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d 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 communication avoiding algorithm that fuses these operations into a single loop increasing the arithmetic intensity it is an online algorithm that computes the following quantities 81 82 z i q t k i m i max z 1 z i max m i 1 z i ℓ i e z 1 m i e z i m i e m i 1 m i ℓ i 1 e z i m i o i e z 1 m i v 1 e z i m i v i e m i 1 m i o i 1 e z i m i v i displaystyle begin aligned z_ i q t k_ i m_ i max z_ 1 dots z_ i max m_ i 1 z_ i ell _ i e z_ 1 m_ i dots e z_ i m_ i e m_ i 1 m_ i ell _ i 1 e z_ i m_ i o_ i e z_ 1 m_ i v_ 1 dots e z_ i m_ i v_ i e m_ i 1 m_ i o_ i 1 e z_ i m_ i v_ i end aligned and returns o n ℓ n displaystyle o_ n ell _ n in practice flashattention operates over multiple queries and keys per loop iteration in a similar way as blocked matrix multiplication if backpropagation is needed then the output vectors and the intermediate arrays m 1 m n ℓ 1 ℓ n displaystyle m_ 1 dots m_ n ell _ 1 dots ell _ n are cached and during the backward pass attention matrices are rematerialized from these making it a form of gradient checkpointing an improved version flashattention 2 83 84 85 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 86 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 87 multi query attention edit comparison between several different forms of attention mechanism and the amount of kv caching necessary for each multi query attention changes the multihead attention mechanism 88 whereas normally 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 left text attention xw_ i q xw_ i k xw_ i v right w o with multi query attention there is just one w k w v displaystyle w k w v thus multiqueryattention q k v concat i n heads attention x w i q x w k x w v w o displaystyle text multiqueryattention q k v text concat _ i in n_ text heads left text attention xw_ i q 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 89 the architecture of v2 showing both mla and a variant of mixture of experts 90 figure 2 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 90 speculative decoding edit main article speculative decoding speculative decoding 91 92 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 displaystyle x_ 1 x_ 2 x_ 512 taking time 512 t gpt 3 displaystyle 512t_ 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 displaystyle x_ t is indeed the token with the largest log likelihood in the t displaystyle 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 x 1 x 2 x 3 x 4 displaystyle tilde x _ 1 tilde x _ 2 tilde x _ 3 tilde x _ 4 this only takes 4 t gpt 3 small displaystyle 4t_ text gpt 3 small these tokens are then run through the larger gpt 3 in one go suppose that x 1 displaystyle tilde x _ 1 and x 2 displaystyle tilde x _ 2 are verified by gpt 3 as what it would have picked then those are kept but x 3 displaystyle tilde x _ 3 is not so x 3 x 4 displaystyle tilde x _ 3 tilde x _ 4 are discarded and gpt 3 is run on those this would take 4 t gpt 3 small 3 t gpt 3 displaystyle 4t_ text gpt 3 small 3t_ text gpt 3 which might be shorter than 4 t gpt 3 displaystyle 4t_ 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 91 93 multi token prediction 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 94 95 sub quadratic transformers edit training transformer based architectures can be expensive especially for long inputs 96 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 97 in the audio domain septr decouples the attention in time and frequency domains 98 long range arena 2020 99 is a standard benchmark for comparing the behavior of transformer architectures over long inputs alternative attention graphs edit the standard attention graph is either all to all or causal both of which scales as o n 2 displaystyle o n 2 where n displaystyle n is the number of tokens in a sequence reformer 2020 96 100 reduces the computational load from o n 2 displaystyle o n 2 to o n ln n displaystyle o n ln n by using locality sensitive hashing and reversible layers 101 sparse attention 102 uses attention graphs that grows slower than o n 2 displaystyle o n 2 for example bigbird 2020 103 uses random small world networks which grows as o n displaystyle o n ordinary transformers require a memory size that is quadratic in the size of the context window attention free transformers 104 reduce this to a linear dependence while still retaining the advantages of a transformer by linking the key to the value random feature attention edit random feature attention 2021 105 uses fourier random features φ x 1 d cos w 1 x sin w 1 x cos w d x sin w d x t displaystyle 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 t where w 1 w d displaystyle w_ 1 w_ d are independent samples from the normal distribution n 0 σ 2 i displaystyle n 0 sigma 2 i this choice of parameters satisfy e φ x φ y e x y 2 2 σ 2 displaystyle mathbb e langle varphi x varphi y rangle e frac x y 2 2 sigma 2 or e x y σ 2 e e x 2 2 σ 2 φ x e y 2 2 σ 2 φ y e x 2 2 σ 2 φ x e y 2 2 σ 2 φ y displaystyle 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 a...
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