On the dynamics of three-layer neural networks: initial condensation
This work provides theoretical insights into training dynamics for researchers in deep learning, though it is incremental as it extends known phenomena from two-layer to three-layer networks.
The paper investigates the condensation phenomenon in three-layer neural networks, where input weights converge to isolated orientations during training, and establishes a sufficient condition for its occurrence through theoretical analysis and experiments.
Empirical and theoretical works show that the input weights of two-layer neural networks, when initialized with small values, converge towards isolated orientations. This phenomenon, referred to as condensation, indicates that the gradient descent methods tend to spontaneously reduce the complexity of neural networks during the training process. In this work, we elucidate the mechanisms behind the condensation phenomena occurring in the training of three-layer neural networks and distinguish it from the training of two-layer neural networks. Through rigorous theoretical analysis, we establish the blow-up property of effective dynamics and present a sufficient condition for the occurrence of condensation, findings that are substantiated by experimental results. Additionally, we explore the association between condensation and the low-rank bias observed in deep matrix factorization.