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| "text": "Recurrent neural networks, long short-term memory [13] and gated recurrent [7] neural networks\r in particular, have been firmly established as state of the art approaches in sequence modeling and\r transduction problems such as language modeling and machine translation [ 35 , 2 , 5]. Numerous\r efforts have since continued to push the boundaries of recurrent language models and encoder-decoder\r architectures [38, 24, 15].\r Recurrent models typically factor computation along the symbol positions of the input and output\r sequences. Aligning the positions to steps in computation time, they generate a sequence of hidden\r states ht, as a function of the previous hidden state ht−1 and the input for position t. This inherently\r sequential nature precludes parallelization within training examples, which becomes critical at longer\r sequence lengths, as memory constraints limit batching across examples. Recent work has achieved\r significant improvements in computational efficiency through factorization tricks [ 21 ] and conditional\r computation [ 32 ], while also improving model performance in case of the latter. The fundamental\r constraint of sequential computation, however, remains." | |
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| "text": "In this work we propose the Transformer, a model architecture eschewing recurrence and instead\r relying entirely on an attention mechanism to draw global dependencies between input and output." | |
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| "text": "The Transformer follows this overall architecture using stacked self-attention and point-wise, fully\r connected layers for both the encoder and decoder, shown in the left and right halves of Figure 1,\r respectively.\r 3.1 Encoder and Decoder Stacks\r Encoder: The encoder is composed of a stack of N = 6 identical layers. Each layer has two\r sub-layers. The first is a multi-head self-attention mechanism, and the second is a simple, position-\r wise fully connected feed-forward network. We employ a residual connection [ 11 ] around each of\r the two sub-layers, followed by layer normalization [1]. That is, the output of each sub-layer is\r LayerNorm(x + Sublayer(x)), where Sublayer(x) is the function implemented by the sub-layer\r itself. To facilitate these residual connections, all sub-layers in the model, as well as the embedding\r layers, produce outputs of dimension dmodel = 512.\r Decoder: The decoder is also composed of a stack of N = 6 identical layers. In addition to the two\r sub-layers in each encoder layer, the decoder inserts a third sub-layer, which performs multi-head\r attention over the output of the encoder stack. Similar to the encoder, we employ residual connections\r around each of the sub-layers, followed by layer normalization. We also modify the self-attention\r sub-layer in the decoder stack to prevent positions from attending to subsequent positions. This\r masking, combined with fact that the output embeddings are offset by one position, ensures that the\r predictions for position i can depend only on the known outputs at positions less than i." | |
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| "text": "An attention function can be described as mapping a query and a set of key-value pairs to an output,\r where the query, keys, values, and output are all vectors. The output is computed as a weighted sum" | |
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| "text": "of the values, where the weight assigned to each value is computed by a compatibility function of the\r query with the corresponding key.\r 3.2.1 Scaled Dot-Product Attention\r We call our particular attention \"Scaled Dot-Product Attention\" (Figure 2). The input consists of\r queries and keys of dimension dk, and values of dimension dv . We compute the dot products of the\r query with all keys, divide each by √dk, and apply a softmax function to obtain the weights on the\r values.\r In practice, we compute the attention function on a set of queries simultaneously, packed together\r into a matrix Q. The keys and values are also packed together into matrices K and V . We compute\r the matrix of outputs as:\r Attention(Q, K, V ) = softmax( QKT\r √dk\r )V (1)\r The two most commonly used attention functions are additive attention [ 2], and dot-product (multi-\r plicative) attention. Dot-product attention is identical to our algorithm, except for the scaling factor\r of 1√dk\r . Additive attention computes the compatibility function using a feed-forward network with\r a single hidden layer. While the two are similar in theoretical complexity, dot-product attention is\r much faster and more space-efficient in practice, since it can be implemented using highly optimized\r matrix multiplication code.\r While for small values of dk the two mechanisms perform similarly, additive attention outperforms\r dot product attention without scaling for larger values of dk [3 ]. We suspect that for large values of\r dk, the dot products grow large in magnitude, pushing the softmax function into regions where it has\r extremely small gradients 4. To counteract this effect, we scale the dot products by 1√dk\r " | |
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| "text": "4To illustrate why the dot products get large, assume that the components of q and k are independent random\r variables with mean 0 and variance 1. Then their dot product, q · k = Pdk\r i=1 qiki, has mean 0 and variance dk ." | |
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| "text": "Instead of performing a single attention function with dmodel-dimensional keys, values and queries,\r we found it beneficial to linearly project the queries, keys and values h times with different, learned\r linear projections to dk, dk and dv dimensions, respectively. On each of these projected versions of\r queries, keys and values we then perform the attention function in parallel, yielding dv -dimensional" | |
