SwiGLU

RMSNorm and SwiGLU: Mathematical Foundations of Scaling-Invariant Normalization, Gated Activations, and FFN Architectures in Modern LLMs

The architectural baseline of modern autoregressive large language models has converged on a distinct set of mathematical primitives. While early Transformer architectures relied on standard Layer Normalization, Post-LN residual routing, and two-layer Multi-Layer Perceptrons with ReLU or GELU activations, state-of-the-art open-weights models such as LLaMA, Mistral, Gemma, Qwen, and DeepSeek utilize a different combination: Root Mean Square Layer Normalization (RMSNorm), Pre-LN residual connectio