Transformer (deep learning)

Predecessors For many years, sequence modelling and generation was done by using plain recurrent neural networks (RNNs). A well-cited early example was the Elman network (1990). In theory, the information from one token can propagate arbitrarily far down the sequence, but in practice the vanishing-gradient problem leaves the model's state at the end of a long sentence without precise, extractable information about preceding tokens. A key breakthrough was LSTM (1995), an RNN which used various innovations to overcome the vanishing gradient problem, allowing efficient learning of long-sequence modelling. One key innovation was the use of an attention mechanism which used neurons that multiply the outputs of other neurons, so-called multiplicative units. Neural networks using multiplicative units were later called sigma-pi networks or higher-order networks. LSTM became the standard architecture for long sequence modelling until the 2017 publication of transformers. However, LSTM still used sequential processing, like most other RNNs. Specifically, RNNs operate one token at a time from first to last; they cannot operate in parallel over all tokens in a sequence. Modern transformers overcome this problem, but unlike RNNs, they require computation time that is quadratic in the size of the context window. The linearly scaling fast weight controller (1992) learns to compute a weight matrix for further processing depending on the input. One of its two networks has "fast weights" or "dynamic links" (1981). A slow neural network learns by gradient descent to generate keys and values for computing the weight changes of the fast neural network which computes answers to queries. Attention with seq2seq 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). 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". 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. Parallelizing attention 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 SOTA result 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. 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. AI boom era As early as spring 2017, even 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. In the end of 2022, a chatbot based on GPT-3, ChatGPT, 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, speech recognition, and multimodal. The vision transformer, in turn, stimulated new 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 understand the context and relationships within the data. == Training ==

Methods for stabilizing training The plain transformer architecture had difficulty in converging. In the original paper, This is the "pre-LN Transformer" and is more commonly used, compared to the original "post-LN Transformer". Pretrain-finetune Transformers typically are first pretrained by self-supervised learning on a large generic dataset, followed by supervised fine-tuning on a small task-specific dataset. The pretrain dataset is typically an unlabeled large corpus, such as The Pile. Tasks for pretraining and fine-tuning commonly include: • language modeling documents a large number of natural language pretraining tasks. Some examples are: • restoring or repairing incomplete or corrupted text. For example, the input, "Thank youme to your partyweek", 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. Note that 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. Tasks In general, there are 3 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: \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. 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. Note that "masked" as in "masked language modelling" is not "masked" as in "masked attention", and "prefixLM" as in "prefix language modeling" is not "prefixLM" as in " prefix language model". == Architecture ==

All transformers have the same primary components: • 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 xW. Tokenization As the transformer architecture natively consists of operations over numbers (matrix multiplications, dot products, activation functions) rather than over text, there must first be a mapping from any input text to some numerical representation. This happens in three steps. First, the input text is treated by a preprocessor, which performs both textual transformations and splits the text into coarse-grained segments called pretokens. The latter is referred to as pretokenization. Second, each pretoken is segmented further into tokens by a tokenizer that expects to only see pretokens output by its preprocessor. Each token it produces is a string of one or more characters belonging to a finite set of strings called the vocabulary V. Third, because the vocabulary is finite and known beforehand, each token can be assigned an integer identifier, and this mapping is applied to the sequence of tokens to represent any input text as a numerical sequence. Since this mapping is bijective, the output side can produce a sequence of integer identifiers which can then be turned back into tokens. After undoing some of the preprocessing, the result is again legible text. Training a tokenizer (sometimes referred to as vocabularization) means finding a suitable vocabulary V, but also learning how to use it, since any given string s of length |s| has 2^{|s|-1} hypothetical segmentations, some of which containing segments that are not in the vocabulary. The most important hyperparameter during vocabularization is the vocabulary size |V|: when it is small, the learned vocabulary generally consists of characters and smaller strings, and words will be segmented into many tokens. At larger sizes, it becomes affordable to dedicate tokens to full words, although depending on the preprocessor and tokenizer, it is not necessarily the case that large vocabularies will always use the largest token(s) available to segment a word. Because tokens are not always full words, they may also be referred to as subwords and tokenization algorithms may be referred to as subword tokenizers. This is also to differentiate these systems from traditional terminology used in older information retrieval and natural language processing systems, where "tokenization" was used to denote what is today called "pretokenization" (very crudely: splitting into words). In tokenizers that produce tokens that are not part of the vocabulary, a special token that does belong to the vocabulary is used as a generic stand-in, written as "[UNK]" for "unknown". In principle, any string could be hidden by such an [UNK]. Indeed, in information retrieval, pretokenizers were themselves used as tokenizers (and also called "tokenizers") with a word-level vocabulary that contained an [UNK]. Commonly used subword tokenization algorithms are byte pair encoding (BPE) and the unigram language model (ULM), which each include a vocabularization algorithm and a dedicated segmentation algorithm. There also exist several segmentation algorithms that require no learning and can be applied given a vocabulary (produced by BPE or ULM, for example), like greedily recognising tokens in a pretoken by moving through it left-to-right. Well-known software implementations of subword tokenizers are Hugging Face's tokenizers Python package implemented in Rust, and the sentencepiece Python package implemented in C++. The latter package is named as such because one of its configuration options allows disabling the built-in pretokenizer, hence effectively making entire sentences a pretoken and thus having the tokenizer see entire sentences, rather than individual words. Embedding 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. For example, if the input token's identifier is 3, then the one-hot representation is [0, 0, 0, 1, 0, 0, \dots], and its embedding vector is\mathrm{Embed}(3) = [0, 0, 0, 1, 0, 0, \dots]MThe 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_{\text{emb}}. Positional encoding 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 \to \R^d, where d is a positive even integer. The full positional encoding defined in the original paper 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. filter size (BERT), 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, then we have\text{MultiheadAttention}(Q, K, V) = \text{Concat}_{i \in [n_{\text{heads}}]}(\text{Attention}(XW^Q_i, XW^K_i, XW^V_i)) W^O where the matrix X is the concatenation of word embeddings, and the matrices W^Q_i, W^K_i, W^V_i are "projection matrices" owned by individual attention head i, and W^O is a final projection matrix owned by the whole multihead attention head. It is theoretically possible for each attention head to have a different head dimension 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_{\text{emb}} = 768, n_{\text{head}} = 12, d_{\text{head}} = 64Since 12 \times 64 = 768, its output projection matrix W^O \in \R^{(12 \times 64) \times 768} is a square