寻找射影等变网络
In Search of Projectively Equivariant Networks
AI总结：
本研究将等变性放宽至射影意义，提出通过乘法修正提升构建射影等变网络，并证明其在线性层构建中的最一般性，实验验证了理论。
摘要：
线性神经网络层的等变性已被广泛研究。在本工作中，我们将等变性条件放宽至仅在射影意义上成立。我们提出了一种通过构建标准等变网络来构造射影等变神经网络的方法，其中作用于每个中间特征空间的线性群表示是射影群表示的“乘法修正提升”。通过理论研究射影等变线性层与线性等变线性层之间的关系，我们证明了在由线性层构建网络时，我们的方法是最一般可能的。该理论在两个简单实验中得到了展示。
英文摘要：
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.
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