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transformer architecture multimodel was published by most authors of that paper 45 other examples include the vision transformer 46 speech recognition 47 robotics 7 and multimodal 48 the vision transformer in turn stimulated new developments in convolutional neural networks 49 image and video generators like dall e 2021 stable diffusion 3 2024 50 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 edit methods for stabilizing training edit the plain transformer architecture had difficulty in converging in the original paper 1 the authors recommended using learning rate warmup that is the learning rate should linearly scale up from 0 to maximal value for the first part of the training usually recommended to be 2 of the total number of training steps before decaying again a 2020 paper found that using layer normalization before instead of after multihead attention and feedforward layers stabilizes training not requiring learning rate warmup 51 this is the pre ln transformer and is more commonly used compared to the original post ln transformer pretrain finetune edit 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 13 next sentence prediction 13 question answering 3 reading comprehension sentiment analysis 1 paraphrasing 1 the t5 transformer report 52 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 53 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 tasks edit see also large language model evaluation in general there are three classes of language modelling tasks masked 54 autoregressive 55 and prefixlm 56 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 54 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 55 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 56 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 architecture edit 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 x w displaystyle xw tokenization edit 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 displaystyle 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 displaystyle v but also learning how to use it since any given string s displaystyle s of length s displaystyle s has 2 s 1 displaystyle 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 displaystyle 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 edit further information word 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 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 38 this size is written as d model displaystyle d_ text model in the original transformer paper 1 un embedding edit an un embedding layer is almost the reverse of an embedding layer whereas an embedding layer converts a token identifier into a vector an un embedding layer converts a vector into a probability distribution over tokens an illustration of the top 16 token probabilities at temperature 1 for each output token in the chain of thought response with colour representing how that output differs from the same prompt but at temperature 0 the un embedding layer is a linear softmax layer u n e m b e d x s o f t m a x x w b displaystyle mathrm unembed x mathrm softmax xw b the matrix has shape d emb v displaystyle d_ text emb v some architectures use the transpose of the embedding matrix m displaystyle m as the un embedding matrix w displaystyle w in order to avoid needing double the amount of embedding related parameters and to avoid divergence during training this practice is called weight tying 57 positional encoding edit illustration of absolute positional encoding with parameters n 10000 d 100 displaystyle n 10000 d 100 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 1 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 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 encoder decoder overview edit one encoder decoder block a transformer is composed of stacked encoder layers and decoder layers 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 58 59 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 59 these feed forward layers contain most of the parameters in a transformer model feedforward network edit the feedforward network module it is a two layered network that maps d emb displaystyle d_ text emb dimensional vectors into d emb displaystyle d_ text emb dimensional vectors 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...
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