new essay: attention-and-multiattention.md
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content/essays/attention-and-multiattention.md
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content/essays/attention-and-multiattention.md
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---
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title: "Attention and Multiattention"
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date: 2022-09-19T20:35:33+08:00
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tags: []
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categories: []
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weight: 50
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show_comments: true
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katex: true
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draft: false
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---
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<!--more-->
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## 自注意力
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众所周知,注意力就是一个 query 和多个 key-value 对的带权和,如下:
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$$
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Attention(Q, K, V) = V.softmax(score(K, V))
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$$
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当 Q == K == V 的时候,这个计算就叫做自注意力
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## 多头注意力
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假如 Head = 4, 那么如下,其中每一个 Q,K,V 都是完整大小的 Q,K,V,相当于做了 3 次注意力,其中每一个 W 都是可以学习的参数(因为 attention 的计算方法中没有可学习的参数,所以在计算 attention 前加一个线性变换,训练这个线性变换的参数)
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$$
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head_1 = Attention(W_1^QQ, W_1^K, W_1^VV)
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\\
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head_2 = Attention(W_2^QQ, W_2^K, W_2^VV)
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\\
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head_3 = Attention(W_3^QQ, W_3^K, W_3^VV)
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\\
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head_4 = Attention(W_4^QQ, W_4^K, W_4^VV)
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$$
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最后,4 次 attention 结果连接起来,使用另外一个大的线性变换:
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$$
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Multihead(Q, K, V) = W^O[head_1, head_2, head_3, head_4]
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$$
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## 参考
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https://www.adityaagrawal.net/blog/deep_learning/attention
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