Latent representations are used extensively for downstream tasks, such as
visualization, interpolation or feature extraction of deep learning models.
Invariant and equivariant neural networks are powerful and well-established
models for enforcing inductive biases. In this paper, we demonstrate that the
inductive bias imposed on the by an equivariant model must also be taken into
account when using latent representations. We show how not accounting for the
inductive biases leads to decreased performance on downstream tasks, and vice
versa, how accounting for inductive biases can be done effectively by using an
invariant projection of the latent representations. We propose principles for
how to choose such a projection, and show the impact of using these principles
in two common examples: First, we study a permutation equivariant variational
auto-encoder trained for molecule graph generation; here we show that invariant
projections can be designed that incur no loss of information in the resulting
invariant representation. Next, we study a rotation-equivariant representation
used for image classification. Here, we illustrate how random invariant
projections can be used to obtain an invariant representation with a high
degree of retained information. In both cases, the analysis of invariant latent
representations proves superior to their equivariant counterparts. Finally, we
illustrate that the phenomena documented here for equivariant neural networks
have counterparts in standard neural networks where invariance is encouraged
via augmentation. Thus, while these ambiguities may be known by experienced
developers of equivariant models, we make both the knowledge as well as
effective tools to handle the ambiguities available to the broader community.

在这篇论文中，我们展示了在使用潜在表示时应考虑的等变模型对归纳偏好的作用，并表明不考虑归纳偏好会导致下游任务的性能降低，相反，通过使用潜在表示的不变投影来有效地考虑归纳偏好，我们提出了选择这种投影的原则，并通过两个常见的例子展示了这些原则的影响：首先，我们研究了用于分子图形生成的置换等变变分自编码器；在这里，我们展示了可以设计一种不变投影，在结果不变表示中没有信息损失。接下来，我们研究了用于图像分类的旋转等变表示；在这里，我们说明了如何使用随机不变投影来获得一个在保留大量信息的不变表示。在这两种情况下，对不变潜在表示的分析证明优于它们的等变对应物。最后，我们证明了等变神经网络中记录的现象在通过数据增强鼓励不变性的标准神经网络中也存在。因此，虽然有经验的等变模型开发人员可能已经知道这些歧义，但我们将这些知识和处理这些歧义的有效工具提供给更广泛的社区。