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Synthesizer: Rethinking Self-Attention in Transformer Models

PreviousOthersNextTransformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kern

Last updated 2 years ago

论文地址：

整体思路以及计算方式

本文的观点很有意思：Attention中的Attention Matrix可以不通过Query和Key计算，通过其他方式得到n×nn\times nn×n矩阵也能得到合理的结果，模型一共有5种，分别如下：

Dense:

  • 输入：X∈Rn×dX\in \mathbb R^{n\times d}X∈Rn×d

  • S1=f(XW1)∈Rn×d1S_1= f(XW_1) \in \mathbb R^{n\times d_1}S1​=f(XW1​)∈Rn×d1​

  • S2=S1W2∈Rn×nS_2= S_1 W_2 \in \mathbb R^{n\times n}S2​=S1​W2​∈Rn×n

  • O=Softmax(S2)(XW3)∈Rn×dO=\mathrm{Softmax}(S_2)(XW_3)\in \mathbb R^{n\times d}O=Softmax(S2​)(XW3​)∈Rn×d

Random：

  • 输入：X∈Rn×dX\in \mathbb R^{n\times d}X∈Rn×d

  • 初始化：S1∈Rn×nS_1 \in \mathbb R^{n\times n}S1​∈Rn×n

  • O=Softmax(S1)(XW1)∈Rn×dO=\mathrm{Softmax}(S_1 )(XW_1)\in \mathbb R^{n\times d}O=Softmax(S1​)(XW1​)∈Rn×d

Factorized Dense（降低空间复杂度）：

  • 输入：X∈Rn×dX\in \mathbb R^{n\times d}X∈Rn×d

  • 初始化：W1∈Rd×k1,W2∈Rd×k2W_1\in \mathbb R^{d\times k_1}, W_2\in \mathbb R^{d\times k_2}W1​∈Rd×k1​,W2​∈Rd×k2​，k1×k2=nk_1 \times k_2 = nk1​×k2​=n

  • S1=(XW1)⊙(XW2)∈Rn×nS_1= (XW_1) \odot (XW_2) \in \mathbb R^{n\times n}S1​=(XW1​)⊙(XW2​)∈Rn×n（复制到相同维度，然后点乘）

  • O=Softmax(S1)(XW3)∈Rn×dO=\mathrm{Softmax}(S_1)(XW_3)\in \mathbb R^{n\times d}O=Softmax(S1​)(XW3​)∈Rn×d

Factorized Random（降低空间复杂度）：

  • 输入：X∈Rn×dX\in \mathbb R^{n\times d}X∈Rn×d

  • 初始化：S1∈Rn×k,S2∈Rn×kS_1\in \mathbb R^{n\times k}, S_2\in \mathbb R^{n\times k}S1​∈Rn×k,S2​∈Rn×k

  • O=Softmax(S1S2⊤)(XW1)∈Rn×dO=\mathrm{Softmax}(S_1 S_2^{\top})(XW_1)\in \mathbb R^{n\times d}O=Softmax(S1​S2⊤​)(XW1​)∈Rn×d

Mixture：

  • 输入：X∈Rn×dX\in \mathbb R^{n\times d}X∈Rn×d

  • 通过不同的方式计算Score Matrix SSS：

    • S=∑αiSi,∑αi=1S=\sum\alpha_i S_i, \sum \alpha_i =1S=∑αi​Si​,∑αi​=1

  • O=Softmax(S)(XW)∈Rn×dO=\mathrm{Softmax}(S)(XW)\in \mathbb R^{n\times d}O=Softmax(S)(XW)∈Rn×d

时间复杂度

本质上还需要计算Attention Matrix，所以依然为O(n2d)O(n^2d)O(n2d)

训练以及loss

不变。

代码

实验以及适用场景

适用于所有场景，性能最好的是Mixture情形，这里使用了QK⊤QK^{\top}QK⊤，所以即使提升性能，其实意义并不大。

细节

模型参数和序列长度有关，如果所以要处理很长的序列，模型应该会非常大。

简评

提供了一个不同的视角，但是从实验上来说，不利用QK⊤\mathbf Q \mathbf K^{\top}QK⊤的情形性能其实比较差。

https://arxiv.org/abs/2005.00743
https://github.com/leaderj1001/Synthesizer-Rethinking-Self-Attention-Transformer-Models