From a2268769b42960999f6ed9bd97a799c732b504c9 Mon Sep 17 00:00:00 2001 From: "ben.guo" <909336740@qq.com> Date: Tue, 30 Apr 2024 15:28:41 +0800 Subject: [PATCH] =?UTF-8?q?Add.=20=E5=A2=9E=E5=8A=A0=E4=BD=8D=E7=BD=AE?= =?UTF-8?q?=E7=BC=96=E7=A0=81=E6=AD=A3=E5=BC=A6=E4=BD=99=E5=BC=A6=E7=9A=84?= =?UTF-8?q?=E5=8F=AF=E8=A7=A3=E9=87=8A=E6=80=A7?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .DS_Store | Bin 10244 -> 10244 bytes assets/image-20240430152239833.png | Bin 0 -> 294379 bytes 人人都能看懂的Transformer/.DS_Store | Bin 6148 -> 6148 bytes .../第三章——位置编码.md | 29 ++++++++++++++++-- 4 files changed, 27 insertions(+), 2 deletions(-) create mode 100644 assets/image-20240430152239833.png diff --git a/.DS_Store b/.DS_Store index ecd16fa3dfd594c4e52cb779c5443682b7be246e..1fe3072ae864a5aecd83483b3609f675a9e02304 100644 GIT binary patch delta 21 ZcmZn(XbITxPL$DX^Lx?%{9sCy2>@jW2weaG delta 21 ZcmZn(XbITxPL$Df^Lx?%{9sCy2>@jD2wMOE diff --git 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zcmZoMXfc@J&&a(oU^g=(_hufJ>x`N_)jEEhRSy(I6h!=e>+|ZxDi|5`7;+g>Jah7s zlXCKt7#J7?7#J9TPQJqGsmoWb6LuS-y8Er4XJB#7@8~qY1Z+B((l_(5wK8sI=lIJH E0CrO&aR2}S delta 32 ocmZoMXfc@J&&atkU^g=(=Vl(3>x`47*{n8}y<*(V&heKY0I1svga7~l diff --git a/人人都能看懂的Transformer/第三章——位置编码.md b/人人都能看懂的Transformer/第三章——位置编码.md index 2b35b94..0f757f3 100644 --- a/人人都能看懂的Transformer/第三章——位置编码.md +++ b/人人都能看懂的Transformer/第三章——位置编码.md @@ -12,6 +12,20 @@ WHAT:位置编码是一种向模型输入的每个单词嵌入向量中添加 +### 位置编码应该怎么设计 + +如何设计我们需要考虑几个问题: + +1. 如果是用整些数值表示,推理时可能会遇到比训练时还要长的序列;而且随着序列长度的增加,位置值会越来越大。 +2. 如果用[-1,+1]之间进行表示,要解决序列长度不同时,能表示token在序列中的绝对位置;而且在序列长度不同时,也要在不同序列中token的相对位置/距离保持一致。 + +所以我们希望: + +1. 它是有界的,即可以处理推理(预测)时,遇到的更长的句子。 +2. 每个时间步长(组),输出的值是唯一的。 +3. 任意两个时间步长(组)之间的距离,在不同长度的序列中应该一致。 +4. 它必须是确定性的。 + ### 位置编码是怎么算的? 在《Attention is all you need》中,位置编码是有正弦和余弦函数计算出来的,且是固定的。 @@ -85,15 +99,26 @@ tensor([-1.0000, 0.0044, -0.9673, -0.2535, -0.8724, -0.4889, -0.7253, -0.6884, image-20240427180954246 -为什么是用正弦和余弦函数,对于正弦函(sin):最大值是 1,最小值是 -1。对于余弦函数(cos):最大值是 1,最小值是 -1。也就是它们可以保证值是比较小的,而且也是符合深度学习模型可学习的参数。 +为什么是用正弦和余弦函数,对于正弦函(sin):最大值是 +1,最小值是 -1。对于余弦函数(cos):最大值是 +1,最小值是 -1。也就是它们可以保证值是比较小的,而且也是符合深度学习模型可学习的参数。 + +其中最重要的是允许模型学习相对位置:由于正弦和余弦函数的周期性(且是不同周期),对于任意固定偏移量 `k`,`PE(pos+k)`可以表示为 `PE(pos)` 的线性函数。这意味着模型可以很容易地通过学习注意力权重来关注相对位置,因为相对位置的编码可以通过简单的线性变换来获得。即我知道了绝对距离,也能知道相对距离。 -其中最重要的是允许模型学习相对位置:由于正弦和余弦函数的周期性,对于任意固定偏移量 `k`,`PE(pos+k)`可以表示为 `PE(pos)` 的线性函数。这意味着模型可以很容易地通过学习注意力权重来关注相对位置,因为相对位置的编码可以通过简单的线性变换来获得。 +正弦和余弦函数是线性函数的基础,因为它们满足以下的加法公式: +$$ +[ \sin(a + b) = \sin(a)\cos(b) + \cos(a)\sin(b) ] +\\ +[ \cos(a + b) = \cos(a)\cos(b) - \sin(a)\sin(b) ] +$$ ~~~markdown 原文: We chose this function because we 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). ~~~ +[可视化地址](https://erdem.pl/2021/05/understanding-positional-encoding-in-transformers#positional-encoding-visualization)你可以看到4个相对靠近的值,但是因为在不同的位置,值相差的完全不一样,也就是由正弦和余弦函数造的数据,在每个位置的值都是唯一的! + +image-20240430152239833 + 我们用更简单的语言来解释这个概念: