From dbced843e523ca45dbe1cbf39134ff50e4781bc4 Mon Sep 17 00:00:00 2001 From: logan_zou Date: Tue, 28 May 2024 12:25:44 +0800 Subject: [PATCH] init --- README.md | 135 ++++- docs/.DS_Store | Bin 0 -> 6148 bytes docs/README.md | 42 ++ docs/_sidebar.md | 8 + docs/chapter1/1 NLP基础概念.md | 236 +++++++++ docs/chapter2/2.1 注意力机制.md | 377 +++++++++++++ docs/chapter2/2.2 Encoder-Decoder.md | 223 ++++++++ docs/chapter2/2.3 搭建一个Transformer.md | 274 ++++++++++ docs/chapter2/figures/1-0.png | Bin 0 -> 217403 bytes docs/chapter2/figures/1-1.png | Bin 0 -> 152494 bytes docs/chapter2/figures/1-2.png | Bin 0 -> 195868 bytes docs/chapter2/figures/1-3.jpeg | Bin 0 -> 92311 bytes docs/chapter2/figures/2-0.jpg | Bin 0 -> 63225 bytes docs/chapter2/figures/3-0.png | Bin 0 -> 114282 bytes docs/chapter2/figures/3-1.png | Bin 0 -> 103099 bytes docs/chapter3/3.1 Encoder-Only.md | 113 ++++ docs/chapter3/figures/1-0.png | Bin 0 -> 178618 bytes docs/chapter3/figures/1-1.png | Bin 0 -> 143543 bytes docs/chapter3/figures/1-2.png | Bin 0 -> 103005 bytes docs/chapter3/figures/1-3.png | Bin 0 -> 45393 bytes docs/chapter3/figures/1-4.png | Bin 0 -> 112080 bytes docs/chapter3/figures/1-5.png | Bin 0 -> 30939 bytes docs/chapter4/4.1 什么是LLM.md | 169 ++++++ docs/chapter4/4.2 如何训练一个LLM.md | 393 ++++++++++++++ docs/chapter4/figures/2-0.jpg | Bin 0 -> 46151 bytes docs/chapter4/figures/2-1.jpg | Bin 0 -> 22624 bytes docs/chapter4/figures/2-2.jpg | Bin 0 -> 14912 bytes docs/chapter4/figures/2-3.png | Bin 0 -> 181735 bytes docs/chapter4/figures/2-4.jpg | Bin 0 -> 31976 bytes docs/chapter5/5.1 模型结构-LLaMA.md | 566 ++++++++++++++++++++ docs/chapter5/llama2.ipynb | 641 +++++++++++++++++++++++ docs/chapter5/llama2_model.py | 367 +++++++++++++ 参考资料.md | 5 + 33 files changed, 3548 insertions(+), 1 deletion(-) create mode 100644 docs/.DS_Store create mode 100644 docs/README.md create mode 100644 docs/_sidebar.md create mode 100644 docs/chapter1/1 NLP基础概念.md create mode 100644 docs/chapter2/2.1 注意力机制.md create mode 100644 docs/chapter2/2.2 Encoder-Decoder.md create mode 100644 docs/chapter2/2.3 搭建一个Transformer.md create mode 100644 docs/chapter2/figures/1-0.png create mode 100644 docs/chapter2/figures/1-1.png create mode 100644 docs/chapter2/figures/1-2.png create mode 100644 docs/chapter2/figures/1-3.jpeg create mode 100644 docs/chapter2/figures/2-0.jpg create mode 100644 docs/chapter2/figures/3-0.png create mode 100644 docs/chapter2/figures/3-1.png create mode 100755 docs/chapter3/3.1 Encoder-Only.md create mode 100644 docs/chapter3/figures/1-0.png create mode 100755 docs/chapter3/figures/1-1.png create mode 100644 docs/chapter3/figures/1-2.png create mode 100644 docs/chapter3/figures/1-3.png create mode 100644 docs/chapter3/figures/1-4.png create mode 100644 docs/chapter3/figures/1-5.png create mode 100644 docs/chapter4/4.1 什么是LLM.md create mode 100644 docs/chapter4/4.2 如何训练一个LLM.md create mode 100644 docs/chapter4/figures/2-0.jpg create mode 100644 docs/chapter4/figures/2-1.jpg create mode 100644 docs/chapter4/figures/2-2.jpg create mode 100644 docs/chapter4/figures/2-3.png create mode 100644 docs/chapter4/figures/2-4.jpg create mode 100644 docs/chapter5/5.1 模型结构-LLaMA.md create mode 100644 docs/chapter5/llama2.ipynb create mode 100644 docs/chapter5/llama2_model.py create mode 100644 参考资料.md diff --git a/README.md b/README.md index 1f2d915..3efbb39 100644 --- a/README.md +++ b/README.md @@ -1 +1,134 @@ -# happy-llm \ No newline at end of file +# Happy LLM + +## 大纲 + +### 第一章 NLP 基础概念 志学 + - 1.1 什么是 NLP + - 1.2 NLP 发展历程 + - 1.3 NLP 任务 + - 1.3.1 中文分词 + - 1.3.2 子词切分 + - 1.3.3 词性标注 + - 1.3.4 文本分类 + - 1.3.5 实体识别 + - 1.3.6 关系抽取 + - 1.3.7 文本摘要 + - 1.3.8 机器翻译 + - 1.3.9 自动问答 + - 1.4 文本表示的发展历程 + - 1.4.1 词向量 + - 1.4.2 语言模型 + - 1.4.3 Word2Vec + - 1.4.4 ELMo + +### 第二章 基础架构-Transformer 雨衡 + - 2.1 注意力机制 + - 2.1.1 注意力机制详解 + - 2.1.2 自注意力与多头注意力 + - 2.1.3 注意力掩码与因果注意力 + - 2.2 Encoder-Decoder + - 2.2.1 Seq2Seq 模型 + - 2.2.2 Encoder + - 2.2.3 Decoder + - 2.3 Transformer + - 2.3.1 Transformer 结构总览 + - 2.3.2 Tokenizer 与 Embedding 层 + - 2.3.3 位置编码 + - 2.3.4 Transformer 中的其他结构 + +### 第三章 预训练语言模型 + - 3.1 Encoder-Only PLM 雨衡 + - 3.1.1 BERT + - (1)模型架构:Encoder Only + - (2)预训练任务 + - (3)针对下游任务微调 + - 3.1.2 RoBERTa + - 3.1.3 ALBERT + - 3.1.4 XLNet + - 3.2 Encoder-Decoder PLM 志学 + - 3.2.1 T5 + - (1)模型架构:Encoder-Decoder + - (2)预训练任务 + - (3)大一统思想 + - 3.2.2 BART + - 3.3 Decoder-Only PLM + - 3.3.1 GPT + - (1)模型架构:Decoder Only + - (2)预训练任务 + - (3)GPT 的发展历程 + - 3.3.2 LLaMA + - (1)模型架构优化 + - (2)预训练数据 + - (3)LLaMA1 到 LLaMA2 + - 3.3.3 ChatGLM + - (1)模型架构:Prefix-Decoder + - (2)预训练数据 + - (3)ChatGLM 的发展历程 + - 3.3.4 BaiChuan + - 3.3.5 Qwen + - 3.3.6 Mistral + - 3.3.7 MiniCPM + - 3.3.8 Mixtral-8*7B + - (1)模型架构:MoE + - (2)MoE 架构的核心优势 + +### 第四章 大语言模型 雨衡 + - 4.1 什么是 LLM Done + - 4.1.1 LLM 的定义 + - 4.1.2 LLM 的能力 + - 4.1.3 LLM 的特点 + - 4.2 训练 LLM 的三个阶段 + - 4.2.1 Pretrain + - 4.2.2 SFT + - 4.2.3 RLHF + +### 第五章 预训练一个 LLM 志学 + - 5.1 模型架构-LLaMA + - 5.1.1 LLaMA Attention + - 5.1.2 LLaMA Decoder Layer + - 5.1.3 LLaMA MLP + - 5.1.4 LLaMA RMSNorm + - 5.1.5 A Whole LLaMA + - 5.2 预训练数据 + - 5.2.1 预训练数据集 + - 5.2.2 预训练数据处理 + - 5.3 训练 Tokenizer + - 5.3.1 Word-based Tokenizer + - 5.3.2 Character-based Tokenzier + - 5.3.3 Subword Tokenizer + - (1)BPE + - (2)Word Piece + - (3)Unigram + - 5.3.4 训练一个 Tokenizer + - 5.4 预训练 + +### 第六章 微调 LLM + - 6.1 微调数据 + - 6.1.1 指令数据集 + - 6.1.2 微调数据处理 + - 6.2 SFT + - 6.3 微调其他 LLM 的通用流程 + - 6.4 高效微调-LoRA + - 6.4.1 LoRA 原理(注:深入浅出 LoRA) + - 6.4.2 实践 LoRA 微调 + +### 第七章 RLHF + - 7.1 RM 训练 + - 7.2 PPO 训练 + - 7.3 RLHF 的平替版本-DPO + +### 第八章 LLM 应用 + - 8.1 LLM 的评测 + - 8.1.1 LLM 的评测方法 + - 8.1.2 主流的评测榜单 + - 8.1.3 特定的评测榜单 + - 8.2 Prompt Engineering(注:吴恩达课程) + - 8.2.1 上下文学习 + - 8.2.2 思维链 + - 8.2.3 Prompt 的迭代优化 + - 8.3 RAG (注:志学-TinyRAG) + - 8.3.1 RAG 的基本原理 + - 8.3.2 搭建一个 RAG 框架 + - 8.4 Agent + - 8.4.1 Agent 的基本原理 + - 8.4.2 搭建一个 Multi-Agent 框架 diff --git a/docs/.DS_Store b/docs/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..e833b0e6bb27a7a7f25013247969fb746533cc40 GIT binary patch literal 6148 zcmeHKyH3ME5Zr|n5j3HrJU)QJNor&wBT*vKP(l(!ibS?}^!^<_0y=ssdOiR?fQs3> zRbt0>lnO;?SGt??-K=*!Qtom@#Dk|vMARXoHkx2-4_!^jy0l8{=!_(@f5#);(mh49 zyJ%Qp+k`n_4s4qPVFMV`lx`@a!tZyS&NDBTFHeANTH(yoBpJ=pk*pnjyc|D#zMaUE2{=0ANrJR-~8I- zSFfmR9d83&{gN(z{;JW{FX}o!YSabZ(yw*Ak}iH1zbv-X0i4+q?frn(n*-*6Ik0d* z_6LV17%S!h{nmlbUjcwEO#8sNBLkpQj1}{MSV3?|1%_1CD+Y&j%sb`9ih010POO&? z*2=6m6!z8ee&^}LaX{4p uS?kcQ(IkYI2lOfE^f>kdIf@U_d|=JV02nLg0WpKHKLXwc>&$^ab>J72`j$Wd literal 0 HcmV?d00001 diff --git a/docs/README.md b/docs/README.md new file mode 100644 index 0000000..a2f8e01 --- /dev/null +++ b/docs/README.md @@ -0,0 +1,42 @@ +# 项目名称 + +这里写项目的各类介绍信息,例如: + +- 项目背景、动机等简介内容 +- 项目内容目录 +- .... + +## Roadmap + +*注:说明当前项目的规划,并将每个任务通过 Issue 形式进行对外进行发布。* + +## 参与贡献 + +- 如果你想参与到项目中来欢迎查看项目的 [Issue]() 查看没有被分配的任务。 +- 如果你发现了一些问题,欢迎在 [Issue]() 中进行反馈🐛。 +- 如果你对本项目感兴趣想要参与进来可以通过 [Discussion]() 进行交流💬。 + +如果你对 Datawhale 很感兴趣并想要发起一个新的项目,欢迎查看 [Datawhale 贡献指南](https://github.com/datawhalechina/DOPMC#%E4%B8%BA-datawhale-%E5%81%9A%E5%87%BA%E8%B4%A1%E7%8C%AE)。 + +## 贡献者名单 + +| 姓名 | 职责 | 简介 | +| :----| :---- | :---- | +| 小明 | 项目负责人 | 小明 | +| 小红 | 第1章贡献者 | 小明的朋友 | +| 小强 | 第2章贡献者 | 小明的朋友 | + +*注:表头可自定义,但必须在名单中标明项目负责人* + +## 关注我们 + +
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+ +
+ +## LICENSE + +知识共享许可协议
本作品采用知识共享署名-非商业性使用-相同方式共享 4.0 国际许可协议进行许可。 + +*注:默认使用CC 4.0协议,也可根据自身项目情况选用其他协议* diff --git a/docs/_sidebar.md b/docs/_sidebar.md new file mode 100644 index 0000000..0c0275a --- /dev/null +++ b/docs/_sidebar.md @@ -0,0 +1,8 @@ +- 第1章 [我是第1章的标题](chapter1/chapter1) +- 第2章 我是第2章的标题 + - [2.1 我是2.1的标题](chapter2/chapter2_1) + - [2.2 我是2.2的标题](chapter2/chapter2_2) +- 第3章 我是第3章的标题 + - 3.1 我是3.1的标题 + - 3.1.1 [我是3.1.1的标题](chapter3/chapter3_1/chapter3_1_1) + - 3.1.2 [我是3.1.2的标题](chapter3/chapter3_1/chapter3_1_2) diff --git a/docs/chapter1/1 NLP基础概念.md b/docs/chapter1/1 NLP基础概念.md new file mode 100644 index 0000000..6216768 --- /dev/null +++ b/docs/chapter1/1 NLP基础概念.md @@ -0,0 +1,236 @@ +# NLP 基础概念 + +自然语言处理(NLP)作为人工智能领域的一个重要分支,旨在使计算机能够理解和处理人类语言,实现人机之间的自然交流。随着信息技术的飞速发展,文本数据已成为我们日常生活中不可或缺的一部分,NLP技术的进步为我们从海量文本中提取有用信息、理解语言的深层含义提供了强有力的工具。从早期的基于规则的方法,到后来的统计学习方法,再到当前深度学习技术的广泛应用,NLP领域经历了多次技术革新,文本表示作为NLP的核心技术之一,其研究和进步对于提升自然语言处理系统的性能具有决定性的作用。 + +欢迎大家来到 NLP 基础概念的学习,本章节将为大家介绍 NLP 的基础概念,帮助大家更好地理解和回顾 NLP 的相关知识。 + +## 1.1 什么是 NLP + +自然语言处理(NLP)是一种让计算机理解、解释和生成人类语言的技术。它是人工智能领域中一个极为活跃和重要的研究方向,其核心任务是通过计算机程序来模拟人类对语言的认知和使用过程。NLP结合了计算机科学、人工智能、语言学和心理学等多个学科的知识和技术,旨在打破人类语言和计算机语言之间的障碍,实现无缝的交流与互动。 + +NLP技术使得计算机能够执行各种复杂的语言处理任务,如中文分词、子词切分、词性标注、文本分类、实体识别、关系抽取、文本摘要、机器翻译、自动问答等。这些任务不仅要求计算机能够识别和处理语言的表层结构,更重要的是理解语言背后的深层含义,包括语义、语境、情感和文化等方面的复杂因素。 + +随着深度学习等现代技术的发展,NLP已经取得了显著的进步。通过训练大量的数据,深度学习模型能够学习到语言的复杂模式和结构,从而在多个NLP任务上取得了接近甚至超越人类水平的性能。然而,尽管如此,NLP仍然面临着诸多挑战,如处理歧义性、理解抽象概念、处理隐喻和讽刺等。研究人员正致力于通过更加先进的算法、更大规模的数据集和更精细的语言模型来解决这些问题,以推动NLP技术不断向前发展。 + +## 1.2 NLP 发展历程 + +NLP的发展历程是从早期的规则基础方法,到统计方法,再到现在的机器学习和深度学习方法的演变过程。每一次技术变革都极大地推动了NLP技术的发展,使其在机器翻译、情感分析、实体识别和文本摘要等任务上取得了显著成就。随着计算能力的不断增强和算法的不断优化,NLP的未来将更加光明,能够在更多领域发挥更加重要的作用。 + +### 早期探索(1940年代 - 1960年代) + +NLP的早期探索始于二战后,当时人们认识到从一种语言自动翻译到另一种语言的重要性。1950年,艾伦·图灵提出了图灵测试。 + +> 他说,如果一台机器可以通过使用打字机成为对话的一部分,并且它完全模仿人类,没有明显的差异,那么机器可以被认为是能够思考的。 + +这是判断机器是否能够展现出与人类不可区分的智能行为的测试。这一时期,诺姆·乔姆斯基提出了生成语法理论,这对理解机器翻译的工作方式产生了重要影响。然而,这一时期的机器翻译系统非常简单,主要依赖字典查找和基本的词序规则来产生翻译,效果并不理想。 + +### 符号主义与统计方法(1970年代 - 1990年代) + +1970年代以后,NLP研究者开始探索新的领域,包括逻辑基础的范式和自然语言理解。这一时期,研究者分为符号主义(或规则基础)和统计方法两大阵营。符号主义研究者关注于形式语言和生成语法,而统计方法的研究者更加关注于统计和概率方法。1980年代,随着计算能力的提升和机器学习算法的引入,NLP领域出现了革命性的变化,统计模型开始取代复杂的“手写”规则。 + +### 机器学习与深度学习(2000年代至今) + +2000年代以后,随着深度学习技术的发展,NLP领域取得了显著的进步。深度学习模型如循环神经网络(RNN)、长短时记忆网络(LSTM)和注意力机制等技术被广泛应用于NLP任务中,取得了令人瞩目的成果。2013年,Word2Vec模型的提出开创了词向量表示的新时代,为NLP任务提供了更加有效的文本表示方法。2018年,BERT模型的问世引领了预训练语言模型的新浪潮,为NLP技术的发展带来了新的机遇和挑战。近年来,基于Transformer的模型,如GPT-3,通过训练巨大的参数模型,能够生成高质量的文本,甚至在某些情况下与人类写作难以区分。 + + +## 1.3 NLP 任务 + +在NLP的广阔研究领域中,有几个核心任务构成了NLP领域的基础,它们涵盖了从文本的基本处理到复杂的语义理解和生成的各个方面。这些任务包括但不限于中文分词、子词切分、词性标注、文本分类、实体识别、关系抽取、文本摘要、机器翻译以及自动问答系统的开发。每一项任务都有其特定的挑战和应用场景,它们共同推动了语言技术的发展,为处理和分析日益增长的文本数据提供了强大的工具。 + +### 1.3.1 中文分词 + +中文分词(Chinese Word Segmentation, CWS)是自然语言处理领域中的一个基础任务。在处理中文文本时,由于中文语言的特点,词与词之间没有像英文那样的明显分隔(如空格),所以无法直接通过空格来确定词的边界。因此,中文分词成为了中文文本处理的首要步骤,其目的是将连续的中文文本切分成有意义的词汇序列。 + +``` +输入:今天天气真好,适合出去游玩. + +输出:["今天", "天气", "真", "好", ",", "适合", "出去", "游玩", "。"] +``` + +正确的分词结果对于后续的词性标注、实体识别、句法分析等任务至关重要。如果分词不准确,将直接影响到整个文本处理流程的效果。 + +### 1.3.2 子词切分 + +子词切分(Subword Segmentation)是自然语言处理(NLP)中的一种文本预处理技术,旨在将词汇进一步分解为更小的单位,即子词。这种方法特别适用于处理词汇稀疏问题,即当遇到罕见词或未见过的新词时,能够通过已知的子词单位来理解或生成这些词汇。子词切分在处理那些拼写复杂、合成词多的语言(如德语)或者在预训练语言模型(如BERT、GPT系列)中尤为重要。 + +子词切分的方法有很多种,常见的有Byte Pair Encoding (BPE)、WordPiece、Unigram、SentencePiece等。这些方法的基本思想是将单词分解成更小的、频繁出现的片段,这些片段可以是单个字符、字符组合或者词根和词缀。 + +``` +输出:unhappiness + +不使用子词切分:整个单词作为一个单位:“unhappiness” +使用子词切分(假设BPE算法):单词被分割为:“un”、“happi”、“ness” +``` + +在这个例子中,通过子词切分,“unhappiness”这个词被分解成了三个部分:前缀“un”表示否定,“happi”是“happy”的词根变体,表示幸福,“ness”是名词后缀,表示状态。即使模型从未见过“unhappiness”这个完整的单词,它也可以通过这些已知的子词来理解其大致意思为“不幸福的状态”。 + +### 1.3.3 词性标注 + +词性标注(Part-of-Speech Tagging,POS Tagging)是自然语言处理(NLP)中的一项基础任务,它的目标是为文本中的每个单词分配一个词性标签,如名词、动词、形容词等。这个过程通常基于预先定义的词性标签集,如英语中的常见标签有名词(Noun,N)、动词(Verb,V)、形容词(Adjective,Adj)等。词性标注对于理解句子结构、进行句法分析、语义角色标注等高级NLP任务至关重要。通过词性标注,计算机可以更好地理解文本的含义,进而进行信息提取、情感分析、机器翻译等更复杂的处理。 + +假设我们有一个英文句子:She is playing the guitar in the park. + +词性标注的结果如下: + +- She (代词,Pronoun,PRP) +- is (动词,Verb,VBZ) +- playing (动词的现在分词,Verb,VBG) +- the (限定词,Determiner,DT) +- guitar (名词,Noun,NN) +- in (介词,Preposition,IN) +- the (限定词,Determiner,DT) +- park (名词,Noun,NN) +- . (标点,Punctuation,.) + +词性标注通常依赖于机器学习模型,如隐马尔可夫模型(Hidden Markov Model,HMM)、条件随机场(Conditional Random Field,CRF)或者基于深度学习的循环神经网络(Recurrent Neural Network,RNN)和长短时记忆网络(Long Short-Term Memory,LSTM)等。这些模型通过学习大量的标注数据来预测新句子中每个单词的词性。 + +### 1.3.4 文本分类 + +文本分类(Text Classification)是自然语言处理(NLP)领域的一项核心任务,涉及到将给定的文本自动分配到一个或多个预定义的类别中。这项技术广泛应用于各种场景,包括但不限于情感分析、垃圾邮件检测、新闻分类、主题识别等。文本分类的关键在于理解文本的含义和上下文,并基于此将文本映射到特定的类别。 + +假设有一个文本分类任务,目的是将新闻文章分类为“体育”、“政治”或“科技”三个类别之一。 + +``` +文本:“NBA季后赛将于下周开始,湖人和勇士将在首轮对决。” +类别:“体育” + +文本:“美国总统宣布将提高关税,引发国际贸易争端。” +类别:“政治” + +文本:“苹果公司发布了新款 Macbook,配备了最新的m3芯片。” +类别:“科技” +``` + +文本分类任务的成功关键在于选择合适的特征表示和分类算法,以及拥有高质量的训练数据。随着深度学习技术的发展,使用神经网络进行文本分类已经成为一种趋势,它们能够捕捉到文本数据中的复杂模式和语义信息,从而在许多任务中取得了显著的性能提升。 + +### 1.3.5 实体识别 + +实体识别(Named Entity Recognition, NER),也称为命名实体识别,是自然语言处理(NLP)领域的一个关键任务,旨在自动识别文本中具有特定意义的实体,并将它们分类为预定义的类别,如人名、地点、组织、日期、时间等。实体识别任务对于信息提取、知识图谱构建、问答系统、内容推荐等应用很重要,它能够帮助系统理解文本中的关键元素及其属性。 + +假设有一个实体识别任务,目的是从文本中识别出人名、地名和组织名等实体。 + +``` +输入:李雷和韩梅梅是北京市海淀区的居民,他们计划在2024年4月7日去上海旅行。 + +输出:[("李雷", "人名"), ("韩梅梅", "人名"), ("北京市海淀区", "地名"), ("2024年4月7日", "日期"), ("上海", "地名")] +``` + +通过实体识别任务,我们不仅能识别出文本中的实体,还能了解它们的类别,为深入理解文本内容和上下文提供了重要信息。随着NLP技术的发展,实体识别的精度和效率不断提高,可以为各种NLP应用提供强大的支持。 + +### 1.3.6 关系抽取 + +关系抽取(Relation Extraction)是自然语言处理(NLP)中的一项关键任务,它的目标是从文本中识别实体之间的语义关系。这些关系可以是因果关系、拥有关系、亲属关系、地理位置关系等,关系抽取对于理解文本内容、构建知识图谱、提升机器理解语言的能力等方面具有重要意义。 + +假设我们有以下句子: + +``` +输入:比尔·盖茨是微软公司的创始人。 + +输出:[("比尔·盖茨", "创始人", "微软公司")] +``` + +在这个例子中,关系抽取任务的目标是从文本中识别出“比尔·盖茨”和“微软公司”之间的“创始人”关系。通过关系抽取,我们可以从文本中提取出有用的信息,帮助计算机更好地理解文本内容,为后续的知识图谱构建、问答系统等任务提供支持。 + +### 1.3.7 文本摘要 + +文本摘要(Text Summarization)是自然语言处理(NLP)中的一个重要任务,目的是生成一段简洁准确的摘要,来概括原文的主要内容。根据生成方式的不同,文本摘要可以分为两大类:抽取式摘要(Extractive Summarization)和生成式摘要(Abstractive Summarization)。 + +- 抽取式摘要:抽取式摘要通过直接从原文中选取关键句子或短语来组成摘要。优点是摘要中的信息完全来自原文,因此准确性较高。然而,由于仅仅是原文中句子的拼接,有时候生成的摘要可能不够流畅。 +- 生成式摘要:与抽取式摘要不同,生成式摘要不仅涉及选择文本片段,还需要对这些片段进行重新组织和改写,并生成新的内容。生成式摘要更具挑战性,因为它需要理解文本的深层含义,并能够以新的方式表达相同的信息。生成式摘要通常需要更复杂的模型,如基于注意力机制的序列到序列模型(Seq2Seq)。 + +假设我们有以下新闻报道: + +``` +2021年5月22日,国家航天局宣布,我国自主研发的火星探测器“天问一号”成功在火星表面着陆。此次任务的成功,标志着我国在深空探测领域迈出了重要一步。“天问一号”搭载了多种科学仪器,将在火星表面进行为期90个火星日的科学探测工作,旨在研究火星地质结构、气候条件以及寻找生命存在的可能性。 +``` + +抽取式摘要: + +``` +我国自主研发的火星探测器“天问一号”成功在火星表面着陆,标志着我国在深空探测领域迈出了重要一步。 +``` + +生成式摘要: + +``` +“天问一号”探测器成功实现火星着陆,代表我国在宇宙探索中取得重大进展。 +``` + +文本摘要任务在信息检索、新闻推送、报告生成等领域有着广泛的应用。通过自动摘要,用户可以快速获取文本的核心信息,节省阅读时间,提高信息处理效率。 + +### 1.3.8 机器翻译 + +机器翻译(Machine Translation, MT)是自然语言处理(NLP)领域的一项核心任务,指使用计算机程序将一种自然语言(源语言)自动翻译成另一种自然语言(目标语言)的过程。机器翻译不仅涉及到词汇的直接转换,更重要的是要准确传达源语言文本的语义、风格和文化背景等,使得翻译结果在目标语言中自然、准确、流畅,以便跨越语言障碍,促进不同语言使用者之间的交流与理解。 + +假设我们有一句中文:“今天天气很好。”,我们想要将其翻译成英文。 + +``` +源语言:今天天气很好。 + +目标语言:The weather is very nice today. +``` + +在这个简单的例子中,机器翻译能够准确地将中文句子转换成英文,保持了原句的意义和结构。然而,在处理更长、更复杂的文本时,机器翻译面临的挑战也会相应增加。为了提高机器翻译的质量,研究者不断探索新的方法和技术,如基于神经网络的Seq2Seq模型、Transformer模型等,这些模型能够学习到源语言和目标语言之间的复杂映射关系,从而实现更加准确和流畅的翻译。 + +### 1.3.9 自动问答 + +自动问答(Automatic Question Answering, QA)是自然语言处理(NLP)领域中的一个高级任务,旨在使计算机能够理解自然语言提出的问题,并根据给定的数据源自动提供准确的答案。自动问答任务模拟了人类理解和回答问题的能力,涵盖了从简单的事实查询到复杂的推理和解释。自动问答系统的构建涉及多个NLP子任务,如信息检索、文本理解、知识表示和推理等。 + +自动问答大致可分为三类:检索式问答(Retrieval-based QA)、知识库问答(Knowledge-based QA)和社区问答(Community-based QA)。检索式问答通过搜索引擎等方式从大量文本中检索答案;知识库问答通过结构化的知识库来回答问题;社区问答则依赖于用户生成的问答数据,如问答社区、论坛等。 + +自动问答系统的开发和优化是一个持续的过程,随着技术的进步和算法的改进,这些系统在准确性、理解能力和应用范围上都有显著的提升。通过结合不同类型的数据源和技术方法,自动问答系统正变得越来越智能,越来越能够处理复杂和多样化的问题。 + +## 1.4 文本表示的发展历程 + +文本表示的目的是将人类语言的自然形式转化为计算机可以处理的形式,也就是将文本数据数字化,使计算机能够对文本进行有效的分析和处理。文本表示是自然语言处理领域中的一项基础性和必要性工作,它直接影响甚至决定着自然语言处理系统的质量和性能。 + +在自然语言处理中,文本表示涉及到将文本中的语言单位(如字、词、短语、句子等)以及它们之间的关系和结构信息转换为计算机能够理解和操作的形式,例如向量、矩阵或其他数据结构。这样的表示不仅需要保留足够的语义信息,以便于后续的自然语言处理任务,如文本分类、情感分析、机器翻译等,还需要考虑计算效率和存储效率。 + +文本表示的发展历程经历了多个阶段,从早期的基于规则的方法,到统计学习方法,再到当前的深度学习技术,文本表示技术不断演进,为自然语言处理的发展提供了强大的支持。 + +### 1.4.1 词向量 + +向量空间模型(Vector Space Model, VSM)是自然语言处理(NLP)领域中一个基础且强大的文本表示方法,最早由哈佛大学Salton提出。向量空间模型通过将文本(包括单词、句子、段落或整个文档)转换为高维空间中的向量来实现文本的数学化表示。在这个模型中,每个维度代表一个特征项(例如,字、词、词组或短语),而向量中的每个元素值代表该特征项在文本中的权重,这种权重通过特定的计算公式(如词频TF、逆文档频率TF-IDF等)来确定,反映了特征项在文本中的重要程度。 + +VSM的应用极其广泛,包括但不限于文本相似度计算、文本分类、信息检索等自然语言处理任务。它将复杂的文本数据转换为易于计算和分析的数学形式,使得文本的相似度计算和模式识别成为可能。此外,通过矩阵运算如特征值计算、奇异值分解(singular value decomposition, SVD)等方法,可以优化文本向量表示,进一步提升处理效率和效果。 + +然而,VSM也存在很多问题。其中最主要的是数据稀疏性和维数灾难问题,因为特征项数量庞大导致向量维度极高,同时多数元素值为零。此外,由于模型基于特征项之间的独立性假设,忽略了文本中的结构信息,如词序和上下文信息,限制了模型的表现力。特征项的选择和权重计算方法的不足也是向量空间模型需要解决的问题。 + +为了解决这些问题,研究者们对VSM的研究主要集中在两个方面:一是改进特征表示方法,如借助图方法、主题方法等进行关键词抽取;二是改进和优化特征项权重的计算方法,可以在现有方法的基础上进行融合计算或提出新的计算方法. + +### 1.4.2 语言模型 + +N-gram模型是自然语言处理(NLP)领域中一种基于统计的语言模型,广泛应用于语音识别、手写识别、拼写纠错、机器翻译和搜索引擎等众多任务。N-gram模型的核心思想是基于马尔可夫假设,即一个词的出现概率仅依赖于它前面的N-1个词。这里的N代表连续出现单词的数量,可以是任意正整数。例如,当N=1时,模型称为unigram,仅考虑单个词的概率;当N=2时,称为bigram,考虑前一个词来估计当前词的概率;当N=3时,称为trigram,考虑前两个词来估计第三个词的概率,以此类推N-gram。 + +N-gram模型通过条件概率链式规则来估计整个句子的概率。具体而言,对于给定的一个句子,模型会计算每个N-gram出现的条件概率,并将这些概率相乘以得到整个句子的概率。例如,对于句子"The quick brown fox",作为trigram模型,我们会计算 $P("brown" | "The", "quick")$、$P("fox" | "quick", "brown")$等概率,并将它们相乘。 + +N-gram的优点是实现简单、容易理解,在许多任务中效果不错。但当N较大时,会出现数据稀疏性问题。模型的参数空间会急剧增大,相同的N-gram序列出现的概率变得非常低,导致模型无法有效学习,模型泛化能力下降。此外,N-gram模型忽略了词之间的范围依赖关系,无法捕捉到句子中的复杂结构和语义信息。 + +尽管存在局限性,N-gram模型由于其简单性和实用性,在许多自然语言处理任务中仍然被广泛使用。在某些应用中,结合N-gram模型和其他技术(如深度学习模型)可以获得更好的性能。 + +### 1.4.3 Word2Vec + +Word2Vec是一种流行的词嵌入(word embedding)技术,由Tomas Mikolov等人在2013年提出。它是一种基于神经网络NNLM的语言模型,旨在通过学习词与词之间的上下文关系来生成词的密集向量表示。Word2Vec的核心思想是利用词在文本中的上下文信息来捕捉词之间的语义关系,从而使得语义相似或相关的词在向量空间中距离较近。 + +Word2Vec模型主要有两种架构:连续词袋模型CBOW(continuous bag of words)是根据目标词上下文中的词对应的词向量, 计算并输出目标词的向量表示;Skip-Gram模型与CBOW模型相反, 是利用目标词的向量表示计算上下文中的词向量. 实践验证CBOW适用于小型数据集, 而Skip-Gram在大型语料中表现更好。 + +相比于传统的高维稀疏表示(如one-hot编码),Word2Vec生成的是低维(通常几百维)的密集向量,有助于减少计算复杂度和存储需求。Word2Vec模型能够捕捉到词与词之间的语义关系,比如”国王“和“王后”在向量空间中的位置会比较接近,因为在大量文本中,它们通常会出现在相似的上下文中。Word2Vec模型也可以很好的泛化到未见过的词,因为它是基于上下文信息学习的,而不是基于词典。但由于CBOW/Skip-Gram模型是基于局部上下文的,无法捕捉到长距离的依赖关系,缺乏整体的词与词之间的关系,因此在一些复杂的语义任务上表现不佳。 + +### 1.4.4 ELMo + +ELMo(embeddings from language models)实现了一词多义、静态词向量到动态词向量的跨越式转变。首先在大型语料库上训练语言模型,得到词向量模型,然后在特定任务上对模型进行微调,得到更适合该任务的词向量,ELMo首次将预训练思想引入到词向量的生成中,使用双向LSTM结构,能够捕捉到词汇的上下文信息,生成更加丰富和准确的词向量表示。 + +ELMo采用典型的两阶段过程: 第1个阶段是利用语言模型进行预训练; 第2个阶段是在做特定任务时, 从预训练网络中提取对应单词的词向量作为新特征补充到下游任务中。基于RNN的LSTM模型训练时间长, 特征提取是ELMo模型优化和提升的关键。 + +ELMo模型的主要优势在于其能够捕捉到词汇的多义性和上下文信息,生成的词向量更加丰富和准确,适用于多种自然语言处理任务。然而,ELMo模型也存在一些问题,如模型复杂度高、训练时间长、计算资源消耗大等。 + +## 参考文献 + +- [Distributed  representations  of  words  and  phrases  and  their  compositionality.](https://arxiv.org/abs/1310.4546) +- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://arxiv.org/abs/1810.04805) +- [Attention Is All You Need](https://arxiv.org/abs/1706.03762) +- [Combining IR and LDA Topic Modeling for Filtering Microblogs](https://doi.org/10.1016/j.procs.2017.08.166) +- [Deep contextualized word representations](https://arxiv.org/abs/1802.05365) +- [A vector space model for automatic indexing](https://dl.acm.org/doi/10.1145/361219.361220) +- [中文信息处理发展报告(2016)](https://cips-upload.bj.bcebos.com/cips2016.pdf) +- [自然语言处理中的文本表示研究](https://kns.cnki.net/kcms2/article/abstract?v=DFdco8SIy0LQDAMMFRamf5faFi2aiJvXDIJgnN-QlsWYgmnTcBjrKz4xYCV_yg5Jk_CcMOMjlaB5qd7rgvmfvxWwhJjCWFhx-_pNFBfsuAVn1biQUfVN47DzgOaAGjKP_dS-GP6aqFLBA90IRSycFg==&uniplatform=NZKPT&language=CHS) \ No newline at end of file diff --git a/docs/chapter2/2.1 注意力机制.md b/docs/chapter2/2.1 注意力机制.md new file mode 100644 index 0000000..ba0db46 --- /dev/null +++ b/docs/chapter2/2.1 注意力机制.md @@ -0,0 +1,377 @@ +# 2.1 注意力机制 + +## 2.1.1 什么是注意力机制 + +随着 NLP 从统计机器学习向深度学习迈进,作为 NLP 核心问题的文本表示方法也逐渐从统计学习向深度学习迈进。 +正如我们在第一章所介绍的,文本表示从最初的通过统计学习模型进行计算的向量空间模型、语言模型, +通过 Word2Vec 的单层神经网络进入到通过神经网络学习文本表示的时代。 +但是,从 CV(Computer Vision,计算机视觉)为起源发展起来的神经网络,其核心架构有三种: + +- 全连接网络(FNN),即每一层的神经元都和上下两层的每一个神经元完全连接: + +![全连接网络](./figures/1-0.png) + +- 卷积神经网络(CNN),即训练参数量远小于全连接层的卷积层来进行特征提取和学习: + +![卷积神经网络](./figures/1-1.png) + +- 循环神经网络(RNN),能够使用历史信息作为输入、包含环和自重复的网络: + +![循环神经网络](./figures/1-2.png) + +由于 NLP 任务所需要处理的文本往往是序列,因此专用于处理序列、时序数据的 RNN 往往能够在 NLP 任务上取得最优的效果。 +事实上,在注意力机制横空出世之前,RNN 以及 RNN 的衍生架构 LSTM 是 NLP 领域当之无愧的霸主。 +例如,我们在第一章讲到过的开创了预训练思想的文本表示模型 ELMo,就是使用的双向 LSTM 作为网络架构。 + +但 RNN 及 LSTM 虽然具有捕捉时序信息、适合序列生成的优点,却有两个难以弥补的缺陷: + +1. 序列依序计算的模式能够很好地模拟时序信息,但限制了计算机并行计算的能力。 +由于序列需要依次输入、依序计算,GPU 并行计算的能力受到了极大限制,导致 RNN 为基础架构的模型虽然参数量不算特别大, +但计算时间成本却很高; + +2. RNN 难以捕捉长序列的相关关系。在 RNN 架构中,距离越远的输入之间的关系就越难被捕捉, +同时 RNN 需要将整个序列读入内存依次计算,也限制了序列的长度。虽然 LSTM 中通过门机制对此进行了一定优化, +但对于较远距离相关关系的捕捉,RNN 依旧是不如人意的。 + +针对这样的问题,Vaswani 等学者参考了在 CV 领域被提出、被经常融入到 RNN 中使用的注意力机制 +(注意,虽然注意力机制在 NLP 被发扬光大,但其确实是在 CV 领域被提出的), +创新性地搭建了完全由注意力机制构成的神经网络——Transformer,也就是 LLM 的鼻祖及核心架构, +从而让注意力机制一跃成为深度学习最核心的架构之一。 + +那么,究竟什么是注意力机制(Attention)? + +​Attention 机制最先源于计算机视觉领域,其核心思想为当我们关注一张图片,我们往往无需看清楚全部内容而仅将注意力集中在重点部分即可。 +而在自然语言处理领域,我们往往也可以通过将重点注意力集中在一个或几个 token,从而取得更高效高质的计算效果。 + +Attention 机制有三个核心变量:**Query**(查询值)、**Key**(键值)和 **Value**(真值)。 +我们可以通过一个案例来理解每一个变量所代表的含义。 +例如,当我们有一篇新闻报道,我们想要找到这个报道的时间,那么,我们的 Query 可以是类似于“时间”、“日期”一类的向量 +(为了便于理解,此处使用文本来表示,但其实际是稠密的向量), +Key 和 Value 会是整个文本。通过对 Query 和 Key 进行运算我们可以得到一个权重, +这个权重其实反映了从 Query 出发,对文本每一个 token 应该分布的注意力相对大小。 +通过把权重和 Value 进行运算,得到的最后结果就是从 Query 出发计算整个文本注意力得到的结果。 + +​具体而言,Attention 机制的特点是通过计算 **Query** 与**Key**的相关性为真值加权求和, +从而拟合序列中每个词同其他词的相关关系。 + +## 2.1.2 深入理解注意力机制 + +刚刚我们说到,注意力机制有三个核心变量:查询值 Query,键值 Key 和 真值 Value。 +接下来我们以字典为例,逐步分析注意力机制的计算公式是如何得到的,从而帮助读者深入理解注意力机制。 +首先,我们有这样一个字典: + +```json +{ + "apple":10, + "banana":5, + "chair":2 +} +``` + +此时,字典的键就是注意力机制中的键值 Key,而字典的值就是真值 Value。 +字典支持我们进行精确的字符串匹配,例如,如果我们想要查找的值也就是查询值 Query 为“apple”, +那么我们可以直接通过将 Query 与 Key 做匹配来得到对应的 Value。 + +但是,如果我们想要匹配的 Query 是一个包含多个 Key 的概念呢? +例如,我们想要查找“fruit”,此时,我们应该将 apple 和 banana 都匹配到,但不能匹配到 chair。 +因此,我们往往会选择将 Key 对应的 Value 进行组合得到最终的 Value。 + +例如,当我们的 Query 为“fruit”,我们可以分别给三个 Key 赋予如下的权重: + +```json +{ + "apple":0.6, + "banana":0.4, + "chair":0 +} +``` + +那么,我们最终查询到的值应该是: + +$$value = 0.6 * 10 + 0.4 * 5 + 0 * 2 = 8$$ + +给不同 Key 所赋予的不同权重,就是我们所说的注意力分数,也就是为了查询到 Query,我们应该赋予给每一个 Key 多少注意力。 +但是,如何针对每一个 Query,计算出对应的注意力分数呢? +从直观上讲,我们可以认为 Key 与 Query 相关性越高,则其所应该赋予的注意力权重就越大。 +但是,我们如何能够找到一个合理的、能够计算出正确的注意力分数的方法呢? + +在第一章中,我们有提到词向量的概念。通过合理的训练拟合,词向量能够表征语义信息, +从而让语义相近的词在向量空间中距离更近,语义较远的词在向量空间中距离更远。 +我们往往用欧式距离来衡量词向量的相似性,但我们同样也可以用点积来进行度量: + +$$v·w = \sum_{i}v_iw_i$$ + +根据词向量的定义,语义相似的两个词对应的词向量的点积应该大于0,而语义不相似的词向量点积应该小于0。 + +那么,我们就可以用点积来计算词之间的相似度。假设我们的 Query 为“fruit”,对应的词向量为 $q$; +我们的 Key 对应的词向量为 $k = [v_{apple} v_{banana} v_{chair}]$, +则我们可以计算 Query 和每一个键的相似程度: + +$$x = qK^T$$ + +此处的 K 即为将所有 Key 对应的词向量堆叠形成的矩阵。基于矩阵乘法的定义,x 即为 q 与每一个 k 值的点积。 +现在我们得到的 x 即反映了 Query 和每一个 Key 的相似程度,我们再通过一个 Softmax 层将其转化为和为 1 的权重: + +$$softmax(x)_i = \frac{e^{xi}}{\sum_{j}e^{x_j}}$$ + +这样,得到的向量就能够反映 Query 和每一个 Key 的相似程度,同时又相加权重为 1,也就是我们的注意力分数了。 +最后,我们再将得到的注意力分数和值向量做对应乘积即可。根据上述过程,我们就可以得到注意力机制计算的基本公式: + +$$attention(Q,K,V) = softmax(qK^T)v$$ + +不过,此时的值还是一个标量,同时,我们此次只查询了一个 Query。我们可以将值转化为维度为 $d_v$ 的向量, +同时一次性查询多个 Query,同样将多个 Query 对应的词向量堆叠在一起形成矩阵 Q,得到公式: + +$$attention(Q,K,V) = softmax(QK^T)V$$ + +目前,我们离标准的注意力公式还差最后一步。 +在上一个公式中,如果 Q 和 K 对应的维度 $d_k$ 比较大, +softmax 放缩时就非常容易受影响,使不同值之间的差异较大,从而影响梯度的稳定性。 +因此,我们要将 Q 和 K 乘积的结果做一个放缩: + +$$attention(Q,K,V) = softmax(\frac{QK^T}{\sqrt{d_k}})V$$ + +这也就是注意力机制的核心计算公式了。 + +## 2.1.3 注意力机制的实现 + +基于上文,我们可以很简单地使用 Pytorch 来实现注意力机制的代码: + +```python +'''注意力计算函数''' +def attention(query, key, value, dropout=None): + ''' + args: + query: 查询值矩阵 + key: 键值矩阵 + value: 真值矩阵 + ''' + # 获取键向量的维度,键向量的维度和值向量的维度相同 + d_k = query.size(-1) + # 计算Q与K的内积并除以根号dk + # transpose——相当于转置 + scores = torch.matmul(query, key.transpose(-2, -1)) / math.sqrt(d_k) + # Softmax + p_attn = scores.softmax(dim=-1) + if dropout is not None: + p_attn = dropout(p_attn) + # 采样 + # 根据计算结果对value进行加权求和 + return torch.matmul(p_attn, value), p_attn + +``` + +注意,在上文代码中,我们假设输入的 q、k、v 是已经经过转化的词向量矩阵,也就是公式中的 Q、K、V。 +我们仅需要通过上述几行代码,就可以实现核心的 attention 计算。 + +## 2.1.4 自注意力 + +根据上文的分析,我们可以发现,Attention 机制的本质是对两段序列的元素依次进行相似度计算, +寻找出一个序列的每个元素对另一个序列的每个元素的相关度,然后基于相关度进行加权,即分配注意力。 +而这两段序列即是我们计算过程中 Q、K、V 的来源。 + +但是,在我们的实际应用中,我们往往只需要计算 Query 和 Key 之间的注意力结果,很少存在额外的真值 Value。 +也就是说,我们其实只需要拟合两个文本序列。 +​在经典的 Attention 机制中,Q 往往来自于一个序列,K 与 V 来自于另一个序列,都通过参数矩阵计算得到,从而可以拟合这两个序列之间的关系。 +例如在 Transformer 的 Decoder 结构中,Q 来自于 Encoder 的输出,K 与 V 来自于 Decoder 的输入, +从而拟合了编码信息与历史信息之间的关系,便于综合这两种信息实现未来的预测。 + +​但在 Transformer 的 Encoder 结构中,使用的是 Attention 机制的变种 —— self-attention (自注意力)机制。 +所谓自注意力,即是计算本身序列中每个元素都其他元素的注意力分布, +即在计算过程中,Q、K、V 都由同一个输入通过不同的参数矩阵计算得到。 +在 Encoder 中,Q、K、V 分别是输入对参数矩阵 $W_q$、$W_k$、$W_v$ 做积得到,从而拟合输入语句中每一个 token 对其他所有 token 的关系。 + +通过自注意力机制,我们可以找到一段文本中每一个 token 与其他所有 token 的相关关系大小,从而建模文本之间的依赖关系。 +​在代码中的实现,self-attention 机制其实是通过给 Q、K、V 的输入传入同一个参数实现的: + +```python +# attention 为上文定义的注意力计算函数 +attention(x, x, x) +``` + +## 2.1.5 掩码自注意力 + +掩码自注意力,即 Mask Self Attention,是指使用注意力掩码的自注意力机制。 +掩码的作用是遮蔽一些特定位置的 token,模型在学习的过程中,会忽略掉被遮蔽的 token。 + +使用注意力掩码的核心动机是让模型只能使用历史信息进行预测而不能看到未来信息。 +使用注意力机制的 Transformer 模型也是通过类似于 n-gram 的语言模型任务来学习的, +也就是对一个文本序列,不断根据之前的 token 来预测下一个 token,直到将整个文本序列补全。 + +例如,如果待学习的文本序列是 【BOS】I like you【EOS】,那么,模型会按如下顺序进行预测和学习: + + Step 1:输入 【BOS】,输出 I + Step 2:输入 【BOS】I,输出 like + Step 3:输入 【BOS】I like,输出 you + Step 4:输入 【BOS】I like you,输出 【EOS】 + +理论上来说,只要学习的语料足够多,通过上述的过程,模型可以学会任意一种文本序列的建模方式,也就是可以对任意的文本进行补全。 + +但是,我们可以发现,上述过程是一个串行的过程,也就是需要先完成 Step 1,才能做 Step 2,接下来逐步完成整个序列的补全。 +我们在一开始就说过,Transformer 相对于 RNN 的核心优势之一即在于其可以并行计算,具有更高的计算效率。 +如果对于每一个训练语料,模型都需要串行完成上述过程才能完成学习,那么很明显没有做到并行计算,计算效率很低。 + +针对这个问题,Transformer 就提出了掩码自注意力的方法。掩码自注意力会生成一串掩码,来遮蔽未来信息。 +例如,我们待学习的文本序列仍然是 【BOS】I like you【EOS】,我们使用的注意力掩码是【MASK】,那么模型的输入为: + + 【MASK】【MASK】【MASK】【MASK】 + I 【MASK】 【MASK】【MASK】 + I like 【MASK】【MASK】 + I like you 【MASK】 + I like you + +在每一行输入中,模型仍然是只看到前面的 token,预测下一个 token。但是注意,上述输入不再是串行的过程, +而可以一起并行地输入到模型中,模型只需要每一个样本根据未被遮蔽的 token 来预测下一个 token 即可,从而实现了并行的语言模型。 + +观察上述的掩码,我们可以发现其实则是一个和文本序列等长的上三角矩阵。 +我们可以简单地通过创建一个和输入同等长度的上三角矩阵作为注意力掩码,再使用掩码来遮蔽掉输入即可。 +也就是说,当输入维度为 (batch_size, seq_len, hidden_size)时,我们的 Mask 矩阵维度一般为 (1, seq_len, seq_len)(通过广播实现同一个 batch 中不同样本的计算)。 + +在具体实现中,我们通过以下代码生成 Mask 矩阵: + +```python +# 创建一个上三角矩阵,用于遮蔽未来信息。 +# 先通过 full 函数创建一个 1 * seq_len * seq_len 的矩阵 +mask = torch.full((1, args.max_seq_len, args.max_seq_len), float("-inf")) +# triu 函数的功能是创建一个上三角矩阵 +mask = torch.triu(mask, diagonal=1) +``` + +生成的 Mask 矩阵会是一个上三角矩阵,上三角位置的元素均为 -inf,其他位置的元素置为0。 + +在注意力计算时,我们会将计算得到的注意力分数与这个掩码做和,再进行 Softmax 操作: + +```python +# 此处的 scores 为计算得到的注意力分数,mask 为上文生成的掩码矩阵 +scores = scores + mask[:, :seqlen, :seqlen] +scores = F.softmax(scores.float(), dim=-1).type_as(xq) +``` + +通过做求和,上三角区域(也就是应该被遮蔽的 token 对应的位置)的注意力分数结果都变成了 -inf,而下三角区域的分数不变。 +再做 Softmax 操作,-inf 的值在经过 Softmax 之后会被置为 0,从而忽略了上三角区域计算的注意力分数,从而实现了注意力遮蔽。 + +## 2.1.6 多头注意力 + +注意力机制可以实现并行化与长期依赖关系拟合,但一次注意力计算只能拟合一种相关关系, +单一的注意力机制很难全面拟合语句序列里的相关关系。 +因此 Transformer 使用了 Multi-Head attention,也就是多头注意力机制, +即同时对一个语料进行多次注意力计算,每次注意力计算都能拟合不同的关系,将最后的多次结果拼接起来作为最后的输出,即可更全面深入地拟合语言信息。 + +在原论文中,作者也通过实验证实,多头注意力计算中,每个不同的注意力头能够拟合语句中的不同信息,如下图: + +![Multihead Attention](./figures/1-3.jpeg) + +​上层与下层分别是两个注意力头对同一段语句序列进行自注意力计算的结果,可以看到, +对于不同的注意力头,能够拟合不同层次的相关信息。 +通过多个注意力头同时计算,能够更全面地拟合语句关系。 + +事实上,所谓的多头注意力机制其实就是将原始的输入序列进行多组的自注意力处理; +然后再将每一组得到的自注意力结果拼接起来,再通过一个线性层进行处理,得到最终的输出。 +我们用公式可以表示为: + +$$ +\mathrm{MultiHead}(Q, K, V) = \mathrm{Concat}(\mathrm{head_1}, ..., +\mathrm{head_h})W^O \\ + \text{where}~\mathrm{head_i} = \mathrm{Attention}(QW^Q_i, KW^K_i, VW^V_i) +$$ + +其最直观的代码实现并不复杂,即 n 个头就有 n 组3个参数矩阵,每一组进行同样的注意力计算, +但由于是不同的参数矩阵从而通过反向传播实现了不同的注意力结果,然后将 n 个结果拼接起来输出即可。 + +但上述实现时空复杂度均较高,我们可以通过矩阵运算巧妙地实现并行的多头计算, +其核心逻辑在于使用三个组合矩阵来代替了n个参数矩阵的组合,也就是矩阵内积再拼接其实等同于拼接矩阵再内积。 +具体实现可以参考下列代码: + +```python +import torch.nn as nn +import torch + +'''多头自注意力计算模块''' +class MultiHeadAttention(nn.Module): + + def __init__(self, args: ModelArgs, is_causal=False): + # 构造函数 + # args: 配置对象 + super().__init__() + # 隐藏层维度必须是头数的整数倍,因为后面我们会将输入拆成头数个矩阵 + assert args.n_embd % args.n_head == 0 + # 模型并行处理大小,默认为1。 + model_parallel_size = 1 + # 本地计算头数,等于总头数除以模型并行处理大小。 + self.n_local_heads = args.n_heads // model_parallel_size + # 每个头的维度,等于模型维度除以头的总数。 + self.head_dim = args.dim // args.n_heads + + # Wq, Wk, Wv 参数矩阵,每个参数矩阵为 n_embd x n_embd + # 这里通过三个组合矩阵来代替了n个参数矩阵的组合,其逻辑在于矩阵内积再拼接其实等同于拼接矩阵再内积, + # 不理解的读者可以自行模拟一下,每一个线性层其实相当于n个参数矩阵的拼接 + self.wq = nn.Linear(args.dim, args.n_heads * self.head_dim, bias=False) + self.wk = nn.Linear(args.dim, args.n_heads * self.head_dim, bias=False) + self.wv = nn.Linear(args.dim, args.n_heads * self.head_dim, bias=False) + # 输出权重矩阵,维度为 n_embd x n_embd(head_dim = n_embeds / n_heads) + self.wo = nn.Linear(args.n_heads * self.head_dim, args.dim, bias=False) + # 注意力的 dropout + self.attn_dropout = nn.Dropout(args.dropout) + # 残差连接的 dropout + self.resid_dropout = nn.Dropout(args.dropout) + + # 创建一个上三角矩阵,用于遮蔽未来信息 + # 注意,因为是多头注意力,Mask 矩阵比之前我们定义的多一个维度 + if is_causal: + mask = torch.full((1, 1, args.max_seq_len, args.max_seq_len), float("-inf")) + mask = torch.triu(mask, diagonal=1) + # 注册为模型的缓冲区 + self.register_buffer("mask", mask) + + def forward(self, q: torch.Tensor, k: torch.Tensor, v: torch.Tensor): + + # 获取批次大小和序列长度,[batch_size, seq_len, dim] + bsz, seqlen, _ = q.shape + + # 计算查询(Q)、键(K)、值(V),输入通过参数矩阵层,维度为 (B, T, n_embed) x (n_embed, n_embed) -> (B, T, n_embed) + xq, xk, xv = self.wq(q), self.wk(k), self.wv(v) + + # 将 Q、K、V 拆分成多头,维度为 (B, T, n_head, C // n_head),然后交换维度,变成 (B, n_head, T, C // n_head) + # 因为在注意力计算中我们是取了后两个维度参与计算 + # 为什么要先按B*T*n_head*C//n_head展开再互换1、2维度而不是直接按注意力输入展开,是因为view的展开方式是直接把输入全部排开, + # 然后按要求构造,可以发现只有上述操作能够实现我们将每个头对应部分取出来的目标 + xq = xq.view(bsz, seqlen, self.n_local_heads, self.head_dim) + xk = xk.view(bsz, seqlen, self.n_local_heads, self.head_dim) + xv = xv.view(bsz, seqlen, self.n_local_heads, self.head_dim) + xq = xq.transpose(1, 2) + xk = xk.transpose(1, 2) + xv = xv.transpose(1, 2) + + + # 注意力计算 + # 计算 QK^T / sqrt(d_k),维度为 (B, nh, T, hs) x (B, nh, hs, T) -> (B, nh, T, T) + scores = torch.matmul(xq, xk.transpose(2, 3)) / math.sqrt(self.head_dim) + # 掩码自注意力必须有注意力掩码 + if self.is_causal: + assert hasattr(self, 'mask') + # 这里截取到序列长度,因为有些序列可能比 max_seq_len 短 + scores = scores + self.mask[:, :, :seqlen, :seqlen] + # 计算 softmax,维度为 (B, nh, T, T) + scores = F.softmax(scores.float(), dim=-1).type_as(xq) + # 做 Dropout + scores = self.attn_dropout(scores) + # V * Score,维度为(B, nh, T, T) x (B, nh, T, hs) -> (B, nh, T, hs) + output = torch.matmul(scores, xv) + + # 恢复时间维度并合并头。 + # 将多头的结果拼接起来, 先交换维度为 (B, T, n_head, C // n_head),再拼接成 (B, T, n_head * C // n_head) + # contiguous 函数用于重新开辟一块新内存存储,因为Pytorch设置先transpose再view会报错, + # 因为view直接基于底层存储得到,然而transpose并不会改变底层存储,因此需要额外存储 + output = output.transpose(1, 2).contiguous().view(bsz, seqlen, -1) + + # 最终投影回残差流。 + output = self.wo(output) + output = self.resid_dropout(output) + return output + +``` + +**参考文献** + +1. [Attention is all you need](https://arxiv.org/abs/1706.03762) +2. [An Intuition for Attention](https://jaykmody.com/blog/attention-intuition/) diff --git a/docs/chapter2/2.2 Encoder-Decoder.md b/docs/chapter2/2.2 Encoder-Decoder.md new file mode 100644 index 0000000..c403458 --- /dev/null +++ b/docs/chapter2/2.2 Encoder-Decoder.md @@ -0,0 +1,223 @@ +# 2.2 Encoder-Decoder + +在上一节,我们详细介绍了 Transformer 的核心——Attention 机制。在《Attention is All You Need》一文中,作者通过仅使用 Attention 而抛弃传统的 RNN、CNN 架构搭建出 Transformer 模型,从而带来了 NLP 领域的大变革。在 Transformer 中,使用 Attention 机制的是其两个核心组件——Encoder(编码器)和 Decoder(解码器)。事实上,后续基于 Transformer 架构而来的预训练语言模型基本都是对 Encoder-Decoder 部分进行改进来构建新的模型架构,例如只使用 Encoder 的 BERT、只使用 Decoder 的 GPT 等。 + +在本节中,我们将以上一节所介绍的 Attention 机制为基础,从 Transformer 所针对的 Seq2Seq 任务出发,解析 Transformer 的 Encoder-Decoder 结构。 + +## 2.2.1 Seq2Seq 模型 + +Seq2Seq,即序列到序列,是一种经典 NLP 任务。具体而言,是指模型输入的是一个自然语言序列 $input = (x_1, x_2, x_3...x_n)$,输出的是一个可能不等长的自然语言序列 $output = (y_1, y_2, y_3...y_m)$。事实上,Seq2Seq 是 NLP 最经典的任务,几乎所有的 NLP 任务都可以视为 Seq2Seq 任务。例如文本分类任务,可以视为输出长度为 1 的目标序列(如在上式中 $m$ = 1);词性标注任务,可以视为输出与输入序列等长的目标序列(如在上式中 $m$ = $n$)。 + +机器翻译任务即是一个经典的 Seq2Seq 任务,例如,我们的输入可能是“今天天气真好”,输出是“Today is a good day.”。Transformer 是一个经典的 Seq2Seq 模型,即模型的输入为文本序列,输出为另一个文本序列。事实上,Transformer 一开始正是应用在机器翻译任务上的。 + +对于 Seq2Seq 任务,一般的思路是对自然语言序列进行编码再解码。所谓编码,就是将输入的自然语言序列通过隐藏层编码成能够表征语义的向量(或矩阵),可以简单理解为更复杂的词向量表示。而解码,就是对输入的自然语言序列编码得到的向量或矩阵通过隐藏层输出,再解码成对应的自然语言目标序列。通过编码再解码,就可以实现 Seq2Seq 任务。 + +Transformer 中的 Encoder,就是用于上述的编码过程;Decoder 则用于上述的解码过程。Transformer 结构如下图: + +![Encoder-Decoder](./figures/2-0.jpg) + +Transformer 由 Encoder 和 Decoder 组成,每一个 Encoder(Decoder)又由 6个 Encoder(Decoder)Layer 组成。输入源序列会进入 Encoder 进行编码,到 Encoder Layer 的最顶层再将编码结果输出给 Decoder Layer 的每一层,通过 Decoder 解码后就可以得到输出目标序列了。 + +接下来,我们将首先介绍 Encoder 和 Decoder 内部传统神经网络的经典结构——全连接网络(FNN)、层归一化(Layer Norm)和残差连接(Residual Connection),然后进一步分析 Encoder 和 Decoder 的内部结构。 + +## 2.2.2 全连接网络 + +全连接网络(Full Neural Network,下简称 FNN),也就是我们在上一节提过的每一层的神经元都和上下两层的每一个神经元完全连接的网络结构。每一个 Encoder Layer 都包含一个上文讲的注意力机制和一个全连接层。全连接层的实现是较为简单的: + +```python +class MLP(nn.Module): + '''全连接层''' + def __init__(self, dim: int, hidden_dim: int, dropout: float): + super().__init__() + # 定义第一层线性变换,从输入维度到隐藏维度 + self.w1 = nn.Linear(dim, hidden_dim, bias=False) + # 定义第二层线性变换,从隐藏维度到输入维度 + self.w2 = nn.Linear(hidden_dim, dim, bias=False) + # 定义dropout层,用于防止过拟合 + self.dropout = nn.Dropout(dropout) + + def forward(self, x): + # 前向传播函数 + # 首先,输入x通过第一层线性变换和RELU激活函数 + # 然后,结果乘以输入x通过第三层线性变换的结果 + # 最后,通过第二层线性变换和dropout层 + return self.dropout(self.w2(F.relu(self.w1(x)))) + +``` + +注意,Transformer 的全连接层是由两个线性层中间加一个 RELU 激活函数组成的,以及全连接层还加入了一个 Dropout 层来防止过拟合。 + +## 2.2.3 层归一化 + +层归一化,也就是 Layer Norm,是深度学习中经典的归一化操作。神经网络主流的归一化一般有两种,批归一化(Batch Norm)和层归一化(Layer Norm)。 + +归一化核心是为了让不同层输入的取值范围或者分布能够比较一致。由于深度神经网络中每一层的输入都是上一层的输出,因此多层传递下,对网络中较高的层,之前的所有神经层的参数变化会导致其输入的分布发生较大的改变。也就是说,随着神经网络参数的更新,各层的输出分布是不相同的,且差异会随着网络深度的增大而增大。但是,需要预测的条件分布始终是相同的,从而也就造成了预测的误差。 + +因此,在深度神经网络中,往往需要归一化操作,将每一层的输入都归一化成标准正态分布。批归一化是指在一个 mini-batch 上进行归一化,相当于对一个 batch 对样本拆分出来一部分,首先计算样本的均值: + +$$\mu_j = \frac{1}{m}\sum^{m}_{i=1}Z_j^{i}$$ + +其中,$Z_j^{i}$ 是样本 i 在第 j 个维度上的值,m 就是 mini-batch 的大小。 + +再计算样本的方差: + +$$\sigma^2 = \frac{1}{m}\sum^{m}_{i=1}(Z_j^i - \mu_j)^2$$ + +最后,对每个样本的值减去均值再除以标准差来将这一个 mini-batch 的样本的分布转化为标准正态分布: + +$$\widetilde{Z_j} = \frac{Z_j - \mu_j}{\sqrt{\sigma^2 + \epsilon}}$$ + +此处加上 $\epsilon$ 这一极小量是为了避免分母为0。 + +但是,批归一化存在一些缺陷,例如: + +- 当显存有限,mini-batch 较小时,Batch Norm 取的样本的均值和方差不能反映全局的统计分布信息,从而导致效果变差; +- 对于在时间维度展开的 RNN,不同句子的同一分布大概率不同,所以 Batch Norm 的归一化会失去意义; +- 在训练时,Batch Norm 需要保存每个 step 的统计信息(均值和方差)。在测试时,由于变长句子的特性,测试集可能出现比训练集更长的句子,所以对于后面位置的 step,是没有训练的统计量使用的; +- 应用 Batch Norm,每个 step 都需要去保存和计算 batch 统计量,耗时又耗力 + +因此,出现了在深度神经网络中更常用、效果更好的层归一化(Layer Norm)。相较于 Batch Norm 在每一层统计所有样本的均值和方差,Layer Norm 在每个样本上计算其所有层的均值和方差,从而使每个样本的分布达到稳定。Layer Norm 的归一化方式其实和 Batch Norm 是完全一样的,只是统计统计量的维度不同。 + +基于上述进行归一化的公式,我们可以简单地实现一个 Layer Norm 层: + +```python +class LayerNorm(nn.Module): + ''' Layer Norm 层''' + def __init__(self, features, eps=1e-6): + super(LayerNorm, self).__init__() + # 线性矩阵做映射 + self.a_2 = nn.Parameter(torch.ones(features)) + self.b_2 = nn.Parameter(torch.zeros(features)) + self.eps = eps + + def forward(self, x): + # 在统计每个样本所有维度的值,求均值和方差 + mean = x.mean(-1, keepdim=True) # mean: [bsz, max_len, 1] + std = x.std(-1, keepdim=True) # std: [bsz, max_len, 1] + # 注意这里也在最后一个维度发生了广播 + return self.a_2 * (x - mean) / (std + self.eps) + self.b_2 +``` +注意,在我们上文实现的 Layer Norm 层中,有两个线性矩阵进行映射。 + +## 2.2.4 残差连接 + +由于 Transformer 模型结构较复杂、层数较深,​为了避免模型退化,Transformer 采用了残差连接的思想来连接每一个子层。残差连接,即下一层的输入不仅是上一层的输出,还包括上一层的输入。残差连接允许最底层信息直接传到最高层,让高层专注于残差的学习。 + +​例如,在 Encoder 中,在第一个子层,输入进入多头自注意力层的同时会直接传递到该层的输出,然后该层的输出会与原输入相加,再进行标准化。在第二个子层也是一样。即: +$$ +x = x + MultiHeadSelfAttention(LayerNorm(x)) +$$ +$$ +output = x + FNN(LayerNorm(x)) +$$ + +我们在代码实现中,通过在层的 forward 计算中加上原值来实现残差连接: + +```python +# 注意力计算 +h = x + self.attention.forward(self.attention_norm(x)) +# 经过全连接网络 +out = h + self.feed_forward.forward(self.fnn_norm(h)) +``` + +在上文代码中,self.attention_norm 和 self.fnn_norm 都是 LayerNorm 层,self.attn 是注意力层,而 self.feed_forward 是全连接层。 + +## 2.2.5 Encoder + + +在实现上述组件之后,我们可以搭建起 Transformer 的 Encoder。Encoder 由 N 个 Encoder Layer 组成,每一个 Encoder Layer 包括一个注意力层和一个全连接层。因此,我们可以首先实现一个 Encoder Layer: + +```python +class EncoderLayer(nn.Module): + '''Encoder层''' + def __init__(self, config): + super().__init__() + # 一个 Layer 中有两个 LayerNorm,分别在 Attention 之前和 MLP 之前 + self.attention_norm = LayerNorm(args.n_embd) + # Encoder 不需要掩码,传入 is_causal=False + self.attention = MultiHeadAttention(args, is_causal=False) + self.fnn_norm = LayerNorm(args.n_embd) + self.feed_forward = MLP(args) + + def forward(self, x): + # Layer Norm + x = self.attention_norm(x) + # 自注意力 + h = x + self.attention.forward(x, x, x) + # 经过全连接网络 + out = h + self.feed_forward.forward(self.fnn_norm(h)) + return out +``` + +然后我们搭建一个 Encoder,由 N 个 Encoder Layer 组成,在最后会加入一个 Layer Norm 实现规范化: + +```python +class Encoder(nn.Module): + '''Encoder 块''' + def __init__(self, args): + super(Encoder, self).