Emergence of hierarchical modes from deep learning

Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight matrices as a hierarchy of latent modes. These modes are akin to patterns in physics studies of memory networks. The mode decomposition learning not only saves a significant large amount of training costs, but also explains the network performance with the leading modes. The mode learning scheme shows a progressively compact latent space across the network hierarchy, and the least number of modes increases only logarithmically with the network width. Our mode decomposition learning is also studied in an analytic on-line learning setting, which reveals multi-stage of learning dynamics. Therefore, the proposed mode decomposition learning points to a cheap and interpretable route towards the magical deep learning.