Complete Technical Paper Content — Self Attention Transformers
1. Executive Abstract, Problem Formulation & Background
In deep learning, the transformer is a family of artificial neural network architectures based on the multi-head attention mechanism, in which input data such as text, images, or audio is converted to a sequence of numerical representations called tokens, and each token is converted into a vector through an embedding layer. At each layer, each token is then contextualized within the scope of the context window with other (unmasked) tokens via a parallel multi-head attention mechanism, allowing the signal for key tokens to be amplified and less important tokens to be diminished. Because self-attention alone is permutation-invariant, transformers inject positional information, typically through positional encodings or learned positional embeddings, so token order can affect the output. Because transformers do not process tokens one at a time, their computations can be parallelized across sequence positions during training more readily than those of recurrent neural networks like long short-term memory (LSTM). Later variations have been widely adopted for training large language models (LLMs) on large (language) datasets.
The original version of the transformer architecture was proposed in the 2017 paper "Attention Is All You Need" by researchers at Google. The predecessors of transformers were developed as an improvement over previous architectures for machine translation, but have found many applications since. They are used in large-scale natural language processing, computer vision (vision transformers), reinforcement learning, audio, multimodal learning, robotics, and playing chess. It has also led to the development of pre-trained systems, such as generative pre-trained transformers (GPTs).
The idea of encoder–decoder sequence transduction had been developed in the early 2010s; commonly cited as the originators that produced seq2seq are two concurrently published papers from 2014. A 380M-parameter model for machine translation uses two long short-term memories (LSTM). Its architecture consists of two parts. The encoder is an LSTM that takes in a sequence of tokens and turns it into a vector. The decoder is another LSTM that converts the vector into a sequence of tokens. Similarly, another 130M-parameter model used gated recurrent units (GRU) instead of LSTM. Later research showed that GRUs are neither better nor worse than LSTMs for seq2seq. These early seq2seq models had no attention mechanism, and the state vector is accessible only after the last word of the source text was processed. Although in theory such a vector retains the information about the whole original sentence, in practice the information is poorly preserved. This is because the input is processed sequentially by one recurrent network into a fixed-size output vector, which is then processed by another recurrent network into an output. If the input is long, then the output vector would not be able to contain all relevant information, degrading the output. As evidence, reversing the input sentence improved seq2seq translation. The RNN search model introduced an attention mechanism to seq2seq for machine translation to solve the bottleneck problem (of the fixed-size output vector), allowing the model to process long-distance dependencies more easily. The name is because it "emulates searching through a source sentence during decoding a translation". The relative performances were compared between global (that of RNN search) and local (sliding window) attention model architectures for machine translation, finding that mixed attention had higher quality than global attention, while local attention reduced translation time. In 2016, Google Translate was revamped to Google Neural Machine Translation, which replaced the previous model based on statistical machine translation. The new model was a seq2seq model where the encoder and the decoder were both 8 layers of bidirectional LSTM. It took nine months to develop, and it outperformed the statistical approach, which took ten years to develop.
Seq2seq models with attention (including self-attention) still suffered from the same issue with recurrent networks, which is that they are hard to parallelize, which prevented them from being accelerated on GPUs. In 2016, decomposable attention applied a self-attention mechanism to feedforward networks, which are easy to parallelize, and achieved state-of-the-art (SOTA) results in textual entailment with an order of magnitude fewer parameters than LSTMs. One of its authors, Jakob Uszkoreit, suspected that attention without recurrence would be sufficient for language translation, thus the title "attention is All you need". That hypothesis was against conventional wisdom at the time, and even his father Hans Uszkoreit, a well-known computational linguist, was skeptical. In the same year, self-attention (called intra-attention or intra-sentence attention) was proposed for LSTMs. On 2017-06-12, the original (100M-parameter) encoder–decoder transformer model was published in the "Attention is All you need" paper. At the time, the focus of the research was on improving seq2seq for machine translation, by removing its recurrence to process all tokens in parallel, but preserving its dot-product attention mechanism to keep its text processing performance. This led to the introduction of a multi-head attention model that was easier to parallelize due to the use of independent heads and the lack of recurrence. Its parallelizability was an important factor to its widespread use in large neural networks.
