Attention Is All You Need阅读笔记

transformer 是一个完全由注意力机制组成的搭建的模型，模型复杂度低，并可以进行并行计算，使得计算速度快。在翻译模型上取得了较好的效果。本篇论文属于经典必读论文，阅读笔记中对一些不清楚的地方进行了汉语解释，读完论文后阅读参考链接以加深理解。

research objective

based solely on attention mechanisms, increase parallezable computation and decrease train time

Problem Statement

recurrent models hidden states depended on previous hidden state and the input for position precludes parallelization

contribution

• Transformer,
• eschewing recurrence and instead relying entirely on an attention mechanism, solve the long dependency problem.
• draw global dependecies between input and output
• allow for significantly more parallelization

Model Architecture

The Transformer uses stacked self-attention and point-wise, fully connected layers for both the encoder and decoder.

Encoder and Decoder Stacks

Encoder

• compose of a stack of N identical layers
• each layers has two sub-layers
2. position-wise fully connected feed forward network
• employ a residual connection around each of the two sub-layers, followed by layer normalization
• the output of each sub-layer is $\text { LayerNorm }(x+\text { Sublayer }(x))$
• encoder中的Q，K，V都是学出来的

Decoder

• composed of a stack of N identical layers
• has the same two sub-layers as the encoder
• the third sub-layer between the two sub-layers
• perform multi-head attention over the output of the encoder stack
• add a mask to modify the self-attention sub-layer to ensure that the predictions for position $i$ can depend only the known outputs at positions less than $i$
• 除了第一子层中Q，K，V是自己学出来的，第二个子层利用了encoder中的K，V。

Attention

Scaled Dot-Product Attention

the calculation process as the left at the figure 2. formula：

• where $\sqrt{d_{k}}$ is to prevent value from getting too large, which will push the softmax function into regions where it has extremely small gradients. 因为量级太大，softmax后就非0即1了，不够“soft”了。也会导致softmax的梯度非常小。也就是让softmax结果不稀疏(问号脸，通常人们希望得到更稀疏的attention吧)。
• $Q, K,V$ is a matrix needed to learn from input.

helps the encoder look at other words in the input sentence as it encodes a specific word

in the figure 2 right.

• it’s beneficial to lineraly project the quries, keys and values $h$ times with different, learned projections to $d_k, d_k, d_v$ dimensions, respectively
• concatenate the output

where $W_{i}^{Q} \in \mathbb{R}^{d_{\text { model }} \times d_{k}}, W_{i}^{K} \in \mathbb{R}^{d_{\text { model }} \times d_{k}}, W_{i}^{V} \in \mathbb{R}^{d_{\text { model }} \times d_{v}}, W^{O} \in \mathbb{R}^{h d_{v} \times d_{\mathrm{model}}}$

Applications of Attention in our Model

• the queries come from the previous decoder layer, and the memory keys and values come from the output of the encoder. mimicing the seq-to-seq
• self -attention can make that each position in the encoder can attend to all positions in the previous layer of the encoder
• We need to prevent leftward information flow in the decoder to preserve the auto-regressive property. We implement this inside of scaled dot-product attention by masking out (setting to −∞) all values in the input of the softmax which correspond to illegal connections. See Figure 2。即我们只能attend到前面已经翻译过的输出的词语，因为翻译过程我们当前还并不知道下一个输出词语，这是我们之后才会推测到的。即将$QK^T$中每行该单词之后的数值做处理，使得前面的单词看不到后面单词所占的重要性程度。

Position-wise Feed-Forward Networks

• applied to each position separately and identically
• feed-forward network consists of tow linear transformations with a ReLU activation. formula:

1. 为什么叫强调position-wise?
• 解释一: 这里FFN层是每个position进行相同且独立的操作，所以叫position-wise。对每个position独立做FFN。
• 解释二：从卷积的角度解释，这里的FFN等价于kernel_size=1的卷积，这样每个position都是独立运算的。如果kernel_size=2，或者其他，position之间就具有依赖性了，貌似就不能叫做position-wise了
2. 为什么要采用全连接层？
• 目的: 增加非线性变换
• 如果不采用FFN呢？有什么替代的设计？
3. 为什么采用2层全连接，而且中间升维？
• 这也是所谓的bottle neck，只不过低维在IO上，中间采用high rank

Embeddings and Softmax

Sharing the same weight maatrix between the two embedding layers and the pre-softmax linear transformation

Positional Encoding

Using sine and xosine functions of different frequencies:

• where $pos$ is the postiiton and $i$ is the dimension

• Authors hypothesized it would allow the model to easily learn to attend by relative positions, since for any fixed offset $k$, $PE_{pos+k}$can be represented as a linear function of $PE_{pos}$

但在语言中，相对位置也很重要，Google选择前述的位置向量公式的一个重要原因是：由于我们有$\sin (\alpha+\beta)=\sin \alpha \cos \beta+\cos \alpha \sin \beta$以及$\cos (\alpha+\beta)=\cos \alpha \cos \beta-\sin \alpha \sin \beta$，这表明位置$p+k$的向量可以表示成位置$p$的向量的线性变换，这提供了表达相对位置信息的可能性。

• Compared with using learned positional embeddings, the sinusoidal version may allow the model to extrapolate to sequence lengths longer than the ones encountered during training.

Why Self-Attention

• total computational complexity per layer
• the amount of computation that can be parallelized
• the path between long-range dependencies in the network

self-attention|：

• $QK^TV$相乘，根据矩阵大小（分别为$nd, nd, nd$需要的复杂度为$O(n^2d2)$（忽略softmax）
• maximum path length：图说明了， 对于self-attention, target node (生成的那个点) 实际上和 输入中的任意一点的距离是相同的

convolutional:

• 每层有k个卷积和，对于input matix（$nd$)矩阵执行卷积需要运算复杂度是$nd*(d-m)$, m为卷积和宽度是一个比较小的常数，所以总复杂度为$O\left(k \cdot n \cdot d^{2}\right)$,作者提到可分离的卷基层暂时还不了解，可以以后查阅。

• maximum path length: 正常卷积和的距离是$O(n/k)$, 但如果是堆叠卷积如图：

就可以减小到$O\left(\log _{k}(n)\right)$

recurrent:

• 计算是每个词向量乘隐藏权重($d*d$)，所以易得计算复杂度：$O\left(n \cdot d^{2}\right)$
• maximum path length: 长度就是n。
• 操作步骤要从第一个到第n个为n步，是有顺序的。其他的都没有顺序要求

self-attentin(restricted)

• 相当于只输入r邻近的句子长度，自然可以得到如图结果

Train

Optimizer

• increasing the learning rate linearly for the first warmup_steps training steps
• decreasing it thereafter proportionally to the inverse square root of the step number

Regularization

Residual Dropout

• apply dropout to the output of each sub-layer, before it is added to the sub-layer input and normalized
• apply dropout to the sums of the embeddings and the positional encodings in both the encoder and decoder stacks

Label Smoothing

• This hurts perplexity, as the model learns to be more unsure, but improves accuracy and BLEU score

Result

machine Translation

Even our base model surpasses all previously published models and ensembles, at a fraction of the training cost of any of the competitive models

缺点

1. 实践上：有些rnn轻易可以解决的问题transformer没做到，比如复制string，尤其是碰到比训练时的sequence更长的时
2. 理论上：transformers非computationally universal（图灵完备），（我认为）因为无法实现“while”循环

总结

Transformer是第一个用纯attention搭建的模型，不仅计算速度更快，在翻译任务上也获得了更好的结果。

reference

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Knowledge Graph Embedding by Translating on Hyperplanes阅读笔记

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