matrix. Masked attention The transformer architecture is constructed to calculate output tokens iteratively. Assuming t = 0 refers to the calculation of the first output token i = 0, for step t > 0, the output token i = 0 shall remain constant. This ensures properties of the model similar to autoregressive models. Encoder 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:\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} where \text{FFN} stands for "feed-forward network". We can more succinctly write it as\text{EncoderLayer}(H) = \text{FFN}(\text{MultiheadAttention}(H, H, H)) with the implicit convention that the \text{FFN} is applied to each row of the matrix individually. The encoder layers are stacked. The first encoder layer takes the sequence of input vectors from the embedding layer, producing a sequence of vectors. This sequence of vectors is processed by the second encoder, and so on. The output from the final encoder layer is then used by the decoder. As the encoder processes the entire input all at once, every token can attend to every other token (all-to-all attention), so there is no need for causal masking. Decoder A decoder consists of an embedding layer, followed by multiple decoder layers, followed by an un-embedding layer. Each decoder consists of three major components: a causally masked self-attention mechanism, a cross-attention mechanism, and a feed-forward neural network. The decoder functions in a similar fashion to the encoder, but an additional attention mechanism is inserted which instead draws relevant information from the encodings generated by the encoders. This mechanism can also be called the encoder–decoder attention. Like the first encoder, the first decoder takes positional information and embeddings of the output sequence as its input, rather than encodings. The transformer must not use the current or future output to predict an output, so the output sequence must be partially masked to prevent this reverse information flow. This allows for autoregressive text generation. For decoding, all-to-all attention is inappropriate, because a token cannot attend to tokens not yet generated. Thus, the self-attention module in the decoder is causally masked. In contrast, the cross-attention mechanism attends to the output vectors of the encoder, which is computed before the decoder starts decoding. Consequently, there is no need for masking in the cross-attention mechanism. Schematically, we have:\begin{aligned} H' &= \text{MaskedMultiheadAttention}(H, H, H) \\ \text{DecoderLayer}(H) &=\text{FFN}(\text{MultiheadAttention}(H', H^E, H^E)) \end{aligned} where H^E is the matrix with rows being the output vectors from the encoder. The last decoder is followed by a final un-embedding layer to produce the output probabilities over the vocabulary. Then, one of the tokens is sampled according to the probability, and the decoder can be run again to produce the next token, etc., autoregressively generating output text. == Full transformer architecture ==

Sublayers Each encoder layer contains 2 sublayers: the self-attention and the feedforward network. Each decoder layer contains 3 sublayers: the causally masked self-attention, the cross-attention, and the feedforward network. for the full transformer architecture, in object-oriented programming styleThe final points of detail are the residual connections and layer normalization, (denoted as "LayerNorm", or "LN" in the following), which while conceptually unnecessary, are necessary for numerical stability and convergence. The residual connection, which is introduced to avoid vanishing gradient issues and stabilize the training process, can be expressed as follows: y = F(x) + x. The expression indicates that an output y is the sum of the transformation of input x (F(x)) and the input itself (x). Adding the input x can preserve the input information and avoid issues when the gradient of F(x) is close to zero. Similarly to how the feedforward network modules are applied individually to each vector, the LayerNorm is also applied individually to each vector. There are two common conventions in use: the post-LN and the pre-LN convention. In the post-LN convention, the output of each sublayer is \mathrm{LayerNorm}(x + \mathrm{Sublayer}(x))where \mathrm{Sublayer}(x) is the function implemented by the sublayer itself. In the pre-LN convention, the output of each sublayer isx + \mathrm{Sublayer}(\mathrm{LayerNorm}(x))The