2. Related Work, Literature Survey & Algorithmic Foundations
In spring 2017, before the "Attention is All you need" preprint was published, one of the co-authors applied the "decoder-only" variation of the architecture to generate fictitious Wikipedia articles. Transformer architecture is now used alongside many generative models that contribute to the ongoing AI boom. The "reference implementation" of the original Transformer was written in a TensorFlow library. In language modelling, ELMo (2018) was a bi-directional LSTM that produces contextualized word embeddings, improving upon the line of research from bag of words and word2vec. It was followed by BERT (2018), an encoder-only transformer model. In October 2019, Google started using BERT to process search queries. In 2020, Google Translate replaced the previous RNN-encoder–RNN-decoder model by a transformer-encoder–RNN-decoder model. Starting in 2018, the OpenAI GPT series of decoder-only transformers became state of the art in natural language generation. At the end of 2022, ChatGPT, a chatbot based on a fine-tuned variant of GPT-3.5, became unexpectedly popular, triggering a boom around large language models. Transformers have been applied in modalities beyond text. Four days after the publication of "Attention is All You Need", a multimodal transformer architecture, MultiModel, was published by most authors of that paper. Other examples include the vision transformer, which has led to developments in convolutional neural networks. Image and video generators like DALL-E (2021), Stable Diffusion 3 (2024), and Sora (2024), use transformers to analyse input data (like text prompts) by breaking it down into "tokens" and then calculating the relevance between each token using self-attention, which helps the model simulate the context and relationships within the data.
reading comprehension sentiment analysis paraphrasing The T5 transformer report documents a large number of natural language pretraining tasks. Some examples are:
restoring or repairing incomplete or corrupted text. For example, the input, "Thank you ~~ me to your party ~~ week", might generate the output, "Thank you for inviting me to your party last week". translation between natural languages (machine translation) judging the pragmatic acceptability of natural language. For example, the following sentence might be judged "not acceptable", because even though it is syntactically well-formed, it is improbable in ordinary human usage: The course is jumping well. While each of these tasks is trivial or obvious for human native speakers of the language (or languages), they have typically proved challenging for previous generations of machine learning architecture.
Knowledge distillation is a method for training a smaller model, called a "student", to reproduce the output behavior of a larger "teacher" model. In transformer models, the student can be trained using the teacher's output probability distribution, intermediate representations, or attention patterns in addition to the original training labels. Distillation can lower computational and memory requirements of deployment while keeping most of the teacher model's performance on a specified task.
3. Dataset Ingestion, Preprocessing & Stochastic Augmentations
In general, there are three classes of language modelling tasks: "masked", "autoregressive", and "prefixLM". These classes are independent of a specific modeling architecture such as transformer, but they are often discussed in the context of transformer. In a masked task, one or more of the tokens is masked out, and the model would produce a probability distribution predicting what the masked-out tokens are based on the context. The loss function for the task is typically sum of log-perplexities for the masked-out tokens: Loss = − ∑ t ∈ masked tokens ln ( probability of t conditional on its context ) {\displaystyle {\text{Loss}}=-\sum _{t\in {\text{masked tokens}}}\ln({\text{probability of }}t{\text{ conditional on its context}})} and the model is trained to minimize this loss function. The BERT series of models are trained for masked token prediction and another task. ("Masked" as in "masked language modelling" is not "masked" as in "masked attention".) In an autoregressive task, the entire sequence is masked at first, and the model produces a probability distribution for the first token. Then the first token is revealed and the model predicts the second token, and so on. The loss function for the task is still typically the same. The GPT series of models are trained by autoregressive tasks. In a prefixLM task, the sequence is divided into two parts. The first part is presented as context, and the model predicts the first token of the second part. Then that would be revealed, and the model predicts the second token, and so on. The loss function for the task is still typically the same. The T5 series of models are trained by prefixLM tasks. ("PrefixLM" as in "prefix language modeling" is not "prefixLM" as in "prefix language model".)