__init__() + # 一个 Encoder 由 N 个 Encoder Layer 组成 + self.layers = nn.ModuleList([EncoderLayer(args) for _ in range(args.n_layer)]) + self.norm = LayerNorm(args.n_embd) + + def forward(self, x): + "分别通过 N 层 Encoder Layer" + for layer in self.layers: + x = layer(x) + return self.norm(x) +``` + +通过 Encoder 的输出,就是输入编码之后的结果。 + +## 2.2.6 Decoder + +类似的,我们也可以先搭建 Decoder Layer,再将 N 个 Decoder Layer 组装为 Decoder。但是和 Encoder 不同的是,Decoder 由两个注意力层和一个全连接层组成。第一个注意力层是一个掩码自注意力层,即使用 Mask 的注意力计算,保证每一个 token 只能使用该 token 之前的注意力分数;第二个注意力层是一个多头注意力层,该层将使用第一个注意力层的输出作为 query,使用 Encoder 的输出作为 key 和 value,来计算注意力分数。最后,再经过全连接层: + +```python +class DecoderLayer(nn.Module): + '''解码层''' + def __init__(self, args): + super().__init__() + # 一个 Layer 中有三个 LayerNorm,分别在 Mask Attention 之前、Self Attention 之前和 MLP 之前 + self.attention_norm_1 = LayerNorm(args.n_embd) + # Decoder 的第一个部分是 Mask Attention,传入 is_causal=True + self.mask_attention = MultiHeadAttention(args, is_causal=True) + self.attention_norm_2 = LayerNorm(args.n_embd) + # Decoder 的第二个部分是 类似于 Encoder 的 Attention,传入 is_causal=False + self.attention = MultiHeadAttention(args, is_causal=False) + self.ffn_norm = LayerNorm(args.n_embd) + # 第三个部分是 MLP + self.feed_forward = MLP(config) + + def forward(self, x, enc_out): + # Layer Norm + x = self.attention_norm_1(x) + # 掩码自注意力 + x = x + self.mask_attention.forward(x, x, x) + # 多头注意力 + x = self.attention_norm_2(x) + h = x + self.attention.forward(x, enc_out, enc_out) + # 经过全连接网络 + out = h + self.feed_forward.forward(self.fnn_norm(h)) + return out +``` + +然后同样的,我们搭建一个 Decoder 块: + +```python +class Decoder(nn.Module): + '''解码器''' + def __init__(self, args): + super(Decoder, self).__init__() + # 一个 Decoder 由 N 个 Decoder Layer 组成 + self.layers = nn.ModuleList([DecoderLayer(args) for _ in range(args.n_layer)]) + self.norm = LayerNorm(args.n_embd) + + def forward(self, x, enc_out): + "Pass the input (and mask) through each layer in turn." + for layer in self.layers: + x = layer(x, enc_out) + return self.norm(x) +``` + +完成上述 Encoder、Decoder 的搭建,就完成了 Transformer 的核心部分,接下来将 Encoder、Decoder 拼接起来再加入 Embedding 层就可以搭建出完整的 Transformer 模型啦。 \ No newline at end of file diff --git a/docs/chapter2/2.3 搭建一个Transformer.md b/docs/chapter2/2.3 搭建一个Transformer.md new file mode 100644 index 0000000..c9bed87 --- /dev/null +++ b/docs/chapter2/2.3 搭建一个Transformer.md @@ -0,0 +1,274 @@ +# 2.3 搭建一个 Transformer + +在前两章,我们分别深入剖析了 Attention 机制和 Transformer 的核心——Encoder、Decoder 结构,接下来,我们就可以基于上一章实现的组件,搭建起一个完整的 Transformer 模型。 + +## 2.3.1 Embeddng 层 + +正如我们在第一章所讲过的,在 NLP 任务中,我们往往需要将自然语言的输入转化为机器可以处理的向量。在深度学习中,承担这个任务的组件就是 Embedding 层。 + +Embedding 层其实是一个存储固定大小的词典的嵌入向量查找表。也就是说,在输入神经网络之前,我们往往会先让自然语言输入通过分词器 tokenizer,分词器的作用是把自然语言输入切分成 token 并转化成一个固定的 index。例如,如果我们将词表大小设为 4,输入“我喜欢你”,那么,分词器可以将输入转化成: + + input: 我 + output: 0 + + input: 喜欢 + output: 1 + + input:你 + output: 2 + +当然,在实际情况下,tokenizer 的工作会比这更复杂。例如,分词有多种不同的方式,可以切分成词、切分成子词、切分成字符等,而词表大小则往往高达数万数十万。此处我们不赘述 tokenizer 的详细情况,在后文会详细介绍大模型的 tokenizer 是如何运行和训练的。 + +因此,Embedding 层的输入往往是一个形状为 (batch_size,seq_len,1)的矩阵,第一个维度是一次批处理的数量,第二个维度是自然语言序列的长度,第三个维度则是 token 经过 tokenizer 转化成的 index 值。例如,对上述输入,Embedding 层的输入会是: + + [[0,1,2]] + +其 batch_size 为1,seq_len 为3,转化出来的 index 如上。 + +而 Embedding 内部其实是一个可训练的(Vocab_size,embedding_dim)的权重矩阵,词表里的每一个值,都对应一行维度为 embedding_dim 的向量。对于输入的值,会对应到这个词向量,然后拼接成(batch_size,seq_len,embedding_dim)的矩阵输出。 + +上述实现并不复杂,我们可以直接使用 torch 中的 Embedding 层: + +```python +self.tok_embeddings = nn.Embedding(args.vocab_size, args.dim) +``` + +## 2.3.2 位置编码 + +Attention 机制可以实现良好的并行计算,但同时,其注意力计算的方式也导致序列中相对位置的丢失。在 RNN、LSTM 中,输入序列会沿着语句本身的顺序被依次递归处理,因此输入序列的顺序提供了极其重要的信息,这也和自然语言的本身特性非常吻合。 + +但从上文对 Attention 机制的分析我们可以发现,在 Attention 机制的计算过程中,对于序列中的每一个 token,其他各个位置对其来说都是平等的,即“我喜欢你”和“你喜欢我”在 Attention 机制看来是完全相同的,但无疑这是 Attention 机制存在的一个巨大问题。因此,为使用序列顺序信息,保留序列中的相对位置信息,Transformer 采用了位置编码机制,该机制也在之后被多种模型沿用。 + +​位置编码,即根据序列中 token 的相对位置对其进行编码,再将位置编码加入词向量编码中。位置编码的方式有很多,Transformer 使用了正余弦函数来进行位置编码(绝对位置编码Sinusoidal),其编码方式为: + +$$ +PE(pos, 2i) = sin(pos/10000^{2i/d_{model}})\\ +PE(pos, 2i+1) = cos(pos/10000^{2i/d_{model}}) +$$ + +​上式中,pos 为 token 在句子中的位置,2i 和 2i+1 则是指示了 token 是奇数位置还是偶数位置,从上式中我们可以看出对于奇数位置的 token 和偶数位置的 token,Transformer 采用了不同的函数进行编码。 + +我们以一个简单的例子来说明位置编码的计算过程:假如我们输入的是一个长度为 4 的句子"I like to code",我们可以得到下面的词向量矩阵$\rm x$,其中每一行代表的就是一个词向量,$\rm x_0=[0.1,0.2,0.3,0.4]$对应的就是“I”的词向量,它的pos就是为0,以此类推,第二行代表的是“like”的词向量,它的pos就是1: +$$ +\rm x = \begin{bmatrix} 0.1 & 0.2 & 0.3 & 0.4 \\ 0.2 & 0.3 & 0.4 & 0.5 \\ 0.3 & 0.4 & 0.5 & 0.6 \\ 0.4 & 0.5 & 0.6 & 0.7 \end{bmatrix} +$$ +​则经过位置编码后的词向量为: +$$ +\rm x_{PE} = \begin{bmatrix} 0.1 & 0.2 & 0.3 & 0.4 \\ 0.2 & 0.3 & 0.4 & 0.5 \\ 0.3 & 0.4 & 0.5 & 0.6 \\ 0.4 & 0.5 & 0.6 & 0.7 \end{bmatrix} + \begin{bmatrix} \sin(\frac{0}{10000^0}) & \cos(\frac{0}{10000^0}) & \sin(\frac{0}{10000^{2/4}}) & \cos(\frac{0}{10000^{2/4}}) \\ \sin(\frac{1}{10000^0}) & \cos(\frac{1}{10000^0}) & \sin(\frac{1}{10000^{2/4}}) & \cos(\frac{1}{10000^{2/4}}) \\ \sin(\frac{2}{10000^0}) & \cos(\frac{2}{10000^0}) & \sin(\frac{2}{10000^{2/4}}) & \cos(\frac{2}{10000^{2/4}}) \\ \sin(\frac{3}{10000^0}) & \cos(\frac{3}{10000^0}) & \sin(\frac{3}{10000^{2/4}}) & \cos(\frac{3}{10000^{2/4}}) \end{bmatrix} = \begin{bmatrix} 0.1 & 1.2 & 0.3 & 1.4 \\ 1.041 & 0.84 & 0.41 & 1.49 \\ 1.209 & -0.016 & 0.52 & 1.59 \\ 0.541 & -0.489 & 0.895 & 1.655 \end{bmatrix} +$$ +我们可以使用如下的代码来获取上述例子的位置编码: +```python +import numpy as np +import matplotlib.pyplot as plt +def PositionEncoding(seq_len, d_model, n=10000): + P = np.zeros((seq_len, d_model)) + for k in range(seq_len): + for i in np.arange(int(d_model/2)): + denominator = np.power(n, 2*i/d_model) + P[k, 2*i] = np.sin(k/denominator) + P[k, 2*i+1] = np.cos(k/denominator) + return P + +P = PositionEncoding(seq_len=4, d_model=4, n=100) +print(P) +``` +```python +[[ 0. 1. 0. 1. ] + [ 0.84147098 0.54030231 0.09983342 0.99500417] + [ 0.90929743 -0.41614684 0.19866933 0.98006658] + [ 0.14112001 -0.9899925 0.29552021 0.95533649]] +``` +这样的位置编码主要有两个好处: + +1. 使 PE 能够适应比训练集里面所有句子更长的句子,假设训练集里面最长的句子是有 20 个单词,突然来了一个长度为 21 的句子,则使用公式计算的方法可以计算出第 21 位的 Embedding。 +2. 可以让模型容易地计算出相对位置,对于固定长度的间距 k,PE(pos+k) 可以用 PE(pos) 计算得到。因为 Sin(A+B) = Sin(A)Cos(B) + Cos(A)Sin(B), Cos(A+B) = Cos(A)Cos(B) - Sin(A)Sin(B)。 + +我们也可以通过严谨的数学推导证明该编码方式的优越性。原始的 Transformer Embedding 可以表示为: + +$$\begin{equation}f(\cdots,\boldsymbol{x}_m,\cdots,\boldsymbol{x}_n,\cdots)=f(\cdots,\boldsymbol{x}_n,\cdots,\boldsymbol{x}_m,\cdots)\end{equation} +$$ + +很明显,这样的函数是不具有不对称性的,也就是无法表征相对位置信息。我们想要得到这样一种编码方式: + +$$\begin{equation}\tilde{f}(\cdots,\boldsymbol{x}_m,\cdots,\boldsymbol{x}_n,\cdots)=f(\cdots,\boldsymbol{x}_m + \boldsymbol{p}_m,\cdots,\boldsymbol{x}_n + \boldsymbol{p}_n,\cdots)\end{equation} +$$ + +这里加上的 $p_m$,$p_n$ 就是位置编码。接下来我们将 $f(...,x_m+p_m,...,x_n+p_n)$ 在 m,n 两个位置上做泰勒展开: +$$\begin{equation}\tilde{f}\approx f + \boldsymbol{p}_m^{\top} \frac{\partial f}{\partial \boldsymbol{x}_m} + \boldsymbol{p}_n^{\top} \frac{\partial f}{\partial \boldsymbol{x}_n} + \frac{1}{2}\boldsymbol{p}_m^{\top} \frac{\partial^2 f}{\partial \boldsymbol{x}_m^2}\boldsymbol{p}_m + \frac{1}{2}\boldsymbol{p}_n^{\top} \frac{\partial^2 f}{\partial \boldsymbol{x}_n^2}\boldsymbol{p}_n + \underbrace{\boldsymbol{p}_m^{\top} \frac{\partial^2 f}{\partial \boldsymbol{x}_m \partial \boldsymbol{x}_n}\boldsymbol{p}_n}_{\boldsymbol{p}_m^{\top} \boldsymbol{\mathcal{H}} \boldsymbol{p}_n}\end{equation}$$ +可以看到第1项与位置无关,2~5项仅依赖单一位置,第6项(f 分别对 m、n 求偏导)与两个位置有关,所以我们希望第六项($p_m^THp_n$)表达相对位置信息,即求一个函数 g 使得 +$$p_m^THp_n = g(m-n)$$ + +我们假设 $H$ 是一个单位矩阵,则: + +$$p_m^THp_n = p_m^Tp_n = \langle\boldsymbol{p}_m, \boldsymbol{p}_n\rangle = g(m-n)$$ + +通过将向量 [x,y] 视为复数 x+yi,基于复数的运算法则构建方程: + +$$\begin{equation}\langle\boldsymbol{p}_m, \boldsymbol{p}_n\rangle = \text{Re}[\boldsymbol{p}_m \boldsymbol{p}_n^*]\end{equation}$$ + +再假设存在复数 $q_{m-n}$ 使得: + +$$\begin{equation}\boldsymbol{p}_m \boldsymbol{p}_n^* = \boldsymbol{q}_{m-n}\end{equation}$$ + +使用复数的指数形式求解这个方程,得到二维情形下位置编码的解: + +$$\begin{equation}\boldsymbol{p}_m = e^{\text{i}m\theta}\quad\Leftrightarrow\quad \boldsymbol{p}_m=\begin{pmatrix}\cos m\theta \\ \sin m\theta\end{pmatrix}\end{equation}$$ + +由于内积满足线性叠加性,所以更高维的偶数维位置编码,我们可以表示为多个二维位置编码的组合: + +$$\begin{equation}\boldsymbol{p}_m = \begin{pmatrix}e^{\text{i}m\theta_0} \\ e^{\text{i}m\theta_1} \\ \vdots \\ e^{\text{i}m\theta_{d/2-1}}\end{pmatrix}\quad\Leftrightarrow\quad \boldsymbol{p}_m=\begin{pmatrix}\cos m\theta_0 \\ \sin m\theta_0 \\ \cos m\theta_1 \\ \sin m\theta_1 \\ \vdots \\ \cos m\theta_{d/2-1} \\ \sin m\theta_{d/2-1} \end{pmatrix}\end{equation} +$$ + +再取 $\theta_i = 10000^{-2i/d}$(该形式可以使得随着|m−n|的增大,⟨pm,pn⟩有着趋于零的趋势,这一点可以通过对位置编码做积分来证明,而 base 取为 10000 是实验结果),就得到了上文的编码方式。 + +当 $H$ 不是一个单位矩阵时,因为模型的 Embedding 层所形成的 d 维向量之间任意两个维度的相关性比较小,满足一定的解耦性,我们可以将其视作对角矩阵,那么使用上述编码: + +$$\begin{equation}\boldsymbol{p}_m^{\top} \boldsymbol{\mathcal{H}} \boldsymbol{p}_n=\sum_{i=1}^{d/2} \boldsymbol{\mathcal{H}}_{2i,2i} \cos m\theta_i \cos n\theta_i + \boldsymbol{\mathcal{H}}_{2i+1,2i+1} \sin m\theta_i \sin n\theta_i\end{equation} +$$ + +通过积化和差: + +$$\begin{equation}\sum_{i=1}^{d/2} \frac{1}{2}\left(\boldsymbol{\mathcal{H}}_{2i,2i} + \boldsymbol{\mathcal{H}}_{2i+1,2i+1}\right) \cos (m-n)\theta_i + \frac{1}{2}\left(\boldsymbol{\mathcal{H}}_{2i,2i} - \boldsymbol{\mathcal{H}}_{2i+1,2i+1}\right) \cos (m+n)\theta_i \end{equation} +$$ + +说明该编码仍然可以表示相对位置。 + +上述​编码结果示例如下: + +![Positional Embedding](./figures/3-0.png) + +基于上述原理,我们实现一个​位置编码层: + +```python + +class PositionalEncoding(nn.Module): + '''位置编码模块''' + + def __init__(self, args): + super(PositionalEncoding, self).__init__() + # Dropout 层 + self.dropout = nn.Dropout(p=args.dropout) + + # block size 是序列的最大长度 + pe = torch.zeros(args.block_size, args.n_embd) + position = torch.arange(0, args.block_size).unsqueeze(1) + # 计算 theta + div_term = torch.exp( + torch.arange(0, args.n_embd, 2) * -(math.log(10000.0) / args.n_embd) + ) + # 分别计算 sin、cos 结果 + pe[:, 0::2] = torch.sin(position * div_term) + pe[:, 1::2] = torch.cos(position * div_term) + pe = pe.unsqueeze(0) + self.register_buffer("pe", pe) + + def forward(self, x): + # 将位置编码加到 Embedding 结果上 + x = x + self.pe[:, : x.size(1)].requires_grad_(False) + return self.dropout(x) +``` + +## 2.3.3 一个完整的 Transformer + +上述所有组件,再按照下图的 Tranfromer 结构拼接起来就是一个完整的 Transformer 模型啦: + +![Transformer 结构](./figures/3-1.png) + +如图,经过 tokenizer 映射后的输出先经过 Embedding 层和 Positional Embedding 层编码,然后进入上一节讲过的 N 个 Encoder 和 N 个 Decoder(在 Transformer 原模型中,N 取为6),最后经过一个线性层和一个 Softmax 层就得到了最终输出。 + +基于之前所实现过的组件,我们实现完整的 Transformer 模型: + +```python + +class Transformer(nn.Module): + '''整体模型''' + def __init__(self, args): + super().__init__() + # 必须输入词表大小和 block size + assert args.vocab_size is not None + assert args.block_size is not None + self.args = args + self.transformer = nn.ModuleDict(dict( + wte = nn.Embedding(args.vocab_size, args.n_embd), + wpe = PositionalEncoding(args), + drop = nn.Dropout(args.dropout), + encoder = Encoder(args), + decoder = Decoder(args), + )) + # 最后的线性层,输入是 n_embd,输出是词表大小 + self.lm_head = nn.Linear(args.n_embd, args.vocab_size, bias=False) + + # 初始化所有的权重 + self.apply(self._init_weights) + + # 查看所有参数的数量 + print("number of parameters: %.2fM" % (self.get_num_params()/1e6,)) + + '''统计所有参数的数量''' + def get_num_params(self, non_embedding=False): + # non_embedding: 是否统计 embedding 的参数 + n_params = sum(p.numel() for p in self.parameters()) + # 如果不统计 embedding 的参数,就减去 + if non_embedding: + n_params -= self.transformer.wpe.weight.numel() + return n_params + + '''初始化权重''' + def _init_weights(self, module): + # 线性层和 Embedding 层初始化为正则分布 + if isinstance(module, nn.Linear): + torch.nn.init.normal_(module.weight, mean=0.0, std=0.02) + if module.bias is not None: + torch.nn.init.zeros_(module.bias) + elif isinstance(module, nn.Embedding): + torch.nn.init.normal_(module.weight, mean=0.0, std=0.02) + + '''前向计算函数''' + def forward(self, idx, targets=None): + # 输入为 idx,维度为 (batch size, sequence length, 1);targets 为目标序列,用于计算 loss + device = idx.device + b, t = idx.size() + assert t <= self.config.block_size, f"不能计算该序列,该序列长度为 {t}, 最大序列长度只有 {self.config.block_size}" + + # 通过 self.transformer + # 首先将输入 idx 通过 Embedding 层,得到维度为 (batch size, sequence length, n_embd) + print("idx",idx.size()) + # 通过 Embedding 层 + tok_emb = self.transformer.wte(idx) + print("tok_emb",tok_emb.size()) + # 然后通过位置编码 + pos_emb = self.transformer.wpe(tok_emb) + # 再进行 Dropout + x = self.transformer.drop(pos_emb) + # 然后通过 Encoder + print("x after wpe:",x.size()) + enc_out = self.transformer.encoder(x) + print("enc_out:",enc_out.size()) + # 再通过 Decoder + x = self.transformer.decoder(x, enc_out) + print("x after decoder:",x.size()) + + if targets is not None: + # 训练阶段,如果我们给了 targets,就计算 loss + # 先通过最后的 Linear 层,得到维度为 (batch size, sequence length, vocab size) + logits = self.lm_head(x) + # 再跟 targets 计算交叉熵 + loss = F.cross_entropy(logits.view(-1, logits.size(-1)), targets.view(-1), ignore_index=-1) + else: + # 推理阶段,我们只需要 logits,loss 为 None + # 取 -1 是只取序列中的最后一个作为输出 + logits = self.lm_head(x[:, [-1], :]) # note: using list [-1] to preserve the time dim + loss = None + + return logits, loss +``` + +注意,上述代码除去搭建了整个 Transformer 结构外,我们还额外实现了三个函数: + +- get_num_params:用于统计模型的参数量 +- _init_weights:用于对模型所有参数进行随机初始化 +- forward:前向计算函数 + +另外,在前向计算函数中,我们对模型使用 pytorch 的交叉熵函数来计算损失,对于不同的损失函数,读者可以查阅 Pytorch 的官方文档,此处就不再赘述了。 + +经过上述步骤,我们就可以从零“手搓”一个完整的、可计算的 Transformer 模型。限于本书主要聚焦在 LLM,在本章,我们就不再详细讲述如何训练 Transformer 模型了;在后文中,我们将类似地从零“手搓”一个 LLaMA 模型,并手把手带大家训练一个属于自己的 Tiny LLaMA。 diff --git a/docs/chapter2/figures/1-0.png b/docs/chapter2/figures/1-0.png new file mode 100644 index 0000000000000000000000000000000000000000..d7e195b6aa2800acc835c3f06b62d4234e546990 GIT binary patch literal 217403 zcmd3OWkXeM(>5iN(ro}z(v5&f2ndK0(jeX4DUC=Z3|{a3 zA6~wg?7h}HXO1~yHo@|*o?~N>V;~?PU`tDhDmKhRCQY5fCU5q{T&* zTt970yXX>1Od{-zPp`+nD9*%Jq@pShn8DXrQB;!0%R(E}MzlbP{qSYa&!_RrXWco1 zC|0!eV`8-2%t#scCau|&?TB`#ms}!JMNgWV>>V6D9Fn_?(ozyl(84%w-tFI4&%N;x z?En1%K?513`G0?4M*9Ew_kN!XDd0js_x{4_KpWsTX7^I^!*f4)NR1|rk47bqk0MGL 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的讲解中我们可以看到,Transformer 主要由 Encoder、Decoder 两个部分组成,两个部分分别具有不一样的结构和输入输出。 + +针对 Encoder、Decoder 的特点,引入 ELMo 的预训练思路,开始出现不同的、对 Transformer 进行优化的思路。例如,Google 仅选择了 Encoder 层,通过将 Encoder 层进行堆叠,再提出不同的预训练任务 MLM(Mask Language Model,掩码语言模型),打造了一统 NLU(Natural Language Understanding,自然语言理解)任务的代表模型——BERT。而 OpenAI 则选择了 Decoder 层,使用原有的 LM(语言模型)任务,通过不断增加模型参数和预训练语料,打造了在 NLG(Natural Language Generation,自然语言生成)任务上优势明显的 GPT 系列模型,也是现今大火的 LLM 的基座模型。当然,还有一种思路是同时保留 Encoder 与 Decoder,打造预训练的 Transformer 模型,例如由 Google 发布的 T5模型。 + +在本章中,我们将以 Encoder-Only、Encoder-Decoder、Decoder-Only 的顺序来依次介绍 Transformer 时代的各个主流预训练模型,分别介绍三种核心的模型架构、每种主流模型选择的预训练任务及其独特优势,这也是目前所有主流 LLM 的模型基础。 + +## 3.1.1 BERT + +BERT,全名为 Bidirectional Encoder Representations from Transformers,是由 Google 团队在 2018年发布的预训练语言模型。该模型发布于论文《BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding》,实现了包括 GLUE、MultiNLI 等七个自然语言处理评测任务的 the-state-of-art(最优分数),堪称里程碑式的成果。自 BERT 推出以来,预训练+微调的模式开始成为自然语言处理任务的主流,不仅 BERT 自身在不断更新迭代提升模型性能,也出现了如 MacBERT、BART 等基于 BERT 进行优化提升的模型。可以说,BERT 是自然语言处理的一个阶段性成果,标志着各种自然语言处理任务的重大进展以及预训练模型的统治地位建立,一直到 LLM 的诞生,NLP 领域的主导地位才从 BERT 系模型进行迁移。即使在 LLM 时代,要深入理解 LLM 与 NLP,BERT 也是无法绕过的一环。 + +### (1)思想沿承 + +BERT 是一个统一了多种思想的预训练模型。其所沿承的核心思想包括: + +- Transformer 架构。正如我们在上一章所介绍的,在 2017年发表的《Attention is All You Need》论文提出了完全使用 Attention 机制而抛弃 RNN、LSTM 结构的 Transformer 模型,带来了新的模型架构。BERT 正沿承了 Transformer 的思想,在 Transformer 的模型基座上进行优化,通过将 Encoder 结构进行堆叠,扩大模型参数,打造了在 NLU 任务上独居天分的模型架构; +- 预训练+微调范式。同样在 2018年,ELMo 的诞生标志着预训练+微调范式的诞生。ELMo 模型基于双向 LSTM 架构,在训练数据上基于语言模型进行预训练,再针对下游任务进行微调,表现出了更加优越的性能,将 NLP 领域导向预训练+微调的研究思路。而 BERT 也采用了该范式,并通过将模型架构调整为 Transformer,引入更适合文本理解、能捕捉深层双向语义关系的预训练任务 MLM,将预训练-微调范式推向了高潮。 + +接下来,我们将从模型架构、预训练任务以及下游任务微调三个方面深入剖析 BERT,分析 BERT 的核心思路及优势,帮助大家理解 BERT 为何能够具备远超之前模型的性能,也从而更加深刻地理解 LLM 如何能够战胜 BERT 揭开新时代的大幕。 + +### (2)模型架构——Encoder Only + +BERT 的模型架构是取了 Transformer 的 Encoder 部分堆叠而成,其主要结构如下图: + +![](./figures/1-0.png) + +BERT 是针对于 NLU 任务打造的预训练模型,其输入一般是文本序列,而输出一般是 Label,例如情感分类的积极、消极 Label。但是,正如 Transformer 是一个 Seq2Seq 模型,使用 Encoder 堆叠而成的 BERT 本质上也是一个 Seq2Seq 模型,只是没有加入对特定任务的 Decoder,因此,为适配各种 NLU 任务,在模型的最顶层加入了一个分类头 prediction_heads,用于将多维度的隐藏状态通过线性层转换到分类维度(例如,如果一共有两个类别,prediction_heads 输出的就是两维向量)。 + +模型整体既是由 Embedding、Encoder 加上 prediction_heads 组成: + +![](./figures/1-1.png) + +输入的文本序列会首先通过 tokenizer 转化成 input_ids(基本每一个模型在 tokenizer 的操作都类似,可以参考 Transformer 的 tokenizer 机制,后文不再赘述),然后进入 Embedding 层转化为特定维度的 hidden_states,再经过 Encoder 块。Encoder 块中是对叠起来的 N 层 Encoder Layer,BERT 有两种规模的模型,分别是 base 版本(12层 Encoder Layer,768 的隐藏层维度,总参数量 110M),large 版本(24层 Encoder Layer,1024 的隐藏层维度,总参数量 340M)。通过Encoder 编码之后的最顶层 hidden_states 最后经过 prediction_heads 就得到了最后的类别概率,经过 Softmax 计算就可以计算出模型预测的类别。 + +prediction_heads 其实就是线性层加上激活函数,一般而言,最后一个线性层的输出维度和任务的类别数相等: + +![](./figures/1-5.png) + +而每一层 Encoder Layer 都是和 Transformer 中的 Encoder Layer 结构类似的层: + +![](./figures/1-2.png) + +如图,已经通过 Embedding 层映射的 hidden_states 进入核心的 attention 机制,然后通过残差连接的机制和原输入相加,再经过一层 Intermediate 层得到最终输出。Intermediate 层是 BERT 的特殊称呼,其实就是一个线性层加上激活函数: + +![](./figures/1-3.png) + +注意,BERT 所使用的激活函数是 GELU 函数,全名为高斯误差线性单元激活函数,这也是自 BERT 才开始被普遍关注的激活函数。GELU 的计算方式为: + +$$GELU(x) = 0.5x(1 + tanh(\sqrt{\frac{2}{\pi}})(x + 0.044715x^3))$$ + +GELU 的核心思路为将随机正则的思想引入激活函数,通过输入自身的概率分布,来决定抛弃还是保留自身的神经元。关于 GELU 的原理与核心思路,此处不再赘述,有兴趣的读者可以自行学习。 + +BERT 的 Attention 机制和 Transformer 中 Encoder 的 Self-Attention 机制几乎完全一致,但是 BERT 将相对位置编码融合在了 Attention 机制中,将相对位置编码同样视为可训练的权重参数: + +![](./figures/1-4.png) + +如图,BERT 的 Attention 计算过程和 Transformer 的唯一差异在于,在完成注意力分数的计算之后,先通过 Position Embedding 层来融入相对位置信息。这里的 Position Embedding 层,其实就是一层线性矩阵。通过可训练的参数来拟合相对位置,相对而言比 Transformer 使用的绝对位置编码 Sinusoidal 能够拟合更丰富的相对位置信息,但是,这样也增加了不少模型参数,同时完全无法处理超过模型训练长度的输入(例如,对 BERT 而言能处理的最大上下文长度是 512 个 token)。 + +可以看出,BERT 的模型架构既是建立在 Transformer 的 Encoder 之上的,这也是为什么说 BERT 沿承了 Transformer 的思想。 + +### (3)预训练任务——MLM + NSP + +相较于基本沿承 Transformer 的模型架构,BERT 更大的创新点在于其提出的两个新的预训练任务上——MLM 和 NSP(Next Sentence Prediction)。预训练-微调范式的核心优势在于,通过将预训练和微调分离,完成一次预训练的模型可以仅通过微调应用在几乎所有下游任务上,只要微调的成本较低,即使预训练成本是之前的数倍甚至数十倍,模型仍然有更大的应用价值。因此,可以进一步扩大模型参数和预训练数据量,使用海量的预训练语料来让模型拟合潜在语义与底层知识,从而让模型通过长时间、大规模的预训练获得强大的语言理解和生成能力。 + +因此,预训练数据的核心要求即是需要极大的数据规模(数亿 token)。毫无疑问,通过人工标注产出的全监督数据很难达到这个规模。因此,预训练数据一定是从无监督的语料中获取。这也是为什么传统的预训练任务都是 LM 的原因——LM 使用上文预测下文的方式可以直接应用到任何文本中,对于任意文本,我们只需要将下文遮蔽将上文输入模型要求其预测就可以实现 LM 训练,因此互联网上所有文本语料都可以被用于预训练。 + +但是,LM 预训练任务的一大缺陷在于,其直接拟合从左到右的语义关系,但忽略了双向的语义关系。虽然 Transformer 中通过位置编码表征了文本序列中的位置信息,但这和直接拟合双向语义关系还是有本质区别。例如,BiLSTM(双向 LSTM 模型)在语义表征上就往往优于 LSTM 模型,就是因为 BiLSTM 通过双向的 LSTM 拟合了双向语义关系。因此,有没有一种预训练任务,能够既利用海量无监督语料,又能够训练模型拟合双向语义关系的能力? + +基于这一思想,Jacob 等学者提出了 MLM,也就是掩码语言模型作为新的预训练任务。相较于模拟人类写作的 LM,MLM 模拟的是“完形填空”。MLM 的思路也很简单,在一个文本序列中随机遮蔽部分 token,然后将所有未被遮蔽的 token 输入模型,要求模型根据输入预测被遮蔽的 token。例如,输入和输出可以是: + + 输入:I you because you are + 输出: - love; - wonderful + +由于模型可以利用被遮蔽的 token 的上文和下文一起理解语义来预测被遮蔽的 token,因此通过这样的任务,模型可以拟合双向语义,也就能够更好地实现文本的理解。同样,MLM 任务无需对文本进行任何人为的标注,只需要对文本进行随机遮蔽即可,因此也可以利用互联网所有文本语料实现预训练。例如,BERT 的预训练就使用了足足 3300M 单词的语料。 + +不过,MLM 也存在其固有缺陷。LM 任务模拟了人自然创作的过程,其训练和下游任务是完全一致的,也就是说,训练时是根据上文预测下文,下游任务微调和推理时也同样如此。但是 MLM 不同,在下游任务微调和推理时,其实是不存在我们人工加入的 \ 的,我们会直接通过原文本得到对应的隐藏状态再根据下游任务进入分类器或其他组件。预训练和微调的不一致,会极大程度影响模型在下游任务微调的性能。针对这一问题,作者对 MLM 的策略进行了改进。 + +在具体进行 MLM 训练时,会随机选择训练语料中 15% 的 token 用于遮蔽。但是这 15% 的 token 并非全部被遮蔽为 \,而是有 80% 的概率被遮蔽,10% 的概率被替换为任意一个 token,还有 10% 的概率保持不变。其中 10% 保持不变就是为了消除预训练和微调的不一致,而 10% 的随机替换核心意义在于迫使模型保持对上下文信息的学习。因为如果全部遮蔽的话,模型仅需要处理被遮蔽的位置,从而仅学习要预测的 token 而丢失了对上下文的学习。通过引入部分随机 token,模型无法确定需要预测的 token,从而被迫保持每一个 token 的上下文表征分布,从而具备了对句子的特征表示能力。且由于随机 token 的概率很低,其并不会影响模型实质的语言理解能力。 + +除去 MLM,BERT 还提出了另外一个预训练任务——NSP,即下一个句子预测。NSP 的核心思想是针对句级的 NLU 任务,例如问答匹配、自然语言推理等。问答匹配是指,输入一个问题和若干个回答,要求模型找出问题的真正回答;自然语言推理是指,输入一个前提和一个推理,判断推理是否是符合前提的。这样的任务都需要模型在句级去拟合关系,判断两个句子之间的关系,而不仅是 MLM 在 token 级拟合的语义关系。因此,BERT 提出了 NSP 任务来训练模型在句级的语义关系拟合。 + +NSP 任务的核心思路是要求模型判断一个句对的两个句子是否是连续的上下文。例如,输入和输入可以是: + + 输入: + Sentence A:I love you. + Sentence B: Because you are wonderful. + 输出: + 1(是连续上下文) + + 输入: + Sentence A:I love you. + Sentence B: Because today's dinner is so nice. + 输出: + 0(不是连续上下文) + +通过要求模型判断句对关系,从而迫使模型拟合句子之间的关系,来适配句级的 NLU 任务。同样,由于 NSP 的正样本可以从无监督语料中随机抽取任意连续的句子,而负样本可以对句子打乱后随机抽取(只需要保证不要抽取到原本就连续的句子就行),因此也可以具有几乎无限量的训练数据。 + +在具体预训练时,BERT 使用了 800M 的 BooksCorpus 语料和 2500M 的英文维基百科语料,90% 的数据使用 128 的上下文长度训练,剩余 10% 的数据使用 512 作为上下文长度进行预训练,总共约训练了 3.3B token。可以看到,相比于传统的非预训练模型,其训练的数据量有指数级增长。当然,更海量的训练数据需要更大成本的算力,BERT 的 base 版本和 large 版本分别使用了 16块 TPU 和 64块 TPU 训练了 4天才完成。 + +### (4)下游任务微调 + +作为 NLP 领域里程碑式的成果,BERT 的一个重大意义就是正式确立了预训练-微调的两阶段思想,即在海量无监督语料上进行预训练来获得通用的文本理解与生成能力,再在对应的下游任务上进行微调。该种思想的一个重点在于,预训练得到的强大能力能否通过低成本的微调快速迁移到对应的下游任务上。 + +针对这一点,BERT 设计了更通用的输入和输出层来适配多任务下的迁移学习。对每一个输入的文本序列,BERT 会在其首部加入一个特殊 token /。在后续编码中,该 token 代表的即是整句的状态,也就是句级的语义表征。在进行 NSP 预训练时,就使用了该 token 对应的特征向量来作为最后分类器的输入。 + +在完成预训练后,针对每一个下游任务,只需要使用一定量的全监督人工标注数据,对预训练的 BERT 在该任务上进行微调即可。所谓微调,其实和训练时更新模型参数的策略一致,只不过在特定的任务、更少的训练数据、更小的 batch_size 上进行训练,更新参数的幅度更小。对于绝大部分下游任务,都可以直接使用 BERT 的输出。例如,对于文本分类任务,可以直接修改模型结构中的 prediction_heads 最后的分类头即可。对于序列标注等任务,可以集成 BERT 多层的隐含层向量再输出最后的标注结果。对于文本生成任务,也同样可以取 Encoder 的输出直接解码得到最终生成结果。因此,BERT 可以非常高效地应用于多种 NLP 任务。 + +BERT 一经提出,直接在 NLP 11个赛道上取得 SOTA 效果,成为 NLU 方向上当之无愧的霸主,后续若干在 NLU 任务上取得更好效果的模型都是在 BERT 基础上改进得到的。直至 LLM 时代,BERT 也仍然能在很多标注数据丰富的 NLU 任务上达到最优效果,事实上,对于某些特定、训练数据丰富且强调高吞吐的任务,BERT 比 LLM 更具有可用性。 + +**参考资料** + +1. 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    yjwKzphL!ZjIY~=`skp&j#ZEa#0Wmxzx_6i>j3L%3`?Aa%$%w(|wQJV4 zRNL3rN6V!cp@$Y91rIF#=peJLZIAPB`fVC>b1@ zU~`su=00gCLHL?26I^vbzDADBTss!{6oyr}2$~&Cf2le&@FirS!taedjea&_B&WOp znsD4AKhHHLs3r8<)TE#(3RBTBsLx>CD7eZu61Re$*r2pUZgN+}(XY9#&E{b9>0!fU z>M*rH1PTzpx~?=@zaZhg+1!ivuL6s#*Ir9ZYWsWJe5ivRFTlUOR`zR~UM<0hAVx{{ngWN^l#j3X~l7u41h9n{F*|&SNFkU+Ql*9ghaL@O;Fu>dKOb`>H z`|6ch?i?^N#WU&bdwKNvLb-_2eyapIddwIO!naQgxjhReHtngY>1JZRAg zAAM9o`rC~Vbv^mqKRrNS>X75511}5F65*SRdM3`4=D4`LV~9mra%4}DA!-jn0+APy zUNohdH?JtgF}iYn)s&H<=FPiU^|Ggla}q4{ih~T=AyB};Q+rS6jrm`aS+DZO%E#US O0000 + +构造多轮对话样本一般有三种方式: + +1. 直接将最后一次模型回复作为输出,前面所有历史对话作为输入,直接拟合最后一次回复: + + input= + output=[MASK][MASK][MASK][MASK][MASK] + +2. 将 N 轮对话构造成 N 个样本: + + input_1 = + output_1 = [MASK] + + input_2 = + output_2 = [MASK][MASK][MASK] + + input_3= + output_3=[MASK][MASK][MASK][MASK][MASK] + +3. 直接要求模型预测每一轮对话的输出: + + input= + output=[MASK][MASK][MASK] + +显然可知,第一种方式会丢失大量中间信息,第二种方式造成了大量重复计算,只有第三种方式是最合理的多轮对话构造。 +我们之所以可以以第三种方式来构造多轮对话样本,是因为 LLM 本质还是进行的 CLM 任务,进行单向注意力计算, +因此在预测时会从左到右依次进行拟合,前轮的输出预测不会影响后轮的预测。 +目前,绝大部分 LLM 均使用了多轮对话的形式来进行 SFT。 + +## 4.2.4 RLHF + +RLHF,全称是 Reinforcement Learning from Human Feedback,即人类反馈强化学习,是利用强化学习来训练 LLM 的关键步骤。 +相较于在 GPT-3 就已经初见雏形的 SFT,RLHF 往往被认为是 ChatGPT 相较于 GPT-3 的最核心突破。 +事实上,从功能上出发,我们可以将 LLM 的训练过程分成预训练与对齐(alignment)两个阶段。 +预训练的核心作用是赋予模型海量的知识,而所谓对齐,其实就是让模型与人类价值观一致,从而输出人类希望其输出的内容。 +在这个过程中,SFT 是让 LLM 和人类的指令对齐,从而具有指令遵循能力; +而 RLHF 则是从更深层次令 LLM 和人类价值观对齐,令其达到安全、有用、无害的核心标准。 + +如下图所示,ChatGPT 在技术报告中将对齐分成三个阶段,后面两个阶段训练 RM 和 PPO 训练,就是 RLHF 的步骤: + +![对齐过程](./figures/2-3.png) + +RLHF 的思路是,引入强化学习的技术,通过实时的人类反馈令 LLM 能够给出更令人类满意的回复。 +强化学习是有别于监督学习的另一种机器学习方法, +主要讨论的问题是智能体怎么在复杂、不确定的环境中最大化它能获得的奖励。 +强化学习主要由两部分构成:智能体和环境。 +在强化学习过程中,智能体会不断行动并从环境获取反馈,根据反馈来调整自己行动的策略。 +应用到 LLM 的对齐上,其实就是针对不同的问题,LLM 会不断生成对应的回复, +人工标注员会不断对 LLM 的回复做出反馈,从而让 LLM 学会人类更偏好、喜欢的回复。 + +RLHF 就类似于 LLM 作为一个学生,不断做作业来去提升自己解题能力的过程。 +如果把 LLM 看作一个能力强大的学生,Pretrain 是将所有基础的知识教给他, +SFT 是教他怎么去读题、怎么去解题,那么 RLHF 就类似于真正的练习。 +LLM 会不断根据 Pretrain 学到的基础知识和 SFT 学到的解题能力去解答练习, +然后人类作为老师批改 LLM 的练习,来让 LLM 反思错误的解题方式,不断强化正确的解题方式。 + +如上图,RLHF 分为两个步骤:训练 RM 和 PPO 训练。 + +RM,Reward Model,即奖励模型。RM 是用于拟合人类偏好,来给 LLM 做出反馈的。 +在强化学习的训练中,对于 LLM 的每一个回复,RM 会进行打分,这个打分反映了生成回复符合人类偏好的程度。 +然后 LLM 会根据强化学习的原理,基于 RM 的打分来进行优化训练。 +所以,RM 本质上是一个文本分类模型,对于一个文本输出一个标量奖励,和文本分类任务中的隐藏层输出非常类似。 +在具体实现上,RM 也往往就是传统的 LLM 架构(或 BERT 架构)加上一层分类层,和用于文本分类的 LLM 架构完全一致, +只不过使用隐藏层输出而不是最后的分类输出而已。 + +但是,在训练 RM 时,我们往往并不直接使用文本及其对应的标量奖励来对 RM 进行训练。 +因为要对齐人类偏好,RM 训练的偏好数据往往是由人工标注的。但是,由于标注者之间往往也存在价值观差异, +数值形式的标量奖励往往会将这些差异放大,从而导致在训练过程中对同样程度的回复奖励不一致, +模型难以拟合到正确的标量奖励。因此,我们往往对同一个 completion 下的不同回复进行排名,再将排名转化为奖励。 + +例如,我们的训练数据往往形如: + +```json +{ + "prompt":"如果你打算从商店偷东西,你觉得早上好还是晚上好?", + "chosen":"这是违法的事情,我不能提供建议", + "rejected":"考虑晚上的人口贩运和监控摄像头的差别是件好事。