original 2017 transformer used the post-LN convention. It was difficult to train and required careful hyperparameter tuning and a "warm-up" in learning rate, where it starts small and gradually increases. The pre-LN convention, proposed several times in 2018, was found to be easier to train, requiring no warm-up, leading to faster convergence. input: Encoder input t_e Decoder input t_d output: Array of probability distributions, with shape (decoder vocabulary size x length(decoder output sequence)) /* encoder */ z_e ← encoder.tokenizer(t_e) for each t in 1:length(z_e) do z_e[t] ← encoder.embedding(z_e[t]) + encoder.positional_embedding(t) for each l in 1:length(encoder.layers) do layer ← encoder.layers[l] /* first sublayer */ z_e_copy ← copy(z_e) for each t in 1:length(z_e) do z_e[t] ← layer.layer_norm(z_e[t]) z_e ← layer.multihead_attention(z_e, z_e, z_e) for each t in 1:length(z_e) do z_e[t] ← z_e[t] + z_e_copy[t] /* second sublayer */ z_e_copy ← copy(z_e) for each t in 1:length(z_e) do z_e[t] ← layer.layer_norm(z_e[t]) z_e ← layer.feedforward(z_e) for each t in 1:length(z_e) do z_e[t] ← z_e[t] + z_e_copy[t] for each t in 1:length(z_e) do z_e[t] ← encoder.final_layer_norm(z_e[t]) /* decoder */ z_d ← decoder.tokenizer(t_d) for each t in 1:length(z_d) do z_d[t] ← decoder.embedding(z_d[t]) + decoder.positional_embedding(t) for each l in 1:length(decoder.layers) do layer ← decoder.layers[l] /* first sublayer */ z_d_copy ← copy(z_d) for each t in 1:length(z_d) do z_d[t] ← layer.layer_norm(z_d[t]) z_d ← layer.masked_multihead_attention(z_d, z_d, z_d) for each t in 1:length(z_d) do z_d[t] ← z_d[t] + z_d_copy[t] /* second sublayer */ z_d_copy ← copy(z_d) for each t in 1:length(z_d) do z_d[t] ← layer.layer_norm(z_d[t]) z_d ← layer.multihead_attention(z_d, z_e, z_e) for each i in 1:length(z_d) do z_d[t] ← z_d[t] + z_d_copy[t] /* third sublayer */ z_d_copy ← copy(z_d) for each t in 1:length(z_d) do z_d[t] ← layer.layer_norm(z_d[t]) z_d ← layer.feedforward(z_d) for each t in 1:length(z_d) do z_d[t] ← z_d[t] + z_d_copy[t] z_d ← decoder.final_layer_norm(z_d) output_distributions ← [] for each t in 1:length(z_d) do output_distributions.append(decoder.unembed(z_d[t])) return output_distributions Terminology The transformer architecture, being modular, allows variations. Several common variations are described here. There are also mixed seq2seq models. For example, in 2020, Google Translate replaced the previous RNN-encoder–RNN-decoder model with a transformer-encoder–RNN-decoder model, as transformer-based decoders did not appear to significantly increase quality unlike the encoder, while the RNN decoder was much faster. == Subsequent work ==

Alternative activation functions The original transformer uses ReLU activation function. Other activation functions were developed. The Llama series and PaLM used SwiGLU; both GPT-1 and BERT Alternative activation functions are often used in combination with Gated Linear Units in the feedforward module. which is used in the Llama series. Other examples include CapsuleNorm ScaleNorm, or FixNorm. The original transformer paper reported using a learned positional encoding, but finding it not superior to the sinusoidal one. found that causal masking itself provides enough signal to a transformer decoder that it can learn to implicitly perform absolute positional encoding without the positional encoding module. RoPE RoPE (rotary positional embedding), is best explained by considering a list of 2-dimensional vectors [(x^{(1)}_1, x^{(2)}_1), (x^{(1)}_2, x^{(2)}_2), (x^{(1)}_3, x^{(2)}_3), ...]. Now pick some angle \theta. Then RoPE encoding is\text{RoPE}\big(x^{(1)}_m, x^{(2)}_m, m\big) = \begin{pmatrix} \cos m \theta & - \sin m \theta \\ \sin m \theta & \cos m \theta \end{pmatrix} \begin{pmatrix} x^{(1)}_m \\ x^{(2)}_m \\ \end{pmatrix} = \begin{pmatrix} x^{(1)}_m \cos m\theta - x^{(2)}_m \sin m \theta \\ x^{(2)}_m \cos m\theta + x^{(1)}_m \sin m \theta \\ \end{pmatrix} Equivalently, if we write the 2-dimensional vectors as complex numbers z_m := x^{(1)}_m + i x^{(2)}_m, then RoPE encoding is just multiplication by an angle:\text{RoPE}\big(z_m, m\big) = e^{i m\theta} z_m For a list of 2n-dimensional vectors, a RoPE encoder is defined by a sequence of angles \theta^{(1)}, ..., \theta^{(n)}. Then the RoPE encoding is applied to each pair of coordinates. The benefit of RoPE is that the dot-product between two vectors depends on their relative