Weight Initialization and Variance Dynamics in Deep Neural Networks and Large Language Models

Weight initialization governs signal propagation and gradient flow at the start of training. This paper offers a theory-grounded and empirically validated study across two regimes: compact ReLU multilayer perceptrons and GPT-2-style transformers. First, a logarithmic sweep of the initial standard deviation maps vanishing and exploding regimes and identifies a broad stability band with standard deviations between 1e-2 and 1e-1. Second, a controlled comparison shows that Kaiming (fan-in) initialization converges faster and more stably than Xavier under ReLU, consistent with variance-preserving theory. Third, in a from-scratch 12-layer GPT-2-style model, this paper tracks layerwise Q/K/V weight variance through pretraining and observe depth-dependent equilibration into narrow bands: shallow layers expand rapidly while deeper layers change more gradually. Together, these results connect classic initialization principles with modern transformer behavior and yield simple, practical recipes for robust training.