论文标题
寻找投影性的模棱两可的网络
In Search of Projectively Equivariant Networks
论文作者
论文摘要
线性神经网络层的模棱两可。在这项工作中，我们放宽了肩variance条件，只有在投影意义上才能正确。我们提出了一种通过构建标准的模棱两可的网络来构建一个投影性的神经网络的方法，在该网络中，作用在每个中间特征空间上的线性组表示是“多样化修改的型号升降机”。从理论上讲，通过研究型和线性的线性线性层的关系，我们表明，当通过线性层构建网络时，我们的方法是最笼统的。该理论在两个简单的实验中展示了。
Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building a standard equivariant network where the linear group representations acting on each intermediate feature space are "multiplicatively modified lifts" of projective group representations. By theoretically studying the relation of projectively and linearly equivariant linear layers, we show that our approach is the most general possible when building a network out of linear layers. The theory is showcased in two simple experiments.