Tokenizers, which convert text into tokens. Embedding layer, which converts tokens and positions of the tokens into vector representations. Transformer layers, which carry out repeated transformations on the vector representations, extracting more and more linguistic information. These consist of alternating attention and feedforward layers. There are two major types of transformer layers: encoder layers and decoder layers, with further variants. Un-embedding layer, which converts the final vector representations back to a probability distribution over the tokens. The following description follows exactly the transformer as described in the original paper. There are variants, described in the following section. By convention, we write all vectors as row vectors. For example, pushing a vector through a linear layer means multiplying it by a weight matrix on the right, as x W {\displaystyle xW} .
Each integer token identifier is converted into an embedding vector via a lookup table. Equivalently stated, it multiplies a one-hot representation of the token identifier by an embedding matrix M {\displaystyle M} . For example, if the input token's identifier is 3 {\displaystyle 3} , then the one-hot representation is [ 0 , 0 , 0 , 1 , 0 , 0 , … ] {\displaystyle [0,0,0,1,0,0,\dots ]} , and its embedding vector is E m b e d ( 3 ) = [ 0 , 0 , 0 , 1 , 0 , 0 , … ] M {\displaystyle \mathrm {Embed} (3)=[0,0,0,1,0,0,\dots ]M} The token embedding vectors are added to their respective positional encoding vectors (see below), producing the sequence of input vectors. The dimension of an embedding vector is called hidden size or embedding size and written as d emb {\displaystyle d_{\text{emb}}} . This size is written as d model {\displaystyle d_{\text{model}}} in the original transformer paper.
A positional encoding is a fixed-size vector representation of the relative positions of tokens within a sequence: it provides the transformer model with information about where the words are in the input sequence. This induces a bias towards the order of the input sequence, so that, for example, the input sequence "man bites dog" is processed differently from "dog bites man". The positional encoding is defined as a function of type f : R → R d {\displaystyle f:\mathbb {R} \to \mathbb {R} ^{d}} , where d {\displaystyle d} is a positive even integer. The full positional encoding defined in the original paper is: ( f ( t ) 2 k , f ( t ) 2 k + 1 ) = ( sin ( θ ) , cos ( θ ) ) ∀ k ∈ { 0 , 1 , … , d / 2 − 1 } {\displaystyle (f(t)_{2k},f(t)_{2k+1})=(\sin(\theta ),\cos(\theta ))\quad \forall k\in \{0,1,\ldots ,d/2-1\}} where θ = t r k , r = N 2 / d {\displaystyle \theta ={\frac {t}{r^{k}}},r=N^{2/d}} . Here, N {\displaystyle N} is a free parameter that should be significantly larger than the biggest k {\displaystyle k} that would be input into the positional encoding function. The original paper uses N = 10000 {\displaystyle N=10000} . The function is in a simpler form when written as a complex function of type f : R → C d / 2 {\displaystyle f:\mathbb {R} \to \mathbb {C} ^{d/2}}
4. Neural Network Backbone, Layer Specifications & Loss Formulations
f ( t ) = ( e i t / r k ) k = 0 , 1 , … , d 2 − 1 {\displaystyle f(t)=\left(e^{it/r^{k}}\right)_{k=0,1,\ldots ,{\frac {d}{2}}-1}} where r = N 2 / d {\displaystyle r=N^{2/d}} . The main reason for using this positional encoding function is that using it, shifts are linear transformations: f ( t + Δ t ) = d i a g ( f ( Δ t ) ) f ( t ) {\displaystyle f(t+\Delta t)=\mathrm {diag} (f(\Delta t))f(t)} where Δ t ∈ R {\displaystyle \Delta t\in \mathbb {R} } is the distance one wishes to shift. This allows the transformer to take any encoded position, and find the encoding of the position n-steps-ahead or n-steps-behind, by a matrix multiplication. By taking a linear sum, any convolution can also be implemented as linear transformations: ∑ j c j f ( t + Δ t j ) = ( ∑ j c j d i a g ( f ( Δ t j ) ) ) f ( t ) {\displaystyle \sum _{j}c_{j}f(t+\Delta t_{j})=\left(\sum _{j}c_{j}\,\mathrm {diag} (f(\Delta t_{j}))\right)f(t)} for any constants c j {\displaystyle c_{j}} . This allows the transformer to take any encoded position and find a linear sum of the encoded locations of its neighbors. This sum of encoded positions, when fed into the attention mechanism, would create attention weights on its neighbors, much like what happens in a convolutional neural network language model. In the author's words, "we hypothesized it would allow the model to easily learn to attend by relative position." In typical implementations, all operations are done over the real numbers, not the complex numbers, but since complex multiplication can be implemented as real 2-by-2 matrix multiplication, this is a mere notational difference.
