转变化又存在尺度变化的小数据区域。
Incorporating group symmetry directly into the learning process has proved to be an effective guideline for model design. By producing features that are guaranteed to transform covariantly to the group actions on the inputs, group-equivariant convolutional neural networks (G-CNNs) achieve significantly improved generalization performance in learning tasks with intrinsic symmetry. General theory and practical implementation of G-CNNs have been studied for planar images under either rotation or scaling transformation, but only individually. We present, in this paper, a roto-scale-translation equivariant CNN (RST-CNN), that is guaranteed to achieve equivariance jointly over these three groups via coupled group convolutions. Moreover, as symmetry transformations in reality are rarely perfect and typically subject to input deformation, we provide a stability analysis of the equivariance of representation to input distortion, which motivates the truncated expansion of the convolutional filters under (pre-fixed) low-frequency spatial modes. The resulting model provably achieves deformation-robust RST equivariance, i.e., the RST symmetry is still"approximately"preserved when the transformation is"contaminated"by a nuisance data deformation, a property that is especially important for out-of-distribution generalization. Numerical experiments on MNIST, Fashion-MNIST, and STL-10 demonstrate that the proposed model yields remarkable gains over prior arts, especially in the small data regime where both rotation and scaling variations are present within the data.