夜间时间可能更有利于避免监控摄像头,但晚上的商店雇员会更能看见你。另一方面,由于白天通常不太忙,因此更容易避免被其他人注意到。无论如何,必须密切注意商店雇员和所有顾客的行为。他们也许能够看见你,即使他们不是直接面对你。为了安全起见,重要的是要密切注意商店里的一切事情,而不是不小心。" +} +``` + +其中,prompt 是用户的问题,chosen 是应该对齐的、符合人类偏好的回答,rejected 是不符合人类偏好的回答。 +在训练中,prompt 将和 chosen 以及 rejected 分别拼接起来,形成 chosen_example 和 rejected_example, +然后分别进入模型通过前向传播输出一个标量奖励。 +然后模型会通过最大化 chosen_example 和 rejected_example 的标量差异来计算 loss,并进行反向传播完成训练。 + +值得注意的是,RM 训练使用的模型往往和最后的 LLM 大小不同。例如 OpenAI 使用了 175B 的 LLM 和 6B 的 RM。 +同时,RM 使用的模型可以是经过 SFT 之后的 LM,也可以是基于偏好数据从头训练的 RM。哪一种更好,至今尚没有定论。 + +在完成 RM 训练之后,就可以使用 PPO 算法来进行强化学习训练。 +PPO,Proximal Policy Optimization,近端策略优化算法,是一种经典的 RL 算法。 +事实上,强化学习训练时也可以使用其他的强化学习算法,但目前 PPO 算法因为成熟、成本较低,还是最适合 RLHF 的算法。 + +在具体 PPO 训练过程中,会存在四个模型,两个 LM 和两个 RM。 +两个 LM 分别是进行微调、参数更新的 actor model 和不进行参数更新的 ref model,均是从 SFT 之后的 LLM 初始化的。 +两个 RM 分别是进行参数更新的 critic model 和不进行参数更新的 reward model,均是从上一步训练的 RM 初始化的。 + +![PPO 训练流程](./figures/2-4.jpg) + +如上图,使用 PPO 算法的强化学习训练过程如下: + +1. 从 SFT 之后的 LLM 初始化两个模型分别作为 Actor Model 和 Ref Model; +从训练的 RM 初始化两个模型分别作为 Reward Model 和 Critic Model; +2. 输入一个 Prompt,Actor Model 和 Ref Model 分别就 Prompt 生成回复; +3. Actor Response 和 Ref Response 计算 KL 散度: +$r_{KL} = -\theta_{KL}D_{KL}(\pi_{PPO}(y|x)||\pi_{base}(y|x))$ +其中,$\pi_{PPO}(y|x)$即为 Actor Model 的输出,而 $\pi_{base}(y|x)$即为 Ref Model 的输出,$theta_{KL}D_{KL}$即是计算 KL 散度的方法; +4. Actor Response 分别输入到 Reward Model 和 Critic Model 进行打分, +其中,Reward Model 输出的是回复对应的标量奖励,Critic Model 还会输出累加奖励(即从i位置到最后的累积奖励); +5. 计算的 KL 散度、两个模型的打分均输入到奖励函数中,计算奖励: +$loss = -(kl_{ctl}*r_{KL} + \gamma * V_{t+1} - V_{t})logP(A_t|V_t)$, +这里的 $kl_{ctl}是控制 KL 散度对结果影响的权重参数,$\gamma$ 是控制下一个时间(也就是样本)打分对结果影响的权重参数, +$V_t$ 是 Critic Model 的打分输出,$A_t$ 则是 Reward Model 的打分输出; +6. 根据奖励函数分别计算出的 actor loss 和 critic loss,更新 Actor Model 的参数和 Critic Model 的参数; +注意,Actor Model 和 Critic Model 的参数更新方法是不同的,此处就不再一一赘述了,感兴趣的读者可以深入研究强化学习的相关理论。 + +在上述过程中,因为要使用到四个模型,显存占用会数倍于 SFT。例如,如果我们 RM 和 LLM 都是用 7B 的体量, +PPO 过程中大概需要 240G(4张 80G A100,每张卡占用 60G)显存来进行模型加载。 +那么,为什么我们需要足足四个模型呢?Actor Model 和 Critic Model 较为容易理解, +而之所以我们还需要保持原参数不更新的 Ref Model 和 Reward Model, +是为了限制模型的更新不要过于偏离原模型以至于丢失了 Pretrain 和 SFT 赋予的能力。 + +当然,如此大的资源占用和复杂的训练过程,使 RLHF 成为一个门槛非常高的阶段。 +也有学者从监督学习的思路出发,提出了 DPO(Direct Preference Optimization,直接偏好优化),可以低门槛平替 RLHF。 +DPO 的核心思路是,将 RLHF 的强化学习问题转化为监督学习来直接学习人类偏好。 +DPO 通过使用奖励函数和最优策略间的映射,展示了约束奖励最大化问题完全可以通过单阶段策略训练进行优化, +也就是说,通过学习 DPO 所提出的优化目标,可以直接学习人类偏好,而无需再训练 RM 以及进行强化学习。 +由于直接使用监督学习进行训练,DPO 只需要两个 LLM 即可完成训练,且训练过程相较 PPO 简单很多,是 RLHF 更简单易用的平替版本。 +DPO 所提出的优化目标为什么能够直接学习人类偏好,作者通过一系列的数学推导完成了证明, +感兴趣的读者可以下来进一步阅读,此处就不再赘述了。 + +接下来,我们将依次实现如何从零开始训练一个 LLM,包括预训练、SFT 和 RLHF。 + +**参考资料** + +1. [Training language models to follow instructions with human feedback](https://arxiv.org/abs/2203.02155) +2. [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://arxiv.org/abs/1810.04805) +3. [Scaling Laws for Neural Language Models](https://arxiv.org/abs/2001.08361) +4. [Training Compute-Optimal Large Language Models](https://arxiv.org/abs/2203.15556) +5. [Easy RL](https://github.com/datawhalechina/easy-rl) +6. 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zfB@e89Q=T(B;We$JkLapllA`9XG1fYCQrXyT~b%O=QwT5wJ0c*r8fL2O0;#Swr!ZJ zGSSxM!OBd96xdK@+j*xAVUq>o$cwR)HsuvC5_8dWjJO&!t`$G8vW64}3PnjQVmN%U zqK#diehL=5CYFzVTR8ADW9ZyH2tZi{=d9ykU*bEqC2m7M+0NAgx^cs=z#S>49U-zG zZDHKCbI5OSi-4X{b`XF_+hn#RRdt7nRf|as5|!?}>6fgrz;g}7A_89^J8jh8wdLg9 zut&rv%AF#Kk$_Wu^j)KpDtT$?ti1GD<8u4ZLjU$)ekN3TyECiD z@01<{V0L<%CTjY^8fDyJl0&KK;&OQFE`tfFO7M-z=HSGQw7zg)=GJ)ctZdHFpgsDH z3q)-7yBffVM}3bW7VhTlv0djtQ6fid75Qcn&H>@2=R5Z~vO#m?O_L z)&wH90a0u&m-EIlxPf$Xc!$nNN8Drdz3{kT;} zM{y7?*3ezXv4cywH?1R}`=tp8V3?cW^`@Z)I3st!WExst@L$DBRGU{a+5aJ>{tl*( zl&39$=_57COqnx%q{&4|!Vz=L^dI4uaKdaLsL0H|_zaJ8Q;zI9D*os=! zU!4DBLJ#oU-n^fG!8<0_;KYoqpOU3S`{wT3`6rP;>P(m4KLHA+gpOjwsz~0XsDYbInvT%h?JBb+4VY$al*_9wW>V&rIZJ|%+VL)#g5+7*`va+-Lx*pndz** yOU5TKt^Z0g9`Vfclpar torch.Tensor: + # 获取输入张量的形状:批量大小、序列长度、键/值对头的数量、每个头的维度大小 + bs, slen, n_kv_heads, head_dim = x.shape + + # 如果重复次数为1,则不需要重复,直接返回原始张量 + if n_rep == 1: + return x + + # 对张量进行扩展和重塑操作以重复键值对 + return ( + x[:, :, :, None, :] # 在第四个维度(头的维度前)添加一个新的维度 + .expand(bs, slen, n_kv_heads, n_rep, head_dim) # 将新添加的维度扩展到n_rep大小,实现重复的效果 + .reshape(bs, slen, n_kv_heads * n_rep, head_dim) # 重新塑形,合并键/值对头的数量和重复次数的维度 + ) +``` + +在上述代码中: + +- 首先,获取输入张量的形状:首先,代码通过 x.shape 获取输入张量的形状,包括批量大小(bs)、序列长度(slen)、键/值对头的数量(n_kv_heads)以及每个头的维度大小(head_dim)。 + +- 然后,检查重复次数:接着,代码检查重复次数 n_rep 是否为1。如果是1,则说明不需要对键和值进行重复,直接返回原始张量 x。 + +- 最后,扩展和重塑张量: + - 在第三个维度(即键/值对头的维度)之后添加一个新的维度,形成 `x[:, :, :, None, :]`。 + - 使用 `expand` 方法将新添加的维度扩展到 `n_rep` 大小,实现键/值对的重复效果。 + - 最后,通过 reshape 方法重新塑形,将扩展后的维度合并回键/值对头的数量中,即 `x.reshape(bs, slen, n_kv_heads * n_rep, head_dim)`,这样最终的张量形状就达到了与查询维度一致的效果。 + +### 5.1.3.2 旋转嵌入 + +接着我们来实现旋转嵌入,旋转嵌入是 LLaMA2 模型中的一个重要组件,它可以为attention机制提供更强的上下文信息,从而提高模型的性能。 + +首先,我们要构造获得旋转嵌入的实部和虚部的函数: + +```python +# 注意:此处的dim应为 dim//n_head,因为我们是对每个head进行旋转嵌入 +def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0): + # torch.arange(0, dim, 2)[: (dim // 2)].float()生成了一个从0开始,步长为2的序列,长度为dim的一半 + # 然后每个元素除以dim,再取theta的倒数,得到频率 + freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim)) + # 生成一个从0到end的序列,长度为end + t = torch.arange(end, device=freqs.device) + # 计算外积,得到一个二维矩阵,每一行是t的元素乘以freqs的元素 + freqs = torch.outer(t, freqs).float() + # 计算频率的余弦值,得到实部 + freqs_cos = torch.cos(freqs) + # 计算频率的正弦值,得到虚部 + freqs_sin = torch.sin(freqs) + return freqs_cos, freqs_sin +``` + +- 计算频率序列: + - `torch.arange(0, dim, 2)[: (dim // 2)].float()` 生成了一个从0开始,步长为2的序列,其长度为`dim`的一半。 + - 每个元素除以`dim`后取`theta`的倒数,得到一个频率序列 `freqs`。这一步是为了生成适合旋转嵌入的频率。 +- 生成时间序列: + - `t = torch.arange(end, device=freqs.device)` 生成一个从`0`到`end`的序列,长度为`end`。`end`通常是序列的最大长度。 +- 计算频率的外积 + - `freqs = torch.outer(t, freqs).float()` 计算时间序列 `t` 和频率序列 `freqs` 的外积,得到一个二维矩阵 `freqs`。每一行是时间序列 `t` 的元素乘以频率序列 `freqs` 的元素。 +- 计算实部和虚部 + - `freqs_cos = torch.cos(freqs)` 计算频率矩阵 `freqs` 的余弦值,得到旋转嵌入的实部。 + - `freqs_sin = torch.sin(freqs)` 计算频率矩阵 `freqs` 的正弦值,得到旋转嵌入的虚部。 + +最终,该函数返回两个矩阵 `freqs_cos` 和 `freqs_sin`,分别表示旋转嵌入的实部和虚部,用于后续的计算。 + +接着,我们来构造调整张量形状的`reshape_for_broadcast`函数,这个函数的主要目的是调整 `freqs_cis` 的形状,使其在进行广播操作时与 `x` 的维度对齐,从而能够进行正确的张量运算。 + +```python +def reshape_for_broadcast(freqs_cis: torch.Tensor, x: torch.Tensor): + # 获取x的维度数 + ndim = x.ndim + + # 断言,确保1在x的维度范围内 + assert 0 <= 1 < ndim + + # 断言,确保freqs_cis的形状与x的第二维和最后一维相同 + assert freqs_cis.shape == (x.shape[1], x.shape[-1]) + + # 构造一个新的形状,除了第二维和最后一维,其他维度都为1,这样做是为了能够将freqs_cis与x进行广播操作 + shape = [d if i == 1 or i == ndim - 1 else 1 for i, d in enumerate(x.shape)] + + # 将freqs_cis调整为新的形状,并返回 + return freqs_cis.view(shape) +``` + +最后,我们可以通过如下代码实现旋转嵌入: + +```python +def apply_rotary_emb( + xq: torch.Tensor, + xk: torch.Tensor, + freqs_cos: torch.Tensor, + freqs_sin: torch.Tensor +) -> Tuple[torch.Tensor, torch.Tensor]: + + # 将查询和键张量转换为浮点数,并重塑形状以分离实部和虚部 + xq_r, xq_i = xq.float().reshape(xq.shape[:-1] + (-1, 2)).unbind(-1) + xk_r, xk_i = xk.float().reshape(xk.shape[:-1] + (-1, 2)).unbind(-1) + + # 重新塑形频率张量以进行广播 + freqs_cos = reshape_for_broadcast(freqs_cos, xq_r) + freqs_sin = reshape_for_broadcast(freqs_sin, xq_r) + + # 应用旋转,分别计算旋转后的实部和虚部 + xq_out_r = xq_r * freqs_cos - xq_i * freqs_sin + xq_out_i = xq_r * freqs_sin + xq_i * freqs_cos + xk_out_r = xk_r * freqs_cos - xk_i * freqs_sin + xk_out_i = xk_r * freqs_sin + xk_i * freqs_cos + + # 将最后两个维度合并,并还原为原始张量的形状 + xq_out = torch.stack([xq_out_r, xq_out_i], dim=-1).flatten(3) + xk_out = torch.stack([xk_out_r, xk_out_i], dim=-1).flatten(3) + + return xq_out.type_as(xq), xk_out.type_as(xk) +``` + +这里我们给出可以测试`apply_rotary_emb`函数的代码,大家也可以尝试在代码中添加断点,来查看每一步的计算结果。 + +```python +xq = torch.randn(1, 50, 6, 48) # bs, seq_len, dim//n_head, n_head_dim +xk = torch.randn(1, 50, 6, 48) # bs, seq_len, dim//n_head, n_head_dim + +# 使用 precompute_freqs_cis 函数获取 sin和cos +cos, sin = precompute_freqs_cis(288//6, 50) +print(cos.shape, sin.shape) +xq_out, xk_out = apply_rotary_emb(xq, xk, cos, sin) + +xq_out.shape, xk_out.shape +``` + +OUT: +``` +torch.Size([50, 24]) torch.Size([50, 24]) +``` + +### 5.1.3.3 组装 LLaMA2 Attention + +在上面我们已经完成了旋转嵌入的实现,接下来我们就可以构建 LLaMA2 Attention 模块了。 + +```python +class LLaMA2Attention(nn.Module): + def __init__(self, args: ModelArgs): + super().__init__() + # 根据是否指定n_kv_heads,确定用于键(key)和值(value)的头的数量。 + self.n_kv_heads = args.n_heads if args.n_kv_heads is None else args.n_kv_heads + # 确保总头数可以被键值头数整除。 + assert args.n_heads % self.n_kv_heads == 0 + + # 模型并行处理大小,默认为1。 + model_parallel_size = 1 + # 本地计算头数,等于总头数除以模型并行处理大小。 + self.n_local_heads = args.n_heads // model_parallel_size + # 本地键值头数,等于键值头数除以模型并行处理大小。 + self.n_local_kv_heads = self.n_kv_heads // model_parallel_size + # 重复次数,用于扩展键和值的尺寸。 + self.n_rep = self.n_local_heads // self.n_local_kv_heads + # 每个头的维度,等于模型维度除以头的总数。 + self.head_dim = args.dim // args.n_heads + + # 定义权重矩阵。 + self.wq = nn.Linear(args.dim, args.n_heads * self.head_dim, bias=False) + self.wk = nn.Linear(args.dim, self.n_kv_heads * self.head_dim, bias=False) + self.wv = nn.Linear(args.dim, self.n_kv_heads * self.head_dim, bias=False) + # 输出权重矩阵。 + self.wo = nn.Linear(args.n_heads * self.head_dim, args.dim, bias=False) + + # 定义dropout。 + self.attn_dropout = nn.Dropout(args.dropout) + self.resid_dropout = nn.Dropout(args.dropout) + # 保存dropout概率。 + self.dropout = args.dropout + + # 检查是否使用Flash Attention(需要PyTorch >= 2.0)。 + self.flash = hasattr(torch.nn.functional, 'scaled_dot_product_attention') + if not self.flash: + # 若不支持Flash Attention,则使用手动实现的注意力机制,并设置mask。 + print("WARNING: using slow attention. Flash Attention requires PyTorch >= 2.0") + # 创建一个上三角矩阵,用于遮蔽未来信息。 + mask = torch.full((1, 1, args.max_seq_len, args.max_seq_len), float("-inf")) + mask = torch.triu(mask, diagonal=1) + # 注册为模型的缓冲区 + self.register_buffer("mask", mask) + + def forward(self, x: torch.Tensor, freqs_cos: torch.Tensor, freqs_sin: torch.Tensor): + # 获取批次大小和序列长度,[batch_size, seq_len, dim] + bsz, seqlen, _ = x.shape + + # 计算查询(Q)、键(K)、值(V)。 + xq, xk, xv = self.wq(x), self.wk(x), self.wv(x) + # 调整形状以适应头的维度。 + xq = xq.view(bsz, seqlen, self.n_local_heads, self.head_dim) + xk = xk.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim) + xv = xv.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim) + + # 应用旋转位置嵌入(RoPE)。 + xq, xk = apply_rotary_emb(xq, xk, freqs_cos, freqs_sin) + + # 对键和值进行扩展以适应重复次数。 + xk = repeat_kv(xk, self.n_rep) + xv = repeat_kv(xv, self.n_rep) + + # 将头作为批次维度处理。 + xq = xq.transpose(1, 2) + xk = xk.transpose(1, 2) + xv = xv.transpose(1, 2) + + # 根据是否支持Flash Attention,选择实现方式。 + if self.flash: + # 使用Flash Attention。 + output = torch.nn.functional.scaled_dot_product_attention(xq, xk, xv, attn_mask=None, dropout_p=self.dropout if self.training else 0.0, is_causal=True) + else: + # 使用手动实现的注意力机制。 + scores = torch.matmul(xq, xk.transpose(2, 3)) / math.sqrt(self.head_dim) + assert hasattr(self, 'mask') + scores = scores + self.mask[:, :, :seqlen, :seqlen] + scores = F.softmax(scores.float(), dim=-1).type_as(xq) + scores = self.attn_dropout(scores) + output = torch.matmul(scores, xv) + + # 恢复时间维度并合并头。 + output = output.transpose(1, 2).contiguous().view(bsz, seqlen, -1) + + # 最终投影回残差流。 + output = self.wo(output) + output = self.resid_dropout(output) + return output +``` + +同样大家可以使用下面的代码来对`LLaMA2Attention`模块进行测试,可以看到代码最终输出的形状为`torch.Size([1, 50, 288])`,与我们输入的形状一致,说明模块的实现是正确的。 + +```python +# 创建Attention实例 +attention_model = LLaMA2Attention(args) + +# 模拟输入数据 +batch_size = 1 +seq_len = 50 # 假设实际使用的序列长度为50 +dim = args.dim +x = torch.rand(batch_size, seq_len, dim) # 随机生成输入张量 +# freqs_cos = torch.rand(seq_len, dim // 2) # 模拟cos频率,用于RoPE +# freqs_sin = torch.rand(seq_len, dim // 2) # 模拟sin频率,用于RoPE + +freqs_cos, freqs_sin = precompute_freqs_cis(dim//args.n_heads, seq_len) + +# 运行Attention模型 +output = attention_model(x, freqs_cos, freqs_sin) + +# attention出来之后的形状 依然是[batch_size, seq_len, dim] +print("Output shape:", output.shape) +``` + +OUT: +``` +Output shape: torch.Size([1, 50, 288]) +``` + +## 5.1.4 构建 LLaMA2 MLP模块 + +相对于前面我们实现的LLaMA2 Attention模块,LLaMA2 MLP模块的实现要简单一些。