Deconstructing the Goldilocks Zone of Neural Network Initialization
This work addresses a foundational issue in deep learning optimization for researchers, but it is incremental as it builds on prior studies to refine and analyze the relationship.
The paper tackles the problem of understanding the 'Goldilocks zone' of neural network initialization, which is linked to trainability through excess positive curvature in the loss Hessian, and finds that strong model performance does not perfectly align with this zone, calling for further research.
The second-order properties of the training loss have a massive impact on the optimization dynamics of deep learning models. Fort & Scherlis (2019) discovered that a large excess of positive curvature and local convexity of the loss Hessian is associated with highly trainable initial points located in a region coined the "Goldilocks zone". Only a handful of subsequent studies touched upon this relationship, so it remains largely unexplained. In this paper, we present a rigorous and comprehensive analysis of the Goldilocks zone for homogeneous neural networks. In particular, we derive the fundamental condition resulting in excess of positive curvature of the loss, explaining and refining its conventionally accepted connection to the initialization norm. Further, we relate the excess of positive curvature to model confidence, low initial loss, and a previously unknown type of vanishing cross-entropy loss gradient. To understand the importance of excessive positive curvature for trainability of deep networks, we optimize fully-connected and convolutional architectures outside the Goldilocks zone and analyze the emergent behaviors. We find that strong model performance is not perfectly aligned with the Goldilocks zone, calling for further research into this relationship.