Emergence of hierarchical modes from deep learning

TL;DR

This paper introduces a mode decomposition learning method that interprets deep neural network weights as hierarchical latent modes, reducing training costs and enhancing interpretability by revealing a compact, disentangled latent space.

Contribution

It proposes a novel mode decomposition approach that explains network performance through hierarchical modes, which grow logarithmically with network width and simplify understanding of deep learning models.

Findings

Modes increase logarithmically with network width

Mode decomposition reduces training costs significantly

Modes provide a more disentangled, interpretable latent space

Abstract

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, but the least number of modes increases only logarithmically with the network width, and becomes even a constant when the width further grows. The mode decomposition learning not only saves a significant large amount of training costs, but also explains the network performance with the leading modes, displaying a striking piecewise power-law behavior. The modes specify a progressively compact latent space across the network hierarchy, making a more disentangled subspaces compared to standard training. Our mode decomposition learning is also studied in an analytic on-line learning setting, which reveals multi-stage of learning dynamics with a continuous specialization of hidden nodes. Therefore, the proposed mode decomposition learning points to a cheap and interpretable route towards the magical deep learning.