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| "text": "output values. These are concatenated and once again projected, resulting in the final values, as\r depicted in Figure 2.\r Multi-head attention allows the model to jointly attend to information from different representation\r subspaces at different positions. With a single attention head, averaging inhibits this.\r MultiHead(Q, K, V ) = Concat(head1, ..., headh)W O\r where headi = Attention(QW Q\r i , KW K\r i , V W V\r i )\r Where the projections are parameter matrices W Q\r i ∈ Rdmodel×dk , W K\r i ∈ Rdmodel×dk , W V\r i ∈ Rdmodel×dv\r and W O ∈ Rhdv ×dmodel .\r In this work we employ h = 8 parallel attention layers, or heads. For each of these we use\r dk = dv = dmodel/h = 64. Due to the reduced dimension of each head, the total computational cost\r is similar to that of single-head attention with full dimensionality." | |
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| "text": "The Transformer uses multi-head attention in three different ways:\r • In \"encoder-decoder attention\" layers, the queries come from the previous decoder layer,\r and the memory keys and values come from the output of the encoder. This allows every\r position in the decoder to attend over all positions in the input sequence. This mimics the\r typical encoder-decoder attention mechanisms in sequence-to-sequence models such as\r [38, 2, 9].\r • The encoder contains self-attention layers. In a self-attention layer all of the keys, values\r and queries come from the same place, in this case, the output of the previous layer in the\r encoder. Each position in the encoder can attend to all positions in the previous layer of the\r encoder.\r • Similarly, self-attention layers in the decoder allow each position in the decoder to attend to\r all positions in the decoder up to and including that position. We need to prevent leftward\r information flow in the decoder to preserve the auto-regressive property. We implement this\r inside of scaled dot-product attention by masking out (setting to −∞) all values in the input\r of the softmax which correspond to illegal connections" | |
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| "text": "In addition to attention sub-layers, each of the layers in our encoder and decoder contains a fully\r connected feed-forward network, which is applied to each position separately and identically. This\r consists of two linear transformations with a ReLU activation in between.\r FFN(x) = max(0, xW1 + b1)W2 + b2 (2)\r While the linear transformations are the same across different positions, they use different parameters\r from layer to layer. Another way of describing this is as two convolutions with kernel size 1.\r The dimensionality of input and output is dmodel = 512, and the inner-layer has dimensionality\r df f = 2048." | |
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| "text": "Similarly to other sequence transduction models, we use learned embeddings to convert the input\r tokens and output tokens to vectors of dimension dmodel. We also use the usual learned linear transfor-\r mation and softmax function to convert the decoder output to predicted next-token probabilities. In\r our model, we share the same weight matrix between the two embedding layers and the pre-softmax\r linear transformation, similar to [ 30 ]. In the embedding layers, we multiply those weights by √dmodel." | |
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| "text": "Since our model contains no recurrence and no convolution, in order for the model to make use of the\r order of the sequence, we must inject some information about the relative or absolute position of the\r tokens in the sequence. To this end, we add \"positional encodings\" to the input embeddings at the\r bottoms of the encoder and decoder stacks. The positional encodings have the same dimension dmodel\r as the embeddings, so that the two can be summed. There are many choices of positional encodings,\r learned and fixed [9].\r In this work, we use sine and cosine functions of different frequencies:\r P E(pos,2i) = sin(pos/100002i/dmodel )\r P E(pos,2i+1) = cos(pos/100002i/dmodel )\r where pos is the position and i is the dimension. That is, each dimension of the positional encoding\r corresponds to a sinusoid. The wavelengths form a geometric progression from 2π to 10000 · 2π. We\r chose this function because we hypothesized it would allow the model to easily learn to attend by\r relative positions, since for any fixed offset k, P Epos+k can be represented as a linear function of\r P Epos.\r We also experimented with using learned positional embeddings [9] instead, and found that the two\r versions produced nearly identical results (see Table 3 row (E)). We chose the sinusoidal version\r because it may allow the model to extrapolate to sequence lengths longer than the ones encountered\r during training." | |
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| "text": "Motivating our use of self-attention we\r consider three desiderata.\r One is the total computational complexity per layer. Another is the amount of computation that can\r be parallelized, as measured by the minimum number of sequential operations required.\r The third is the path length between long-range dependencies in the network. Learning long-range\r dependencies is a key challenge in many sequence transduction tasks. One key factor affecting the\r ability to learn such dependencies is the length of the paths forward and backward signals have to\r traverse in the network. The shorter these paths between any combination of positions in the input\r and output sequences, the easier it is to learn long-range dependencies [12]. Hence we also compare\r the maximum path length between any two input and output positions in networks composed of the\r different layer types.\r As noted in Table 1, a self-attention layer connects all positions with a constant number of sequentially\r executed operations, whereas a recurrent layer requires O(n) sequential operations. In terms of\r computational complexity, self-attention layers are faster than recurrent layers when the sequence" | |
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| "text": "length n is smaller than the representation dimensionality d, which is most often the case with\r sentence representation" | |
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