arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.03506cs.CVcs.LGstat.ML
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深层神经网络中的分层成核

Hierarchical nucleation in deep neural networks

Diego Doimo, Aldo Glielmo, Alessio Ansuini, Alessandro Laio

摘要:

深度卷积网络(DCN)学习有意义的表示,其中共享相同抽象特征的数据位置越来越近。理解这些表征以及它们是如何产生的,无疑具有实践和理论意义。在这项工作中,我们研究了ImageNet数据集在一些最先进的DCN中隐藏层的概率密度的演变。我们发现,初始层产生的单峰概率密度摆脱任何结构无关的分类。在随后的层中,密度峰值以分层的方式出现,反映了概念的语义层次。对应于单一类别的密度峰仅出现在输出附近,并通过非常急剧的过渡,这类似于非均质液体的成核过程。该过程在输出层的概率密度中留下足迹,其中峰的形貌允许重建类别的语义关系。

英文摘要:

Deep convolutional networks (DCNs) learn meaningful representations where data that share the same abstract characteristics are positioned closer and closer. Understanding these representations and how they are generated is of unquestioned practical and theoretical interest. In this work we study the evolution of the probability density of the ImageNet dataset across the hidden layers in some state-of-the-art DCNs. We find that the initial layers generate a unimodal probability density getting rid of any structure irrelevant for classification. In subsequent layers density peaks arise in a hierarchical fashion that mirrors the semantic hierarchy of the concepts. Density peaks corresponding to single categories appear only close to the output and via a very sharp transition which resembles the nucleation process of a heterogeneous liquid. This process leaves a footprint in the probability density of the output layer where the topography of the peaks allows reconstructing the semantic relationships of the categories.

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