Like earlier seq2seq models, the original transformer model used an encoder–decoder architecture. The encoder consists of encoding layers that process all the input tokens together one layer after another, while the decoder consists of decoding layers that iteratively process the encoder's output and the decoder's output tokens so far. The purpose of each encoder layer is to create contextualized representations of the tokens, where each representation corresponds to a token that "mixes" information from other input tokens via self-attention mechanism. Each decoder layer contains two attention sublayers: (1) cross-attention for incorporating the output of encoder (contextualized input token representations), and (2) self-attention for "mixing" information among the input tokens to the decoder (i.e. the tokens generated so far during inference time). Both the encoder and decoder layers have a feed-forward neural network for additional processing of their outputs and contain residual connections and layer normalization steps. These feed-forward layers contain most of the parameters in a transformer model.
The feedforward network (FFN) modules in a transformer are 2-layered multilayer perceptrons: F F N ( x ) = ϕ ( x W ( 1 ) + b ( 1 ) ) W ( 2 ) + b ( 2 ) {\displaystyle \mathrm {FFN} (x)=\phi (xW^{(1)}+b^{(1)})W^{(2)}+b^{(2)}} where W ( 1 ) {\displaystyle W^{(1)}} and W ( 2 ) {\displaystyle W^{(2)}} are weight matrices and b ( 1 ) {\displaystyle b^{(1)}} and b ( 2 ) {\displaystyle b^{(2)}} are bias vectors, and ϕ {\displaystyle \phi } is its activation function. The original transformer used ReLU activation. The number of neurons in the middle layer is called intermediate size (GPT), filter size (BERT), or feedforward size (BERT). It is typically larger than the embedding size. For example, in both GPT-2 series and BERT series, the intermediate size of a model is 4 times its embedding size: d ffn = 4 d emb {\displaystyle d_{\text{ffn}}=4d_{\text{emb}}} .
