We study whether inputs from the same class can be connected by a continuous
path, in original or latent representation space, such that all points on the
path are mapped by the neural network model to the same class. Understanding
how the neural network views its own input space and how the latent spaces are
structured has value for explainability and robustness. We show that paths,
linear or nonlinear, connecting same-class inputs exist in all cases studied.

本文研究了是否可以通过连续路径将同一类别的输入在原始或潜在的表征空间中连接起来，以使神经网络模型将路径上的所有点映射到相同的类别。理解神经网络如何看待自己的输入空间以及潜在空间的结构对于可解释性和鲁棒性具有价值。我们证明，在所研究的所有情况下，存在连接同类别输入的线性或非线性路径。

深度神经网络中的原始空间和潜空间连接性

On original and latent space connectivity in deep neural networks

The recently developed variational autoencoders (VAEs) have proved to be an
effective confluence of the rich representational power of neural networks with
Bayesian methods. However, most work on VAEs use a rather simple prior over the
latent variables such as standard normal distribution, thereby restricting its
applications to relatively simple phenomena. In this work, we propose
hierarchical nonparametric variational autoencoders, which combines
tree-structured Bayesian nonparametric priors with VAEs, to enable infinite
flexibility of the latent representation space. Both the neural parameters and
Bayesian priors are learned jointly using tailored variational inference. The
resulting model induces a hierarchical structure of latent semantic concepts
underlying the data corpus, and infers accurate representations of data
instances. We apply our model in video representation learning. Our method is
able to discover highly interpretable activity hierarchies, and obtain improved
clustering accuracy and generalization capacity based on the learned rich
representations.

本文提出了一种层次非参数变分自编码器模型，以结合树状结构的贝叶斯非参数先验和变分自编码器来实现无限灵活性的潜在表征空间，进而在视频表征学习上取得更好的效果。