Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions, to reduce the spatial dimensions of feature maps and to allow the receptive fields to grow exponentially with depth. However, it is known that such subsampling operations are not translation equivariant, unlike convolutions that are translation equivariant. Here, we first introduce translation equivariant subsampling/upsampling layers that can be used to construct exact translation equivariant CNNs. We then generalise these layers beyond translations to general groups, thus proposing group equivariant subsampling/upsampling. We use these layers to construct group equivariant autoencoders (GAEs) that allow us to learn low-dimensional equivariant representations. We empirically verify on images that the representations are indeed equivariant to input translations and rotations, and thus generalise well to unseen positions and orientations. We further use GAEs in models that learn object-centric representations on multi-object datasets, and show improved data efficiency and decomposition compared to non-equivariant baselines.

中文翻译：

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组等变二次抽样

子采样以池化或跨步卷积的形式在卷积神经网络 (CNN) 中使用，以减少特征图的空间维度并允许感受野随深度呈指数增长。然而，众所周知，这种子采样操作不是平移等变的，与平移等变的卷积不同。在这里，我们首先介绍可用于构建精确平移等变 CNN 的平移等变子采样/上采样层。然后我们将这些层推广到一般组的翻译之外，从而提出组等变子采样/上采样。我们使用这些层来构建组等变自编码器 (GAE)，使我们能够学习低维等变表示。我们凭经验在图像上验证表示确实与输入平移和旋转等变，因此可以很好地推广到看不见的位置和方向。我们进一步在模型中使用 GAE，在多对象数据集上学习以对象为中心的表示，并显示出与非等变基线相比提高的数据效率和分解。