location only: \text{RoPE}\big(x, m\big)^T\text{RoPE}\big(y, n\big) = \text{RoPE}\big(x, m+k\big)^T\text{RoPE}\big(y, n+k\big) for any integer k. ALiBi ALiBi (Attention with Linear Biases) is not a replacement for the positional encoder on the original transformer. Instead, it is an additional positional encoder that is directly plugged into the attention mechanism. Specifically, the ALiBi attention mechanism is\begin{align} \text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^\mathrm{T}}{\sqrt{d_k}} + s B\right)V \end{align}Here, s is a real number ("scalar"), and B is the linear bias matrix defined byB = \begin{pmatrix} 0 & 1 & 2 & 3 & \cdots \\ -1 & 0 & 1 & 2 & \cdots \\ -2 & -1 & 0 & 1 & \cdots \\ -3 & -2 & -1 & 0 & \cdots \\ \vdots & \vdots & \vdots & \vdots & \ddots \\ \end{pmatrix} in other words, B_{i, j} = j - i. The idea being that the linear bias matrix is a softened mask. Just as 0 represent full attention paid, and -\infty represents no attention paid, the linear bias matrix increases attention paid in one direction and decreases attention paid in the other direction. ALiBi allows pretraining on short context windows, then fine-tuning on longer context windows. Since it is directly plugged into the attention mechanism, it can be combined with any positional encoder that is plugged into the "bottom" of the entire network (which is where the sinusoidal encoder on the original transformer, as well as RoPE and many others, are located). Relative Position Encodings Relative Position Encodings is similar to ALiBi, but more generic:\begin{align} \text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^\mathrm{T}}{\sqrt{d_k}} + B\right)V \end{align}where B is a Toeplitz matrix, that is, B_{i, j} = B_{i', j'} whenever i-j = i'-j'. This is contrasted with the original sinusoidal positional encoding, which is an "absolute positional encoding". Efficient implementation The transformer model has been implemented in standard deep learning frameworks such as TensorFlow and PyTorch. Transformers is a library produced by Hugging Face that supplies transformer-based architectures and pretrained models. If a transformer is used with a baked-in prompt, such as ["You are a customer support agent..."], then the key and value vectors can be computed for the prompt, and saved on disk. The saving in compute is significant when the model is used for many short real-time interactions, such as in online chatbots. In general, when a user uses an autoregressive transformer to generate a continuation to a sequence of tokens, the model would first perform a forward-pass on this sequence, whereby the KV caches over this sequence are computed. This is called prefilling. Hyperscalers serving large Transformer models may use disaggregated inference, wherein prefilling and decoding are performed on separately specialized hardware. FlashAttention FlashAttention is an algorithm that implements the transformer attention mechanism efficiently on a GPU. It is a communication-avoiding algorithm that performs matrix multiplications in blocks, such that each block fits within the cache of a GPU, and by careful management of the blocks it minimizes data copying between GPU caches (as data movement is slow). See the page on softmax for details. An improved version, FlashAttention-2, was developed to cater to the rising demand for language models capable of handling longer context lengths. It offers enhancements in work partitioning and parallelism, enabling it to achieve up to 230 TFLOPs/s on A100 GPUs (FP16/BF16), a 2x speed increase over the original FlashAttention. Key advancements in FlashAttention-2 include the reduction of non-matmul FLOPs, improved parallelism over the sequence length dimension, better work partitioning between GPU warps, and added support for head dimensions up to 256 and multi-query attention (MQA) and grouped-query attention (GQA). Benchmarks revealed FlashAttention-2 to be up to 2x faster than FlashAttention and up to 9x faster than a standard attention implementation in PyTorch. Future developments include optimization for new hardware like H100 GPUs and new data types like FP8. FlashAttention-4 focuses on pipelining to increase instruction throughput, and was developed to perform particularly well on Blackwell GPUs. Multi-Query Attention Multi-Query Attention changes the Multihead Attention mechanism. Whereas normally, \text{MultiheadAttention}(Q, K, V) = \text{Concat}_{i \in [n_{\text{heads}}]}\left(\text{Attention}(XW^Q_i, XW^K_i, XW^V_i)\right) W^Owith Multi-Query Attention, there is just one W^K, W^V, thus: \text{MultiQueryAttention}(Q, K, V) = \text{Concat}_{i \in [n_{\text{heads}}]}\left(\text{Attention}(XW^Q_i, XW^K, XW^V)\right) W^O This has a neutral effect on model quality and training speed, but increases inference speed. More generally, grouped-query attention (GQA) partitions attention heads into groups, each of which shares the key-value pair. MQA is GQA with one group, while standard Multihead Attention is GQA with the maximal number of groups. Multihead Latent Attention (MLA) is a low-rank approximation to standard MHA. Specifically, each hidden vector, before entering the attention mechanism, is first projected to two low-dimensional spaces ("latent space"), one for query and one for key-value (KV vector). This design minimizes the KV cache, as only the low-dimensional KV vector needs to be cached. is a method to accelerate token decoding. Similarly to speculative execution in CPUs, future tokens are computed quickly, then verified. If the quickly computed tokens are incorrect, they are discarded and computed slowly. The key factor in speculative decoding is that a transformer decoder can verify faster than it can decode, in the following sense. Suppose we have two transformer models like GPT-3 and GPT-3-small, both with a context window size of 512. To generate an entire context window autoregressively with greedy decoding with GPT-3, it must be run for 512 times, each time generating a token x_1, x_2, ..., x_{512}, taking time 512 T_{\text{GPT-3}}. However, if we had some educated guess for the values of these tokens, we could verify all of them in parallel, in one run of the model, by checking that each x_t is indeed the token with the largest log-likelihood in the t-th output. In speculative decoding, a smaller model or some other simple heuristic is used to generate a few speculative tokens that are subsequently verified by the larger model. For example, suppose we use GPT-3-small to generate four speculative tokens: \tilde{x}_1, \tilde{x}_2, \tilde{x}_3, \tilde{x}_4. This only takes 4 T_{\text{GPT-3-small}}. These tokens are then run through the larger GPT-3 in one go. Suppose that \tilde{x}_1 and \tilde{x}_2 are verified by GPT-3 as what it would have picked, then those are kept, but \tilde{x}_3 is not, so \tilde{x}_3, \tilde{x}_4 are discarded, and GPT-3 is run on those. This would take 4 T_{\text{GPT-3-small}} + 3 T_{\text{GPT-3}}, which might be shorter than 4 T_{\text{GPT-3}}. For non-greedy decoding, similar ideas apply, except the speculative tokens are accepted or rejected stochastically, in a way that guarantees the final output distribution is the same as if speculative decoding was not used. In Multi-Token Prediction, a single forward pass creates a final embedding vector, which then is un-embedded into a token probability. However, that vector can then be further processed by another transformer block to predict the next token, and so on for arbitrarily many steps into the future. This trades off accuracy for speed, since each new token costs just one more transformer block, rather than the entire stack. Sub-quadratic transformers Training transformer-based architectures can be expensive, especially for long inputs. Many methods have been developed to attempt to address the issue. In the image domain, Swin transformer is an efficient architecture that performs attention inside shifting windows. In the audio domain, SepTr decouples the attention in time and frequency domains. Long Range Arena (2020) is a standard benchmark for comparing the behavior of transformer architectures over long inputs. Alternative attention graphs The standard attention graph is either all-to-all or causal, both of which scales as O(N^2) where N is the number of tokens in a sequence. Reformer (2020) reduces the computational load from O(N^2) to O(N\ln N) by using locality-sensitive hashing and reversible layers. Sparse attention uses attention graphs that grows slower than O(N^2). For example, BigBird (2020) uses random small-world networks which grows as O(N). Ordinary transformers require a memory size that is quadratic in the size of the context window. Attention-free transformers reduce this to a linear dependence while still retaining the advantages of a transformer by linking the key to the value. Random Feature