Department of Complexity Science and Engineering, The University of Tokyo, Chiba, 277-8561, Japan.
Research Fellow of the Japan Society for the Promotion of Science, Tokyo, 102-0083, Japan.
Sci Rep. 2020 Sep 29;10(1):16001. doi: 10.1038/s41598-020-72593-4.
Deep neural networks are good at extracting low-dimensional subspaces (latent spaces) that represent the essential features inside a high-dimensional dataset. Deep generative models represented by variational autoencoders (VAEs) can generate and infer high-quality datasets, such as images. In particular, VAEs can eliminate the noise contained in an image by repeating the mapping between latent and data space. To clarify the mechanism of such denoising, we numerically analyzed how the activity pattern of trained networks changes in the latent space during inference. We considered the time development of the activity pattern for specific data as one trajectory in the latent space and investigated the collective behavior of these inference trajectories for many data. Our study revealed that when a cluster structure exists in the dataset, the trajectory rapidly approaches the center of the cluster. This behavior was qualitatively consistent with the concept retrieval reported in associative memory models. Additionally, the larger the noise contained in the data, the closer the trajectory was to a more global cluster. It was demonstrated that by increasing the number of the latent variables, the trend of the approach a cluster center can be enhanced, and the generalization ability of the VAE can be improved.
深度神经网络擅长提取低维子空间（潜在空间），这些子空间代表高维数据集中的基本特征。变分自编码器（VAEs）等深度生成模型可以生成和推断高质量数据集，如图像。特别是，VAEs 可以通过重复在潜在空间和数据空间之间的映射来消除图像中包含的噪声。为了阐明这种去噪的机制，我们通过数值分析来研究在推断过程中，经过训练的网络在潜在空间中的活动模式如何变化。我们考虑了特定数据的活动模式随时间的发展，将其视为潜在空间中的一条轨迹，并研究了许多数据的这些推断轨迹的集体行为。我们的研究表明，当数据集中存在聚类结构时，轨迹会迅速接近聚类中心。这种行为与联想记忆模型中报告的概念检索定性一致。此外，数据中包含的噪声越大，轨迹越接近更全局的聚类。结果表明，通过增加潜在变量的数量，可以增强接近聚类中心的趋势，从而提高 VAEs 的泛化能力。