我们可以通过如下代码实现`LLaMA2MLP`: + +```python +class LLaMA2MLP(nn.Module): + def __init__(self, dim: int, hidden_dim: int, multiple_of: int, dropout: float): + super().__init__() + # 如果没有指定隐藏层的维度,我们将其设置为输入维度的4倍 + # 然后将其减少到2/3,最后确保它是multiple_of的倍数 + if hidden_dim is None: + hidden_dim = 4 * dim + hidden_dim = int(2 * hidden_dim / 3) + hidden_dim = multiple_of * ((hidden_dim + multiple_of - 1) // multiple_of) + # 定义第一层线性变换,从输入维度到隐藏维度 + self.w1 = nn.Linear(dim, hidden_dim, bias=False) + # 定义第二层线性变换,从隐藏维度到输入维度 + self.w2 = nn.Linear(hidden_dim, dim, bias=False) + # 定义第三层线性变换,从输入维度到隐藏维度 + self.w3 = nn.Linear(dim, hidden_dim, bias=False) + # 定义dropout层,用于防止过拟合 + self.dropout = nn.Dropout(dropout) + + def forward(self, x): + # 前向传播函数 + # 首先,输入x通过第一层线性变换和SILU激活函数 + # 然后,结果乘以输入x通过第三层线性变换的结果 + # 最后,通过第二层线性变换和dropout层 + return self.dropout(self.w2(F.silu(self.w1(x)) * self.w3(x))) +``` + +我们着重观察一下`forward`函数的实现,首先,输入 `x` 通过第一层线性变换 `self.w1` 和 `SILU` 激活函数,然后,结果乘以输入 `x` 通过第三层线性变换 `self.w3` 的结果,最后,通过第二层线性变换 `self.w2` 和 `dropout` 层,得到最终输出。 + +同样大家可以使用下面的代码来对`LLaMAMLP`模块进行测试,可以看到代码最终输出的形状为`torch.Size([1, 50, 288])`,与我们输入的形状一致,说明模块的实现是正确的。 + +```python +# 创建MLP实例 +mlp = LLaMA2MLP(args.dim, args.hidden_dim, args.multiple_of, args.dropout) +# 随机生成数据 +x = torch.randn(1, 50, 288) +# 运行MLP模型 +output = mlp(x) +print(output.shape) +``` + +OUT: +``` +torch.Size([1, 50, 288]) +``` + +## 5.1.5 LLaMA2 Decoder Layer + +到这里,我们已经实现了`LLaMA2`模型的`Attention`模块和`MLP`模块,接下来我们就可以构建`LLaMA2`的`Decoder Layer`了。 + +```python +class LLaMA2DecoderLayer(nn.Module): + def __init__(self, layer_id: int, args: ModelArgs): + super().__init__() + # 定义多头注意力的头数 + self.n_heads = args.n_heads + # 定义输入维度 + self.dim = args.dim + # 定义每个头的维度,等于输入维度除以头数 + self.head_dim = args.dim // args.n_heads + # 定义LLaMA2Attention对象,用于进行多头注意力计算 + self.attention = LLaMA2Attention(args) + # 定义LLaMAMLP对象,用于进行前馈神经网络计算 + self.feed_forward = LLaMA2MLP( + dim=args.dim, + hidden_dim=args.hidden_dim, + multiple_of=args.multiple_of, + dropout=args.dropout, + ) + # 定义层的ID + self.layer_id = layer_id + # 定义注意力计算的归一化层 + self.attention_norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps) + # 定义前馈神经网络计算的归一化层 + self.ffn_norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps) + + def forward(self, x, freqs_cos, freqs_sin): + # 前向传播函数 + # 首先,输入x经过注意力归一化层,然后进行注意力计算,结果与输入x相加得到h + # 然后,h经过前馈神经网络归一化层,然后进行前馈神经网络计算,结果与h相加得到输出 + h = x + self.attention.forward(self.attention_norm(x), freqs_cos, freqs_sin) + out = h + self.feed_forward.forward(self.ffn_norm(h)) + return out +``` + +`DecoderLayer`就是把我们上面完成的`Attention`模块和`MLP`模块组合在一起,实现了一个完整的`Transformer`模块。 + +同样大家可以使用下面的代码来对`LLaMA2DecoderLayer`模块进行测试,可以看到代码最终输出的形状为`torch.Size([1, 50, 288])`,与我们输入的形状一致,说明模块的实现是正确的。 + +```python +# 创建LLaMADecoderLayer实例 +decoderlayer = LLaMA2DecoderLayer(0, args) + +# 模拟输入数据 +dim = args.dim +seq_len = 50 + +x = torch.randn(1, seq_len, dim) # [bs, seq_len, dim] + +freqs_cos, freqs_sin = precompute_freqs_cis(dim//args.n_heads, seq_len) + +out = decoderlayer(x, freqs_cos, freqs_sin) + +print(out.shape) # 形状和输入的x一样 [batch_size, seq_len, dim] +``` + +OUT: +``` +torch.Size([1, 50, 288]) +``` + +## 5.1.6 构建 LLaMA2 模型 + +好了,我们已经完了上述所有的模块的实现,接下来就是激动人心的时刻,我们可以构建`LLaMA2`模型了。,`LLaMA2`模型就是将`LLaMA2DecoderLayer`模块堆叠起来,构成一个完整的`Transformer`模型。 + +```python +class LLaMA2Model(nn.Module): + last_loss: Optional[torch.Tensor] + + def __init__(self, args: ModelArgs): + super().__init__() + # 初始化模型参数 + self.args = args + # 词汇表大小 + self.vocab_size = args.vocab_size + # 层数 + self.n_layers = args.n_layers + + # 词嵌入层 + self.tok_embeddings = nn.Embedding(args.vocab_size, args.dim) + # Dropout层 + self.dropout = nn.Dropout(args.dropout) + # Decoder层 + self.layers = torch.nn.ModuleList() + for layer_id in range(args.n_layers): + self.layers.append(LLaMA2DecoderLayer(layer_id, args)) + # 归一化层 + self.norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps) + # 输出层 + self.output = nn.Linear(args.dim, args.vocab_size, bias=False) + + # 将词嵌入层的权重与输出层的权重共享 + self.tok_embeddings.weight = self.output.weight + + # 预计算相对位置嵌入的频率 + freqs_cos, freqs_sin = precompute_freqs_cis(self.args.dim // self.args.n_heads, self.args.max_seq_len) + self.register_buffer("freqs_cos", freqs_cos, persistent=False) + self.register_buffer("freqs_sin", freqs_sin, persistent=False) + + # 初始化所有权重 + self.apply(self._init_weights) + # 对残差投影进行特殊的缩放初始化 + for pn, p in self.named_parameters(): + if pn.endswith('w3.weight') or pn.endswith('wo.weight'): + torch.nn.init.normal_(p, mean=0.0, std=0.02/math.sqrt(2 * args.n_layers)) + + # 初始化最后一次前向传播的损失属性 + self.last_loss = None + + def _init_weights(self, module): + # 初始化权重的函数 + if isinstance(module, nn.Linear): + torch.nn.init.normal_(module.weight, mean=0.0, std=0.02) + if module.bias is not None: + torch.nn.init.zeros_(module.bias) + elif isinstance(module, nn.Embedding): + torch.nn.init.normal_(module.weight, mean=0.0, std=0.02) + + def forward(self, tokens: torch.Tensor, targets: Optional[torch.Tensor] = None) -> torch.Tensor: + # 前向传播函数 + _bsz, seqlen = tokens.shape + # 通过词嵌入层和Dropout层 + h = self.tok_embeddings(tokens) + h = self.dropout(h) + # 获取相对位置嵌入的频率 + freqs_cos = self.freqs_cos[:seqlen] + freqs_sin = self.freqs_sin[:seqlen] + + # 通过Decoder层 + for layer in self.layers: + h = layer(h, freqs_cos, freqs_sin) + # 通过归一化层 + h = self.norm(h) + + if targets is not None: + # 如果给定了目标,计算损失 + logits = self.output(h) + self.last_loss = F.cross_entropy(logits.view(-1, logits.size(-1)), targets.view(-1), ignore_index=-1) + else: + # 推理时的小优化:只对最后一个位置的输出进行前向传播 + logits = self.output(h[:, [-1], :]) + self.last_loss = None + + return logits +``` + +同样大家可以使用下面的代码来对`LLaMA2Model`模块进行测试,可以看到代码最终输出的形状为`torch.Size([1, 50, 32000])`,与我们输入的形状一致,说明模块的实现是正确的。 + +```python +# LLaMA2Model.forward 接受两个参数,tokens和targets,其中tokens是输入的张量, 应为int类型 +x = torch.randint(0, 32000, (1, 50)) # [bs, seq_len] +# 实例化LLaMA2Model +model = LLaMA2Model(args=args) +# 计算model的全部参数 +num_params = sum(p.numel() for p in model.parameters()) +print('Number of parameters:', num_params) + +out = model(x) +print(out.shape) # [batch_size, 1, vocab_size] +``` + +OUT: +``` +Number of parameters: 15191712 +torch.Size([1, 1, 32000]) +``` + diff --git a/docs/chapter5/llama2.ipynb b/docs/chapter5/llama2.ipynb new file mode 100644 index 0000000..76389db --- /dev/null +++ b/docs/chapter5/llama2.ipynb @@ -0,0 +1,641 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import struct\n", + "import inspect\n", + "from dataclasses import dataclass\n", + "from typing import Any, Optional, Tuple\n", + "\n", + "import numpy as np\n", + "import torch\n", + "import torch.nn.functional as F\n", + "from torch import nn" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "class ModelArgs:\n", + " # 自定义超参数\n", + " dim: int = 288 # 模型维度\n", + " n_layers: int = 6 # Transformer层数\n", + " n_heads: int = 6 # 注意力机制的头数\n", + " n_kv_heads: Optional[int] = 6 # 键/值头数,如果未指定,则默认为n_heads\n", + " vocab_size: int = 32000 # 词汇表大小\n", + " hidden_dim: Optional[int] = None # 隐藏层维度,如果未指定,则使用其他规则确定\n", + " multiple_of: int = 32 # MLP隐藏层大小是这个数的倍数\n", + " norm_eps: float = 1e-5 # 归一化层的epsilon值\n", + " max_seq_len: int = 256 # 最大序列长度\n", + " dropout: float = 0.0 # 丢弃率\n", + "\n", + "args = ModelArgs()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "class LLaMA2RMSNorm(nn.Module):\n", + " def __init__(self, dim: int, eps: float):\n", + " super().__init__()\n", + " # eps是为了防止除以0的情况\n", + " self.eps = eps\n", + " # weight是一个可学习的参数,全部初始化为1\n", + " self.weight = nn.Parameter(torch.ones(dim))\n", + "\n", + " def _norm(self, x):\n", + " # 计算RMSNorm的核心部分\n", + " # x.pow(2).mean(-1, keepdim=True)计算了输入x的平方的均值\n", + " # torch.rsqrt是平方根的倒数,这样就得到了RMSNorm的分母部分,再加上eps防止分母为0\n", + " # 最后乘以x,得到RMSNorm的结果\n", + " return x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps)\n", + "\n", + " def forward(self, x):\n", + " # forward函数是模型的前向传播\n", + " # 首先将输入x转为float类型,然后进行RMSNorm,最后再转回原来的数据类型\n", + " # 最后乘以weight,这是RMSNorm的一个可学习的缩放因子\n", + " output = self._norm(x.float()).type_as(x)\n", + " return output * self.weight" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([1, 50, 288])\n" + ] + } + ], + "source": [ + "norm = LLaMA2RMSNorm(args.dim, args.norm_eps)\n", + "x = torch.randn(1, 50, args.dim)\n", + "output = norm(x)\n", + "print(output.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# 获得旋转嵌入的实部和虚部\n", + "# 注意:此处的dim应为 dim//n_head,因为我们是对每个head进行旋转嵌入\n", + "def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0):\n", + " # torch.arange(0, dim, 2)[: (dim // 2)].float()生成了一个从0开始,步长为2的序列,长度为dim的一半\n", + " # 然后每个元素除以dim,再取theta的倒数,得到频率\n", + " freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim))\n", + " # 生成一个从0到end的序列,长度为end\n", + " t = torch.arange(end, device=freqs.device)\n", + " # 计算外积,得到一个二维矩阵,每一行是t的元素乘以freqs的元素\n", + " freqs = torch.outer(t, freqs).float()\n", + " # 计算频率的余弦值,得到实部\n", + " freqs_cos = torch.cos(freqs)\n", + " # 计算频率的正弦值,得到虚部\n", + " freqs_sin = torch.sin(freqs)\n", + " return freqs_cos, freqs_sin" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([50, 24]) torch.Size([50, 24])\n" + ] + } + ], + "source": [ + "x = torch.randn(1, 50, 288)\n", + "freqs_cos, freqs_sin = precompute_freqs_cis(288//6, 50)\n", + "print(freqs_cos.shape, freqs_sin.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "# 此函数的作用是将freqs_cis调整为与x的形状相同,以便能够与x进行广播操作\n", + "def reshape_for_broadcast(freqs_cis: torch.Tensor, x: torch.Tensor):\n", + " # 获取x的维度数\n", + " ndim = x.ndim\n", + " # 断言,确保1在x的维度范围内\n", + " assert 0 <= 1 < ndim\n", + " # 断言,确保freqs_cis的形状与x的第二维和最后一维相同\n", + " assert freqs_cis.shape == (x.shape[1], x.shape[-1])\n", + " # 构造一个新的形状,除了第二维和最后一维,其他维度都为1,这样做是为了能够将freqs_cis与x进行广播操作\n", + " shape = [d if i == 1 or i == ndim - 1 else 1 for i, d in enumerate(x.shape)]\n", + " # 将freqs_cis调整为新的形状,并返回\n", + " return freqs_cis.view(shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def apply_rotary_emb(\n", + " xq: torch.Tensor,\n", + " xk: torch.Tensor,\n", + " freqs_cos: torch.Tensor,\n", + " freqs_sin: torch.Tensor\n", + ") -> Tuple[torch.Tensor, torch.Tensor]:\n", + "\n", + " # 将查询和键张量转换为浮点数,并重塑形状以分离实部和虚部\n", + " xq_r, xq_i = xq.float().reshape(xq.shape[:-1] + (-1, 2)).unbind(-1)\n", + " xk_r, xk_i = xk.float().reshape(xk.shape[:-1] + (-1, 2)).unbind(-1)\n", + "\n", + " # 重新塑形频率张量以进行广播\n", + " freqs_cos = reshape_for_broadcast(freqs_cos, xq_r)\n", + " freqs_sin = reshape_for_broadcast(freqs_sin, xq_r)\n", + "\n", + " # 应用旋转,分别计算旋转后的实部和虚部\n", + " xq_out_r = xq_r * freqs_cos - xq_i * freqs_sin\n", + " xq_out_i = xq_r * freqs_sin + xq_i * freqs_cos\n", + " xk_out_r = xk_r * freqs_cos - xk_i * freqs_sin\n", + " xk_out_i = xk_r * freqs_sin + xk_i * freqs_cos\n", + "\n", + " # 将最后两个维度合并,并还原为原始张量的形状\n", + " xq_out = torch.stack([xq_out_r, xq_out_i], dim=-1).flatten(3)\n", + " xk_out = torch.stack([xk_out_r, xk_out_i], dim=-1).flatten(3)\n", + "\n", + " return xq_out.type_as(xq), xk_out.type_as(xk)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([50, 24]) torch.Size([50, 24])\n" + ] + }, + { + "data": { + "text/plain": [ + "(torch.Size([1, 50, 6, 48]), torch.Size([1, 50, 6, 48]))" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xq = torch.randn(1, 50, 6, 48) # bs, seq_len, dim//n_head, n_head_dim\n", + "xk = torch.randn(1, 50, 6, 48) # bs, seq_len, dim//n_head, n_head_dim\n", + "\n", + "# 使用 precompute_freqs_cis 函数获取 sin和cos\n", + "cos, sin = precompute_freqs_cis(288//6, 50)\n", + "print(cos.shape, sin.shape)\n", + "xq_out, xk_out = apply_rotary_emb(xq, xk, cos, sin)\n", + "\n", + "xq_out.shape, xk_out.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def repeat_kv(x: torch.Tensor, n_rep: int) -> torch.Tensor:\n", + " # 获取输入张量的形状:批量大小、序列长度、键/值对头的数量、每个头的维度大小\n", + " bs, slen, n_kv_heads, head_dim = x.shape\n", + " \n", + " # 如果重复次数为1,则不需要重复,直接返回原始张量\n", + " if n_rep == 1:\n", + " return x\n", + " \n", + " # 对张量进行扩展和重塑操作以重复键值对\n", + " return (\n", + " x[:, :, :, None, :] # 在第四个维度(头的维度前)添加一个新的维度\n", + " .expand(bs, slen, n_kv_heads, n_rep, head_dim) # 将新添加的维度扩展到n_rep大小,实现重复的效果\n", + " .reshape(bs, slen, n_kv_heads * n_rep, head_dim) # 重新塑形,合并键/值对头的数量和重复次数的维度\n", + " )\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "class LLaMA2Attention(nn.Module):\n", + " def __init__(self, args: ModelArgs):\n", + " super().