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n 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 multihead attention edit multihead attention block diagram exact dimension counts within a multihead attention module 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 61 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 i q x w i k x w i v w o displaystyle text multiheadattention q k v text concat _ i in n_ text heads text attention xw_ i q xw_ i k xw_ i v w o where the matrix x displaystyle x is the concatenation of word embeddings and the matrices w i q w i k w i v displaystyle w_ i q w_ i k w_ i v 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 head 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 masked attention edit the transformer architecture is constructed to calculate output tokens iteratively assuming t 0 displaystyle t 0 refers to the calculation of the first output token i 0 displaystyle i 0 for step t 0 displaystyle t 0 the output token i 0 displaystyle i 0 shall remain constant this ensures properties of the model similar to autoregressive models 1 therefore at every time step t displaystyle t the calculation for all outputs i displaystyle i should not have access to tokens at position j displaystyle j for j i displaystyle j i as it naturally is the case for time step t i displaystyle t i when tokens j t displaystyle j t are not yet calculated this behavior may be accomplished before the softmax stage by adding a mask matrix m displaystyle m that is displaystyle infty at entries where the attention link must be cut and 0 displaystyle 0 at other places maskedattention q k v softmax m q k t d k v displaystyle begin aligned text maskedattention q k v text softmax left m frac qk mathrm t sqrt d_ k right v end aligned the following matrix is commonly used in decoder self attention modules called causal masking m causal 0 0 0 0 0 0 0 0 0 0 displaystyle m_ text causal begin bmatrix 0 infty infty dots infty 0 0 infty dots infty 0 0 0 dots infty vdots vdots vdots ddots vdots 0 0 0 dots 0 end bmatrix 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 62 encoder edit one encoder layer 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 where ffn displaystyle text ffn stands for feed forward network we can more succinctly write it as encoderlayer h ffn multiheadattention h h h displaystyle text encoderlayer h text ffn text multiheadattention h h h with the implicit convention that the ffn displaystyle 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 edit one decoder layer 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 1 59 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 1 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 h maskedmultiheadattention h h h decoderlayer h ffn multiheadattention h h e h e displaystyle 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 displaystyle 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 edit sublayers edit a one encoder layer and one decoder layer b two encoder layers and two decoder layers the sublayers are labelled as well 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 transformer encoder with norm first and norm last transformer decoder with norm first and norm last block diagram for the full transformer architecture schematic object hierarchy for the full transformer architecture in object oriented programming style the 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 connections are introduced to avoid vanishing gradient issues and stabilize the training process they can be expressed by x f x x displaystyle x mapsto f x x where f displaystyle f is a given component of the transformer adding the input x displaystyle x can preserve the input information and avoid issues when the gradient of f x displaystyle 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 l a y e r n o r m x s u b l a y e r x displaystyle mathrm layernorm x mathrm sublayer x where s u b l a y e r x displaystyle mathrm sublayer x is the function implemented by the sublayer itself in the pre ln convention the output of each sublayer is x s u b l a y e r l a y e r n o r m x displaystyle x 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 63 was found to be easier to train requiring no warm up leading to faster convergence 51 pseudocode edit the following is the pseudocode for a standard pre ln encoder decoder transformer adapted from formal algorithms for transformers 64 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 t 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 edit the transformer architecture being modular allows variations several common variations are described here 52 an encoder only transformer applies the encoder to map an input text into a sequence of vectors that represent the input text this is usually used for text embedding and representation learning for downstream applications bert is encoder only they are less often used currently as they were found to be not significantly better than training an encoder decoder transformer then taking just the encoder 56 they are also referred to as all to all or bert like a decoder only transformer is not literally decoder only since without an encoder the cross attention mechanism has nothing to attend to thus the decoder layers in a decoder only transformer is composed of just two sublayers the causally masked self attention and the feedforward network this is usually used for text generation and instruction following the models in the gpt series and chinchilla series are decoder only they are also referred to as autoregressive or causal an encoder decoder transformer is generally the same as the original transformer with 2 sublayers per encoder layer and 3 sublayers per decoder layer etc they might have minor architectural improvements such as alternative activation functions changing the location of normalization etc this is also usually used for text generation and instruction following the models in the t5 series are encoder decoder 52 a prefixlm prefix language model is a decoder only architecture but with prefix masking which is different from causal masking specifically it has mask of the form 52 figure 3 m prefixlm 0 0 m causal displaystyle m_ text prefixlm begin bmatrix mathbf 0 infty mathbf 0 m_ text causal end bmatrix where the first columns correspond to the prefix and the subsequent columns correspond to the autoregressively generated text based on the prefix they resemble encoder decoder models but has less sparsity such models are rarely used though they are cited as theoretical possibilities and benchmarked comparisons 56 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 40 subsequent work edit alternative activation functions edit the original transformer uses relu activation function other activation functions were developed the llama series and palm used swiglu 65 both gpt 1 and bert 38 used gelu 66 alternative activation functions are often used in combination with gated linear units in the feedforward module 65 alternative nor...
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