The attention mechanism used in the transformer architecture are scaled dot-product attention units. For each unit, the transformer model learns three weight matrices: the query weights W Q {\displaystyle W^{Q}} , the key weights W K {\displaystyle W^{K}} , and the value weights W V {\displaystyle W^{V}} . The module takes three sequences, a query sequence, a key sequence, and a value sequence. The query sequence is a sequence of length ℓ seq, query {\displaystyle \ell _{\text{seq, query}}} , and each entry is a vector of dimension d emb, query {\displaystyle d_{\text{emb, query}}} . Similarly for the key and value sequences. For each vector x i , query {\displaystyle x_{i,{\text{query}}}} in the query sequence, it is multiplied by a matrix W Q {\displaystyle W^{Q}} to produce a query vector q i = x i , query W Q {\displaystyle q_{i}=x_{i,{\text{query}}}W^{Q}} . The matrix of all query vectors is the query matrix: Q = X query W Q {\displaystyle Q=X_{\text{query}}W^{Q}} Similarly, we construct the key matrix K = X key W K {\displaystyle K=X_{\text{key}}W^{K}} and the value matrix V = X value W V {\displaystyle V=X_{\text{value}}W^{V}} . It is usually the case that all W Q , W K , W V {\displaystyle W^{Q},W^{K},W^{V}} are square matrices, meaning d emb, query = d query {\displaystyle d_{\text{emb, query}}=d_{\text{query}}} , etc. Attention weights are calculated using the query and key vectors: the attention weight a i j {\displaystyle a_{ij}} from token i {\displaystyle i} to token j {\displaystyle j} is the dot product between q i {\displaystyle q_{i}} and k j {\displaystyle k_{j}} . The attention weights are divided by the square root of the dimension of the key vectors, d k {\displaystyle {\sqrt {d_{k}}}} , which stabilizes gradients during training, and passed through a softmax which normalizes the weights. The fact that W Q {\displaystyle W^{Q}} and W K {\displaystyle W^{K}} are different matrices allows attention to be non-symmetric: if token i {\displaystyle i} attends to token j {\displaystyle j} (i.e. q i ⋅ k j {\displaystyle q_{i}\cdot k_{j}} is large), this does not necessarily mean that token j {\displaystyle j} will attend to token i {\displaystyle i} (i.e. q j ⋅ k i {\displaystyle q_{j}\cdot k_{i}} could be small). The output of the attention unit for token i {\displaystyle i} is the weighted sum of the value vectors of all tokens, weighted by a i j {\displaystyle a_{ij}} , the attention from token i {\displaystyle i} to each token. The attention calculation for all tokens can be expressed as one large matrix calculation using the softmax function, which is useful for training due to computational matrix operation optimizations that quickly compute matrix operations. The matrices Q {\displaystyle Q} , K {\displaystyle K} and V {\displaystyle V} are defined as the matrices where the i {\displaystyle i} th rows are vectors q i {\displaystyle q_{i}} , k i {\displaystyle k_{i}} , and v i {\displaystyle v_{i}} respectively. Then we can represent the attention as Attention ( Q , K , V ) = softmax ( Q K T d k ) V {\displaystyle {\begin{aligned}{\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\end{aligned}}}
5. Training Protocol, Convergence Behavior & Experimental Evaluation
where the softmax is applied over each of the rows of the matrix. The number of dimensions in a query vector is query size d query {\displaystyle d_{\text{query}}} and similarly for the key size d key {\displaystyle d_{\text{key}}} and value size d value {\displaystyle d_{\text{value}}} . The output dimension of an attention head is its head dimension d head {\displaystyle d_{\text{head}}} . The attention mechanism requires the following three equalities to hold: ℓ seq, key = ℓ seq, value , d query = d key , d value = d head {\displaystyle \ell _{\text{seq, key}}=\ell _{\text{seq, value}},\;d_{\text{query}}=d_{\text{key}},\;d_{\text{value}}=d_{\text{head}}} but is otherwise unconstrained. If the attention head is used in a self-attention fashion, then X query = X key = X value {\displaystyle X_{\text{query}}=X_{\text{key}}=X_{\text{value}}} . If the attention head is used in a cross-attention fashion, then usually X query ≠ X key = X value {\displaystyle X_{\text{query}}\neq X_{\text{key}}=X_{\text{value}}} . It is theoretically possible for all three to be different, but that is rarely the case in practice.
