When a three-dimensional object moves through a scene, a corresponding change occurs on the image plane and in the visual representation constructed by a learning algorithm. Starting with the idea that a good representation is one that transforms linearly under scene motions, we use standard results from group representation theory to show that any such representation is equivalent to a combination of particularly simple irreducible representations. We derive a striking relationship between irreducibility and the statistical dependency structure of the representation. Under partial observability, as induced by the perspective projection of a scene onto the image plane, the motion group does not have a linear action on the space of images, so that it becomes necessary to perform inference over a latent representation that does transform linearly. This idea is demonstrated in a model of rotating NORB objects that employs a latent representation of the non-commutative 3D rotation group SO(3).

该文利用群表示论和可线性转换的可视化表示概念，证明了任何这种表示都等价于基本不可约表示的组合，并表明在受限条件下，不可约表示是相互独立的。在部分可观察性下，需要对可转换线性的潜在表示执行推理。此想法在利用三维转动群SO（3）的潜在表示的旋转NORB对象的模型中得到了演示。

学习视觉表征的转换属性