  Gradient Descent (GD) has been proven effective in solving various matrix
factorization problems. However, its optimization behavior with large initial
values remains less understood. To address this gap, this paper presents a
novel theoretical framework for examining the convergence trajectory of GD with
a large initialization. The framework is grounded in signal-to-noise ratio
concepts and inductive arguments. The results uncover an implicit incremental
learning phenomenon in GD and offer a deeper understanding of its performance
in large initialization scenarios.