One set of ( W Q , W K , W V ) {\displaystyle \left(W^{Q},W^{K},W^{V}\right)} matrices is called an attention head, and each layer in a transformer model has multiple attention heads. While each attention head attends to the tokens that are relevant to each token, multiple attention heads allow the model to do this for different definitions of "relevance". Specifically, the query and key projection matrices, W Q {\displaystyle W^{Q}} and W K {\displaystyle W^{K}} , which are involved in the attention score computation, defines the "relevance". Meanwhile, the value projection matrix W V {\displaystyle W^{V}} , in combination with the part of the output projection matrix W O {\displaystyle W^{O}} , determines how the attended tokens influence what information is passed to subsequent layers and ultimately the output logits. In addition, the scope of attention, or the range of token relationships captured by each attention head, can expand as tokens pass through successive layers. This allows the model to capture more complex and long-range dependencies in deeper layers. Many transformer attention heads encode relevance relations that are meaningful to humans. For example, some attention heads can attend mostly to the next word, while others mainly attend from verbs to their direct objects. The computations for each attention head can be performed in parallel, which allows for fast processing. The outputs for the attention layer are concatenated to pass into the feedforward neural network layers. Concretely, let the multiple attention heads be indexed by i {\displaystyle i} , then we have MultiheadAttention ( Q , K , V ) = Concat i ∈ [ n heads ] ( Attention ( X W Q , i , X W K , i , X W V , i ) ) W O {\displaystyle \operatorname {MultiheadAttention} (Q,K,V)=\operatorname {Concat} _{i\in [n_{\text{heads}}]}(\operatorname {Attention} (XW^{Q,i},XW^{K,i},XW^{V,i}))W^{O}} where the matrix X {\displaystyle X} is the concatenation of word embeddings, and the matrices W Q , i , W K , i , W V , i {\displaystyle W^{Q,i},W^{K,i},W^{V,i}} are "projection matrices" owned by individual attention head i {\displaystyle i} , and W O {\displaystyle W^{O}} is a final projection matrix owned by the whole multihead attention module. It is theoretically possible for each attention head to have a different head dimension d head {\displaystyle d_{\text{head}}} , but that is rarely the case in practice. As an example, in the smallest GPT-2 model, there are only self-attention mechanisms. It has the following dimensions: d emb = 768 , n head = 12 , d head = 64 {\displaystyle d_{\text{emb}}=768,n_{\text{head}}=12,d_{\text{head}}=64} Since 12 × 64 = 768 {\displaystyle 12\times 64=768} , its output projection matrix W O ∈ R ( 12 × 64 ) × 768 {\displaystyle W^{O}\in \mathbb {R} ^{(12\times 64)\times 768}} is a square matrix.
In words, it means that each token can pay attention to itself, and every token before it, but not any after it. A non-masked attention module can be thought of as a masked attention module where the mask has all entries zero. As an example of an uncommon use of mask matrix, the XLNet considers all masks of the form P M causal P − 1 {\displaystyle PM_{\text{causal}}P^{-1}} , where P {\displaystyle P} is a random permutation matrix.
An encoder consists of an embedding layer, followed by multiple encoder layers. Each encoder layer consists of two major components: a self-attention mechanism and a feed-forward layer. It takes an input as a sequence of input vectors, applies the self-attention mechanism, to produce an intermediate sequence of vectors, then applies the feed-forward layer for each vector individually. Schematically, we have: given input vectors h 0 , h 1 , … combine them into a matrix H = [ h 0 h 1 ⋮ ] EncoderLayer ( H ) = [ FFN ( MultiheadAttention ( H , H , H ) 0 ) FFN ( MultiheadAttention ( H , H , H ) 1 ) ⋮ ] {\displaystyle {\begin{aligned}{\text{given input vectors }}&h_{0},h_{1},\dots \\{\text{combine them into a matrix }}H&={\begin{bmatrix}h_{0}\\h_{1}\\\vdots \end{bmatrix}}\\{\text{EncoderLayer}}(H)&={\begin{bmatrix}{\text{FFN}}({\text{MultiheadAttention}}(H,H,H)_{0})\\{\text{FFN}}({\text{MultiheadAttention}}(H,H,H)_{1})\\\vdots \end{bmatrix}}\\\end{aligned}}}
Model Figures & Evaluation Curves (4 Images)
Deep Learning Execution Pipeline
(Preprocessing)
(Feature Extraction)
(Self-Attention)
(Loss Optimization)