Transformer-Evolution-Paper
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  • Pe
    • A Simple and Effective Positional Encoding for Transformers
    • DeBERTa Decoding-enhanced BERT with Disentangled Attention
    • DecBERT Enhancing the Language Understanding of BERT with Causal Attention Masks
    • Encoding word order in complex embeddings
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    • LLM Details Summary
    • What Language Model to Train if You Have One Million GPU Hours?
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  • 整体思路以及计算方式
  • 时间复杂度
  • 训练以及loss
  • 代码
  • 实验以及适用场景
  • 细节
  • 简评
  1. Pe

Encoding word order in complex embeddings

论文地址：

  • https://arxiv.org/abs/1912.12333

参考资料：

  • https://mp.weixin.qq.com/s?__biz=MzIxMzkwNjM2NQ==&mid=2247484015&idx=1&sn=7e79cf7f2b3abe51b82c4a8beacdf195&chksm=97aee4bda0d96dab57db412e7c9f51e7e9bd5d9d17742f2a522f2dbc881c77fb59183c098d04&scene=21#wechat_redirect

  • https://openreview.net/forum?id=Hke-WTVtwr

整体思路以及计算方式

论文给出新的位置编码方式，整体思路如下。

传统使用位置编码的形式为：

f(j,pos)=fwe(j)+fpe(pos)f(j, p o s)=f_{w e}(j)+f_{p e}(p o s)f(j,pos)=fwe​(j)+fpe​(pos)

其中jjj表示词的index，pos表示该词对应的位置。作者认为这种方式无法表示相对位置关系，给出了另一种位置编码方式为：

f(j,pos)=gj(pos)f(j, {pos})={g}_{j}({pos})f(j,pos)=gj​(pos)

为了给出合理的位置编码，作者提出了两个位置编码应该满足的形式：

  1. 存在函数www，满足：

    g(pos+n)=w(n)g(pos)g(pos+n)=w(n)g(pos)g(pos+n)=w(n)g(pos)

  2. 位置函数ggg有界：

    ∃δ∈R+,∀pos∈N,∣g(pos)∣≤δ\exists \delta \in \mathbb{R}^{+}, \forall {pos} \in \mathbb{N},|g({pos})| \leq \delta∃δ∈R+,∀pos∈N,∣g(pos)∣≤δ

满足上述两个条件的解为：

g(pos)=z2z1pos for z1,z2∈C with ∣z1∣≤1g(pos)=z_{2} z_{1}^{pos} \text { for } z_{1}, z_{2} \in \mathbb{C} \text { with }\left|z_{1}\right| \leq 1g(pos)=z2​z1pos​ for z1​,z2​∈C with ∣z1​∣≤1

利用复数表示，可得

g(pos)=z2z1pos=r2eiθ2(r1eiθ1)pos=r2r1posei(θ2+θ1pos) subject to ∣r1∣≤1g(pos)=z_{2} z_{1}^{pos }=r_{2} e^{i \theta_{2}}\left(r_{1} e^{i \theta_{1}}\right)^{pos }=r_{2} r_{1}^{pos } e^{i\left(\theta_{2}+\theta_{1} pos \right)} \text { subject to }\left|r_{1}\right| \leq 1g(pos)=z2​z1pos​=r2​eiθ2​(r1​eiθ1​)pos=r2​r1pos​ei(θ2​+θ1​pos) subject to ∣r1​∣≤1

特别的，取r1=1r_1=1r1​=1，那么上式可以化简为：

g(pos)=r2ei(θ2+θ1pos)≜rei(ωpos+θ)g(pos)=r_{2}e^{i\left(\theta_{2}+\theta_{1} pos \right)}\triangleq r e^{i(\omega {pos}+\theta)}g(pos)=r2​ei(θ2​+θ1​pos)≜rei(ωpos+θ)

可学习的参数为：

r,w,θr, w, \thetar,w,θ

时间复杂度

假设原始的position embedding形状为L×DL\times DL×D，那么Complex Embedding的参数数量为3×L×D3\times L\times D3×L×D（因为涉及到r,w,θr,w ,\thetar,w,θ），所以该方法会增加空间复杂度；另外，由于复数的分为实部和虚部，所以计算的时候时间复杂度会乘以2。

训练以及loss

不变。

代码

  • https://github.com/iclr-complex-order/complex-order

  • https://github.com/zhaodongh/Encoding-Word-Order-in-Complex-valued-Embedding

实验以及适用场景

适用于所有场景，作者测了LM，机器翻译以及分类任务，均带来一定提升。

细节

暂无。

简评

作者给的思路很简洁，也能带来一定提升，值得进行复现。

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Last updated 2 years ago