The Transformer Family Version 2.0
Lilian Weng
A comprehensive technical post updated Transformer architecture documentation with improvements proposed over the past three years, expanding the original 2020 reference material to approximately twice its length. The updated version 2.0 includes restructured sections, mathematical notations for key components like attention matrices and weight parameters, and coverage of encoder-decoder variants including BERT and GPT models. The expanded resource now serves as a more complete reference for understanding modern Transformer architecture variations and their mathematical foundations.
Why it matters
Many new Transformer architecture improvements have been proposed since my last post on “The Transformer Family” about three years ago. Here I did a big refactoring and enrichment of that 2020 post — restructure the hierarchy of sections and improve many sections with more recent papers. Version 2.0 is a superset of the old version, about twice the length. Notations Symbol Meaning $d$ The model size / hidden state dimension / positional encoding size. $h$ The number of heads in multi-head attention layer. $L$ The segment length of input sequence. $N$ The total number of attention layers in the model; not considering MoE. $\mathbf{X} \in \mathbb{R}^{L \times d}$ The input sequence where each element has been mapped into an embedding vector of shape $d$, same as the model size. $\mathbf{W}^k \in \mathbb{R}^{d \times d_k}$ The key weight matrix. $\mathbf{W}^q \in \mathbb{R}^{d \times d_k}$ The query weight matrix. $\mathbf{W}^v \in \mathbb{R}^{d \times d_v}$ The value weight matrix. Often