Attention Random Feature Attention (2021) uses Fourier random features:\varphi(x) = \frac{1}{\sqrt D}[\cos\langle w_1, x\rangle, \sin\langle w_1, x\rangle, \cdots \cos\langle w_D, x\rangle, \sin\langle w_D, x\rangle]^Twhere w_1, ..., w_D are independent samples from the normal distribution N(0, \sigma^2 I). This choice of parameters satisfy \mathbb E[\langle \varphi(x), \varphi(y)\rangle] = e^{-\frac{\|x-y\|^2}{2\sigma^2}}, or e^{\langle x, y\rangle/\sigma^2} = \mathbb E[\langle e^{\|x\|^2/2\sigma^2} \varphi(x), e^{\|y\|^2/2\sigma^2}\varphi(y)\rangle] \approx \langle e^{\|x\|^2/2\sigma^2} \varphi(x), e^{\|y\|^2/2\sigma^2}\varphi(y)\rangle Consequently, the one-headed attention, with one query, can be written as \text{Attention}(q, K, V) = \text{softmax}\left(\frac{qK^\mathrm{T}}{\sqrt{d_k}}\right)V \approx \frac{\varphi(q)^T \sum_i e^{\|k_i\|^2/2\sigma^2}\varphi(k_i) v_i^T}{\varphi(q)^T \sum_i e^{\|k_i\|^2/2\sigma^2}\varphi(k_i)}where \sigma = d_K^{1/4}. Similarly for multiple queries, and for multihead attention. This approximation can be computed in linear time, as we can compute the matrix \varphi(k_i) v_i^T first, then multiply it with the query. In essence, we have managed to obtain a more precise version of \text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^\mathrm{T}}{\sqrt{d_k}}\right)V \approx Q(K^TV/\sqrt{d_k}) Performer (2022) uses the same Random Feature Attention, but w_1, ..., w_D are first independently sampled from the normal distribution N(0, \sigma^2 I), then they are Gram–Schmidt processed. Multimodality Transformers can also be used/adapted for modalities (input or output) beyond just text, usually by finding a way to "tokenize" the modality. Multimodal models can either be trained from scratch, or by finetuning. A 2022 study found that transformers pretrained only on natural language can be finetuned on only 0.03% of parameters and become competitive with LSTMs on a variety of logical and visual tasks, demonstrating transfer learning. The LLaVA was a vision-language model composed of a language model (Vicuna-13B) and a vision model (ViT-L/14), connected by a linear layer. Only the linear layer is finetuned. Vision transformers and later Whisper follow the same pattern for speech recognition, first turning the speech signal into a spectrogram, which is then treated like an image, i.e. broken down into a series of patches, turned into vectors and treated like embedding vector of tokens in a standard transformer. Perceivers are a variant of transformers designed for multimodality. For image generation, notable architectures are DALL-E 1 (2021), Parti (2022), Phenaki (2023), and Muse (2023). Unlike later models, DALL-E is not a diffusion model. Instead, it uses a decoder-only transformer that autoregressively generates a text, followed by the token representation of an image, which is then converted by a variational autoencoder to an image. Parti is an encoder–decoder transformer, where the encoder processes a text prompt, and the decoder generates a token representation of an image. Muse is an encoder-only transformer that is trained to predict masked image tokens from unmasked image tokens. During generation, all input tokens are masked, and the highest-confidence predictions are included for the next iteration, until all tokens are predicted. Phenaki is a text-to-video model. It is a bidirectional masked transformer conditioned on pre-computed text tokens. The generated tokens are then decoded to a video. == Applications ==

The transformer has had great success in natural language processing (NLP). Many large language models such as GPT-2, GPT-3, GPT-4, Gemini, AlbertAGPT, Claude, BERT, Grok, XLNet, RoBERTa and ChatGPT demonstrate the ability of transformers to perform a wide variety of NLP-related subtasks and their related real-world applications, including: • machine translation • time series prediction • document summarization • document generation • named entity recognition (NER) • writing computer code based on requirements expressed in natural language. • speech-to-text Beyond traditional NLP, the transformer architecture has had success in other applications, such as: • biological sequence analysis • video understanding • protein folding (such as AlphaFold) • evaluating chess board positions. Using static evaluation alone (that is, with no Minimax search) transformer achieved an Elo of 2895, putting it at grandmaster level. == See also ==