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chose this function because we hypothesized it would allow the model to easily learn to attend by |
relative positions, since for any fixed offset k, P Epos+k can be represented as a linear function of |
P Epos. |
We also experimented with using learned positional embeddings [9] instead, and found that the two |
versions produced nearly identical results (see Table 3 row (E)). We chose the sinusoidal version |
because it may allow the model to extrapolate to sequence lengths longer than the ones encountered |
during training. |
4 Why Self-Attention |
In this section we compare various aspects of self-attention layers to the recurrent and convolutional layers commonly used for mapping one variable-length sequence of symbol representations |
(x1, ..., xn) to another sequence of equal length (z1, ..., zn), with xi |
, zi ∈ R |
d |
, such as a hidden |
layer in a typical sequence transduction encoder or decoder. Motivating our use of self-attention we |
consider three desiderata. |
One is the total computational complexity per layer. Another is the amount of computation that can |
be parallelized, as measured by the minimum number of sequential operations required. |
The third is the path length between long-range dependencies in the network. Learning long-range |
dependencies is a key challenge in many sequence transduction tasks. One key factor affecting the |
ability to learn such dependencies is the length of the paths forward and backward signals have to |
traverse in the network. The shorter these paths between any combination of positions in the input |
and output sequences, the easier it is to learn long-range dependencies [12]. Hence we also compare |
the maximum path length between any two input and output positions in networks composed of the |
different layer types. |
As noted in Table 1, a self-attention layer connects all positions with a constant number of sequentially |
executed operations, whereas a recurrent layer requires O(n) sequential operations. In terms of |
computational complexity, self-attention layers are faster than recurrent layers when the sequence |
length n is smaller than the representation dimensionality d, which is most often the case with |
sentence representations used by state-of-the-art models in machine translations, such as word-piece |
[38] and byte-pair [31] representations. To improve computational performance for tasks involving |
very long sequences, self-attention could be restricted to considering only a neighborhood of size r in |
6 |
the input sequence centered around the respective output position. This would increase the maximum |
path length to O(n/r). We plan to investigate this approach further in future work. |
A single convolutional layer with kernel width k < n does not connect all pairs of input and output |
positions. Doing so requires a stack of O(n/k) convolutional layers in the case of contiguous kernels, |
or O(logk(n)) in the case of dilated convolutions [18], increasing the length of the longest paths |
between any two positions in the network. Convolutional layers are generally more expensive than |
recurrent layers, by a factor of k. Separable convolutions [6], however, decrease the complexity |
considerably, to O(k · n · d + n · d |
2 |
). Even with k = n, however, the complexity of a separable |
convolution is equal to the combination of a self-attention layer and a point-wise feed-forward layer, |
the approach we take in our model. |
As side benefit, self-attention could yield more interpretable models. We inspect attention distributions |
from our models and present and discuss examples in the appendix. Not only do individual attention |
heads clearly learn to perform different tasks, many appear to exhibit behavior related to the syntactic |
and semantic structure of the sentences. |
5 Training |
This section describes the training regime for our models. |
5.1 Training Data and Batching |
We trained on the standard WMT 2014 English-German dataset consisting of about 4.5 million |
sentence pairs. Sentences were encoded using byte-pair encoding [3], which has a shared sourcetarget vocabulary of about 37000 tokens. For English-French, we used the significantly larger WMT |
2014 English-French dataset consisting of 36M sentences and split tokens into a 32000 word-piece |
vocabulary [38]. Sentence pairs were batched together by approximate sequence length. Each training |
batch contained a set of sentence pairs containing approximately 25000 source tokens and 25000 |
target tokens. |
5.2 Hardware and Schedule |
We trained our models on one machine with 8 NVIDIA P100 GPUs. For our base models using |
the hyperparameters described throughout the paper, each training step took about 0.4 seconds. We |
trained the base models for a total of 100,000 steps or 12 hours. For our big models,(described on the |
bottom line of table 3), step time was 1.0 seconds. The big models were trained for 300,000 steps |
(3.5 days). |
5.3 Optimizer |
We used the Adam optimizer [20] with β1 = 0.9, β2 = 0.98 and = 10−9 |
. We varied the learning |
rate over the course of training, according to the formula: |
lrate = d |
−0.5 |
model · min(step_num−0.5 |
, step_num · warmup_steps−1.5 |
) (3) |
This corresponds to increasing the learning rate linearly for the first warmup_steps training steps, |
and decreasing it thereafter proportionally to the inverse square root of the step number. We used |
warmup_steps = 4000. |
5.4 Regularization |
We employ three types of regularization during training: |
Residual Dropout We apply dropout [33] to the output of each sub-layer, before it is added to the |
sub-layer input and normalized. In addition, we apply dropout to the sums of the embeddings and the |
positional encodings in both the encoder and decoder stacks. For the base model, we use a rate of |
Pdrop = 0.1. |
7 |
Table 2: The Transformer achieves better BLEU scores than previous state-of-the-art models on the |
English-to-German and English-to-French newstest2014 tests at a fraction of the training cost. |
Model |
BLEU Training Cost (FLOPs) |
EN-DE EN-FR EN-DE EN-FR |
ByteNet [18] 23.75 |
Deep-Att + PosUnk [39] 39.2 1.0 · 1020 |
GNMT + RL [38] 24.6 39.92 2.3 · 1019 1.4 · 1020 |
ConvS2S [9] 25.16 40.46 9.6 · 1018 1.5 · 1020 |
MoE [32] 26.03 40.56 2.0 · 1019 1.2 · 1020 |
Deep-Att + PosUnk Ensemble [39] 40.4 8.0 · 1020 |
GNMT + RL Ensemble [38] 26.30 41.16 1.8 · 1020 1.1 · 1021 |
ConvS2S Ensemble [9] 26.36 41.29 7.7 · 1019 1.2 · 1021 |
Transformer (base model) 27.3 38.1 3.3 · 1018 |
Transformer (big) 28.4 41.8 2.3 · 1019 |
Label Smoothing During training, we employed label smoothing of value ls = 0.1 [36]. This |
hurts perplexity, as the model learns to be more unsure, but improves accuracy and BLEU score. |
6 Results |
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