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yer 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 normalizations edit the normalization used in the transformer can be different from layernorm one example is rmsnorm 67 which is used in the llama series other examples include scalenorm 68 and fixnorm 68 alternative positional encodings edit transformers may use other positional encoding methods than sinusoidal 69 the original transformer paper reported using a learned positional encoding 70 but finding it not superior to the sinusoidal one 1 later 71 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 edit rope rotary positional embedding 72 is best explained by considering a list of 2 dimensional vectors x 1 1 x 1 2 x 2 1 x 2 2 x 3 1 x 3 2 displaystyle x_ 1 1 x_ 1 2 x_ 2 1 x_ 2 2 x_ 3 1 x_ 3 2 now pick some angle θ displaystyle theta then rope encoding is rope x m 1 x m 2 m cos m θ sin m θ sin m θ cos m θ x m 1 x m 2 x m 1 cos m θ x m 2 sin m θ x m 2 cos m θ x m 1 sin m θ displaystyle text rope big x_ m 1 x_ m 2 m big begin pmatrix cos m theta sin m theta sin m theta cos m theta end pmatrix begin pmatrix x_ m 1 x_ m 2 end pmatrix begin pmatrix x_ m 1 cos m theta x_ m 2 sin m theta x_ m 2 cos m theta x_ m 1 sin m theta end pmatrix equivalently if we write the 2 dimensional vectors as complex numbers z m x m 1 i x m 2 displaystyle z_ m x_ m 1 ix_ m 2 then rope encoding is just multiplication by an angle rope z m m e i m θ z m displaystyle text rope big z_ m m big e im theta z_ m for a list of 2 n displaystyle 2n dimensional vectors a rope encoder is defined by a sequence of angles θ 1 θ n displaystyle 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 rope x m t rope y n rope x m k t rope y n k displaystyle 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 displaystyle k alibi edit alibi attention with linear biases 73 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 attention q k v softmax q k t d k s b v displaystyle begin aligned text attention q k v text softmax left frac qk mathrm t sqrt d_ k sb right v end aligned here s displaystyle s is a real number scalar and b displaystyle b is the linear bias matrix defined by b 0 1 2 3 1 0 1 2 2 1 0 1 3 2 1 0 displaystyle b 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 displaystyle b_ i j j i the idea being that the linear bias matrix is a softened mask just as 0 displaystyle 0 represent full attention paid and displaystyle 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 edit relative position encodings 74 is similar to alibi but more generic attention q k v softmax q k t d k b v displaystyle begin aligned text attention q k v text softmax left frac qk mathrm t sqrt d_ k b right v end aligned where b displaystyle b is a toeplitz matrix that is b i j b i j displaystyle b_ i j b_ i j whenever i j i j displaystyle i j i j this is contrasted with the original sinusoidal positional encoding which is an absolute positional encoding 75 efficient implementation edit 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 12 kv caching edit when an autoregressive transformer is used for inference such as generating text the query vector is different at each step but the already computed key and value vectors are always the same the kv caching method saves the computed key and value vectors at each attention block so that they are not recomputed at each new token pagedattention applies memory paging to kv caching 76 77 78 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 79 flashattention edit flashattention 80 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 the flashattention method is a co...