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Why self-attention is Natural for Sequence-to-Sequence Problems? A Perspective from Symmetries

PreviousDo Transformer Modifications Transfer Across Implementations and Applications?NextLongConv

Last updated 2 years ago

论文地址：

简评

文章先把Self Attention的置换不变性（f(PX)=Pf(X)f(\mathbf P\mathbf X)=\mathbf P f(\mathbf X)f(PX)=Pf(X)）推广为正交不变性（P\mathbf PP从置换矩阵推广为正交矩阵），然后证明其形式为：

f(X)=Xg(X⊤X).f(\mathbf X)=\mathbf X g\left(\mathbf X^{\top} \mathbf X\right).f(X)=Xg(X⊤X).

接着推广到一般的Attention，即f(X,Z)f(\mathbf X, \mathbf Z)f(X,Z)，作者证明其形式可以表达为：

f(X,Z)=Xg1(X⊤X,Z⊤X,Z⊤Z)+Zg2(X⊤X,Z⊤X,Z⊤Z)f(\mathbf X, \mathbf Z)=X g_1\left(\mathbf X^{\top}\mathbf X, \mathbf Z^{\top}\mathbf X,\mathbf Z^{\top} \mathbf Z\right)+\mathbf Z g_2\left(\mathbf X^{\top}\mathbf X, \mathbf Z^{\top} \mathbf X, \mathbf Z^{\top} \mathbf Z\right)f(X,Z)=Xg1​(X⊤X,Z⊤X,Z⊤Z)+Zg2​(X⊤X,Z⊤X,Z⊤Z)

那么就和Attention的形式非常类似。

https://arxiv.org/abs/2210.06741