Architecture

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 we have $d_k = d_v = d$. $\mathbf{W}^k_i, \mathbf{W}^q_i \in \mathbb{R}^{d \times d_k/h}; \mathbf{W}^v_i \in \mathbb{R}^{d \times d_v/h}$ The weight matrices per head. $\mathbf{W}^o \in \mathbb{R}^{d_v \times d}$ The output weight matrix. $\mathbf{Q} = \mathbf{X}\mathbf{W}^q \in \mathbb{R}^{L \times d_k}$ The query embedding inputs. $\mathbf{K} = \mathbf{X}\mathbf{W}^k \in \mathbb{R}^{L \times d_k}$ The key embedding inputs. $\mathbf{V} = \mathbf{X}\mathbf{W}^v \in \mathbb{R}^{L \times d_v}$ The value embedding inputs. $\mathbf{q}_i, \mathbf{k}_i \in \mathbb{R}^{d_k}, \mathbf{v}_i \in \mathbb{R}^{d_v}$ Row vectors in query, key, value matrices, $\mathbf{Q}$, $\mathbf{K}$ and $\mathbf{V}$. $S_i$ A collection of key positions for the $i$-th query $\mathbf{q}_i$ to attend to. $\mathbf{A} \in \mathbb{R}^{L \times L}$ The self-attention matrix between a input sequence of lenght $L$ and itself. $\mathbf{A} = \text{softmax}(\mathbf{Q}\mathbf{K}^\top / \sqrt{d_k})$. $a_{ij} \in \mathbf{A}$ The scalar attention score between query $\mathbf{q}_i$ and key $\mathbf{k}_j$. $\mathbf{P} \in \mathbb{R}^{L \times d}$ position encoding matrix, where the $i$-th row $\mathbf{p}_i$ is the positional encoding for input $\mathbf{x}_i$. Transformer Basics The Transformer (which will be referred to as “vanilla Transformer” to distinguish it from other enhanced versions; Vaswani, et al., 2017) model has an encoder-decoder architecture, as commonly used in many NMT models. Later simplified Transformer was shown to achieve great performance in language modeling tasks, like in encoder-only BERT or decoder-only GPT. ...

[Updated on 2023-01-24: add a small section on Distillation.] Large transformer models are mainstream nowadays, creating SoTA results for a variety of tasks. They are powerful but very expensive to train and use. The extremely high inference cost, in both time and memory, is a big bottleneck for adopting a powerful transformer for solving real-world tasks at scale. Why is it hard to run inference for large transformer models? Besides the increasing size of SoTA models, there are two main factors contributing to the inference challenge (Pope et al. 2022): ...

[Updated on 2022-03-13: add expert choice routing.] [Updated on 2022-06-10]: Greg and I wrote a shorted and upgraded version of this post, published on OpenAI Blog: “Techniques for Training Large Neural Networks” ...

Although most popular and successful model architectures are designed by human experts, it doesn’t mean we have explored the entire network architecture space and settled down with the best option. We would have a better chance to find the optimal solution if we adopt a systematic and automatic way of learning high-performance model architectures. ...

[Updated on 2023-01-27: After almost three years, I did a big refactoring update of this post to incorporate a bunch of new Transformer models since 2020. The enhanced version of this post is here: The Transformer Family Version 2.0. Please refer to that post on this topic.] ...

[Updated on 2019-02-14: add ULMFiT and GPT-2.] [Updated on 2020-02-29: add ALBERT.] [Updated on 2020-10-25: add RoBERTa.] [Updated on 2020-12-13: add T5.] [Updated on 2020-12-30: add GPT-3.] [Updated on 2021-11-13: add XLNet, BART and ELECTRA; Also updated the Summary section.] Fig. 0. I guess they are Elmo & Bert? (Image source: here) We have seen amazing progress in NLP in 2018. Large-scale pre-trained language modes like OpenAI GPT and BERT have achieved great performance on a variety of language tasks using generic model architectures. The idea is similar to how ImageNet classification pre-training helps many vision tasks (*). Even better than vision classification pre-training, this simple and powerful approach in NLP does not require labeled data for pre-training, allowing us to experiment with increased training scale, up to our very limit. ...

So far, I’ve written about two types of generative models, GAN and VAE. Neither of them explicitly learns the probability density function of real data, $p(\mathbf{x})$ (where $\mathbf{x} \in \mathcal{D}$) — because it is really hard! Taking the generative model with latent variables as an example, $p(\mathbf{x}) = \int p(\mathbf{x}\vert\mathbf{z})p(\mathbf{z})d\mathbf{z}$ can hardly be calculated as it is intractable to go through all possible values of the latent code $\mathbf{z}$. ...

[Updated on 2018-10-28: Add Pointer Network and the link to my implementation of Transformer.] [Updated on 2018-11-06: Add a link to the implementation of Transformer model.] [Updated on 2018-11-18: Add Neural Turing Machines.] [Updated on 2019-07-18: Correct the mistake on using the term “self-attention” when introducing the show-attention-tell paper; moved it to Self-Attention section.] [Updated on 2020-04-07: A follow-up post on improved Transformer models is here.] ...