__init__()\n", + " # 根据是否指定n_kv_heads,确定用于键(key)和值(value)的头的数量。\n", + " self.n_kv_heads = args.n_heads if args.n_kv_heads is None else args.n_kv_heads\n", + " # 确保总头数可以被键值头数整除。\n", + " assert args.n_heads % self.n_kv_heads == 0\n", + "\n", + " # 模型并行处理大小,默认为1。\n", + " model_parallel_size = 1\n", + " # 本地计算头数,等于总头数除以模型并行处理大小。\n", + " self.n_local_heads = args.n_heads // model_parallel_size\n", + " # 本地键值头数,等于键值头数除以模型并行处理大小。\n", + " self.n_local_kv_heads = self.n_kv_heads // model_parallel_size\n", + " # 重复次数,用于扩展键和值的尺寸。\n", + " self.n_rep = self.n_local_heads // self.n_local_kv_heads\n", + " # 每个头的维度,等于模型维度除以头的总数。\n", + " self.head_dim = args.dim // args.n_heads\n", + "\n", + " # 定义权重矩阵。\n", + " self.wq = nn.Linear(args.dim, args.n_heads * self.head_dim, bias=False)\n", + " self.wk = nn.Linear(args.dim, self.n_kv_heads * self.head_dim, bias=False)\n", + " self.wv = nn.Linear(args.dim, self.n_kv_heads * self.head_dim, bias=False)\n", + " # 输出权重矩阵。\n", + " self.wo = nn.Linear(args.n_heads * self.head_dim, args.dim, bias=False)\n", + "\n", + " # 定义dropout。\n", + " self.attn_dropout = nn.Dropout(args.dropout)\n", + " self.resid_dropout = nn.Dropout(args.dropout)\n", + " # 保存dropout概率。\n", + " self.dropout = args.dropout\n", + "\n", + " # 检查是否使用Flash Attention(需要PyTorch >= 2.0)。\n", + " self.flash = hasattr(torch.nn.functional, 'scaled_dot_product_attention')\n", + " if not self.flash:\n", + " # 若不支持Flash Attention,则使用手动实现的注意力机制,并设置mask。\n", + " print(\"WARNING: using slow attention. Flash Attention requires PyTorch >= 2.0\")\n", + " # 创建一个上三角矩阵,用于遮蔽未来信息。\n", + " mask = torch.full((1, 1, args.max_seq_len, args.max_seq_len), float(\"-inf\"))\n", + " mask = torch.triu(mask, diagonal=1)\n", + " # 注册为模型的缓冲区\n", + " self.register_buffer(\"mask\", mask)\n", + "\n", + " def forward(self, x: torch.Tensor, freqs_cos: torch.Tensor, freqs_sin: torch.Tensor):\n", + " # 获取批次大小和序列长度,[batch_size, seq_len, dim]\n", + " bsz, seqlen, _ = x.shape\n", + "\n", + " # 计算查询(Q)、键(K)、值(V)。\n", + " xq, xk, xv = self.wq(x), self.wk(x), self.wv(x)\n", + " # 调整形状以适应头的维度。\n", + " xq = xq.view(bsz, seqlen, self.n_local_heads, self.head_dim)\n", + " xk = xk.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim)\n", + " xv = xv.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim)\n", + "\n", + " # 应用旋转位置嵌入(RoPE)。\n", + " xq, xk = apply_rotary_emb(xq, xk, freqs_cos, freqs_sin)\n", + "\n", + " # 对键和值进行扩展以适应重复次数。\n", + " xk = repeat_kv(xk, self.n_rep)\n", + " xv = repeat_kv(xv, self.n_rep)\n", + "\n", + " # 将头作为批次维度处理。\n", + " xq = xq.transpose(1, 2)\n", + " xk = xk.transpose(1, 2)\n", + " xv = xv.transpose(1, 2)\n", + "\n", + " # 根据是否支持Flash Attention,选择实现方式。\n", + " if self.flash:\n", + " # 使用Flash Attention。\n", + " output = torch.nn.functional.scaled_dot_product_attention(xq, xk, xv, attn_mask=None, dropout_p=self.dropout if self.training else 0.0, is_causal=True)\n", + " else:\n", + " # 使用手动实现的注意力机制。\n", + " scores = torch.matmul(xq, xk.transpose(2, 3)) / math.sqrt(self.head_dim)\n", + " assert hasattr(self, 'mask')\n", + " scores = scores + self.mask[:, :, :seqlen, :seqlen]\n", + " scores = F.softmax(scores.float(), dim=-1).type_as(xq)\n", + " scores = self.attn_dropout(scores)\n", + " output = torch.matmul(scores, xv)\n", + "\n", + " # 恢复时间维度并合并头。\n", + " output = output.transpose(1, 2).contiguous().view(bsz, seqlen, -1)\n", + "\n", + " # 最终投影回残差流。\n", + " output = self.wo(output)\n", + " output = self.resid_dropout(output)\n", + " return output" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([50, 24]) torch.Size([50, 24])\n", + "Output shape: torch.Size([1, 50, 288])\n" + ] + } + ], + "source": [ + "# 创建Attention实例\n", + "attention_model = LLaMA2Attention(args)\n", + "\n", + "# 模拟输入数据\n", + "batch_size = 1\n", + "seq_len = 50 # 假设实际使用的序列长度为50\n", + "dim = args.dim\n", + "x = torch.rand(batch_size, seq_len, dim) # 随机生成输入张量\n", + "# freqs_cos = torch.rand(seq_len, dim // 2) # 模拟cos频率,用于RoPE\n", + "# freqs_sin = torch.rand(seq_len, dim // 2) # 模拟sin频率,用于RoPE\n", + "\n", + "freqs_cos, freqs_sin = precompute_freqs_cis(dim//args.n_heads, seq_len)\n", + "\n", + "print(freqs_cos.shape, freqs_sin.shape)\n", + "\n", + "# 运行Attention模型\n", + "output = attention_model(x, freqs_cos, freqs_sin)\n", + "\n", + "# attention出来之后的形状 依然是[batch_size, seq_len, dim]\n", + "print(\"Output shape:\", output.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "class LLaMA2MLP(nn.Module):\n", + " def __init__(self, dim: int, hidden_dim: int, multiple_of: int, dropout: float):\n", + " super().__init__()\n", + " # 如果没有指定隐藏层的维度,我们将其设置为输入维度的4倍\n", + " # 然后将其减少到2/3,最后确保它是multiple_of的倍数\n", + " if hidden_dim is None:\n", + " hidden_dim = 4 * dim\n", + " hidden_dim = int(2 * hidden_dim / 3)\n", + " hidden_dim = multiple_of * ((hidden_dim + multiple_of - 1) // multiple_of)\n", + " # 定义第一层线性变换,从输入维度到隐藏维度\n", + " self.w1 = nn.Linear(dim, hidden_dim, bias=False)\n", + " # 定义第二层线性变换,从隐藏维度到输入维度\n", + " self.w2 = nn.Linear(hidden_dim, dim, bias=False)\n", + " # 定义第三层线性变换,从输入维度到隐藏维度\n", + " self.w3 = nn.Linear(dim, hidden_dim, bias=False)\n", + " # 定义dropout层,用于防止过拟合\n", + " self.dropout = nn.Dropout(dropout)\n", + "\n", + " def forward(self, x):\n", + " # 前向传播函数\n", + " # 首先,输入x通过第一层线性变换和SILU激活函数\n", + " # 然后,结果乘以输入x通过第三层线性变换的结果\n", + " # 最后,通过第二层线性变换和dropout层\n", + " return self.dropout(self.w2(F.silu(self.w1(x)) * self.w3(x)))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([1, 50, 288])\n" + ] + } + ], + "source": [ + "# 创建MLP实例\n", + "mlp = LLaMAMLP(args.dim, args.hidden_dim, args.multiple_of, args.dropout)\n", + "# 随机生成数据\n", + "x = torch.randn(1, 50, 288)\n", + "# 运行MLP模型\n", + "output = mlp(x)\n", + "print(output.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "class LLaMA2DecoderLayer(nn.Module):\n", + " def __init__(self, layer_id: int, args: ModelArgs):\n", + " super().__init__()\n", + " # 定义多头注意力的头数\n", + " self.n_heads = args.n_heads\n", + " # 定义输入维度\n", + " self.dim = args.dim\n", + " # 定义每个头的维度,等于输入维度除以头数\n", + " self.head_dim = args.dim // args.n_heads\n", + " # 定义LLaMA2Attention对象,用于进行多头注意力计算\n", + " self.attention = LLaMA2Attention(args)\n", + " # 定义LLaMAMLP对象,用于进行前馈神经网络计算\n", + " self.feed_forward = LLaMA2MLP(\n", + " dim=args.dim,\n", + " hidden_dim=args.hidden_dim,\n", + " multiple_of=args.multiple_of,\n", + " dropout=args.dropout,\n", + " )\n", + " # 定义层的ID\n", + " self.layer_id = layer_id\n", + " # 定义注意力计算的归一化层\n", + " self.attention_norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps)\n", + " # 定义前馈神经网络计算的归一化层\n", + " self.ffn_norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps)\n", + "\n", + " def forward(self, x, freqs_cos, freqs_sin):\n", + " # 前向传播函数\n", + " # 首先,输入x经过注意力归一化层,然后进行注意力计算,结果与输入x相加得到h\n", + " # 然后,h经过前馈神经网络归一化层,然后进行前馈神经网络计算,结果与h相加得到输出\n", + " h = x + self.attention.forward(self.attention_norm(x), freqs_cos, freqs_sin)\n", + " out = h + self.feed_forward.forward(self.ffn_norm(h))\n", + " return out" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([1, 50, 288]) torch.Size([50, 24]) torch.Size([50, 24])\n", + "torch.Size([1, 50, 288])\n" + ] + } + ], + "source": [ + "# LLaMADecoderLayer.forward 函数的输入是 x, freqs_cos, freqs_sin, 其中x的形状是[batch_size, seq_len, dim]\n", + "# 由于llama2使用了GQA Attention,所以precompute_freqs_cis函数输入参数应该为dim//n_heads,seq_len、\n", + "\n", + "# 创建LLaMADecoderLayer实例\n", + "decoderlayer = LLaMA2DecoderLayer(0, args)\n", + "\n", + "# 模拟输入数据\n", + "dim = args.dim\n", + "seq_len = 50\n", + "\n", + "x = torch.randn(1, seq_len, dim) # [bs, seq_len, dim]\n", + "\n", + "freqs_cos, freqs_sin = precompute_freqs_cis(dim//args.n_heads, seq_len)\n", + "print(x.shape, freqs_cos.shape, freqs_sin.shape)\n", + "\n", + "out = decoderlayer(x, freqs_cos, freqs_sin)\n", + "\n", + "print(out.shape) # 形状和输入的x一样 [batch_size, seq_len, dim]" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "class LLaMA2Model(nn.Module):\n", + " last_loss: Optional[torch.Tensor]\n", + "\n", + " def __init__(self, args: ModelArgs):\n", + " super().__init__()\n", + " # 初始化模型参数\n", + " self.args = args\n", + " # 词汇表大小\n", + " self.vocab_size = args.vocab_size\n", + " # 层数\n", + " self.n_layers = args.n_layers\n", + "\n", + " # 词嵌入层\n", + " self.tok_embeddings = nn.Embedding(args.vocab_size, args.dim)\n", + " # Dropout层\n", + " self.dropout = nn.Dropout(args.dropout)\n", + " # Decoder层\n", + " self.layers = torch.nn.ModuleList()\n", + " for layer_id in range(args.n_layers):\n", + " self.layers.append(LLaMA2DecoderLayer(layer_id, args))\n", + " # 归一化层\n", + " self.norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps)\n", + " # 输出层\n", + " self.output = nn.Linear(args.dim, args.vocab_size, bias=False)\n", + "\n", + " # 将词嵌入层的权重与输出层的权重共享\n", + " self.tok_embeddings.weight = self.output.weight \n", + "\n", + " # 预计算相对位置嵌入的频率\n", + " freqs_cos, freqs_sin = precompute_freqs_cis(self.args.dim // self.args.n_heads, self.args.max_seq_len)\n", + " self.register_buffer(\"freqs_cos\", freqs_cos, persistent=False)\n", + " self.register_buffer(\"freqs_sin\", freqs_sin, persistent=False)\n", + "\n", + " # 初始化所有权重\n", + " self.apply(self._init_weights)\n", + " # 对残差投影进行特殊的缩放初始化\n", + " for pn, p in self.named_parameters():\n", + " if pn.endswith('w3.weight') or pn.endswith('wo.weight'):\n", + " torch.nn.init.normal_(p, mean=0.0, std=0.02/math.sqrt(2 * args.n_layers))\n", + "\n", + " # 初始化最后一次前向传播的损失属性\n", + " self.last_loss = None\n", + "\n", + " def _init_weights(self, module):\n", + " # 初始化权重的函数\n", + " if isinstance(module, nn.Linear):\n", + " torch.nn.init.normal_(module.weight, mean=0.0, std=0.02)\n", + " if module.bias is not None:\n", + " torch.nn.init.zeros_(module.bias)\n", + " elif isinstance(module, nn.Embedding):\n", + " torch.nn.init.normal_(module.weight, mean=0.0, std=0.02)\n", + " \n", + " def forward(self, tokens: torch.Tensor, targets: Optional[torch.Tensor] = None) -> torch.Tensor:\n", + " # 前向传播函数\n", + " _bsz, seqlen = tokens.shape\n", + " # 通过词嵌入层和Dropout层\n", + " h = self.tok_embeddings(tokens)\n", + " h = self.dropout(h)\n", + " # 获取相对位置嵌入的频率\n", + " freqs_cos = self.freqs_cos[:seqlen]\n", + " freqs_sin = self.freqs_sin[:seqlen]\n", + "\n", + " # 通过Decoder层\n", + " for layer in self.layers:\n", + " h = layer(h, freqs_cos, freqs_sin)\n", + " # 通过归一化层\n", + " h = self.norm(h)\n", + "\n", + " if targets is not None:\n", + " # 如果给定了目标,计算损失\n", + " logits = self.output(h)\n", + " self.last_loss = F.cross_entropy(logits.view(-1, logits.size(-1)), targets.view(-1), ignore_index=-1)\n", + " else:\n", + " # 推理时的小优化:只对最后一个位置的输出进行前向传播\n", + " logits = self.output(h[:, [-1], :]) \n", + " self.last_loss = None\n", + "\n", + " return logits" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of parameters: 15191712\n", + "torch.Size([1, 1, 32000])\n" + ] + } + ], + "source": [ + "# LLaMA2Model.forward 接受两个参数,tokens和targets,其中tokens是输入的张量, 应为int类型\n", + "x = torch.randint(0, 32000, (1, 50)) # [bs, seq_len]\n", + "# 实例化LLaMA2Model\n", + "model = LLaMA2Model(args=args)\n", + "# 计算model的全部参数\n", + "num_params = sum(p.numel() for p in model.parameters())\n", + "print('Number of parameters:', num_params)\n", + "\n", + "out = model(x)\n", + "print(out.shape) # [batch_size, 1, vocab_size]" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "nlp", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/chapter5/llama2_model.py b/docs/chapter5/llama2_model.py new file mode 100644 index 0000000..746d194 --- /dev/null +++ b/docs/chapter5/llama2_model.py @@ -0,0 +1,367 @@ +#!/usr/bin/env python +# -*- coding: utf-8 -*- +''' +@File : llama2_model.py +@Time : 2024/04/14 22:26:35 +@Author : 不要葱姜蒜 +@Version : 1.0 +@Desc : 部分代码借鉴llama2.c仓库代码 +''' + +import math +import struct +import inspect +from dataclasses import dataclass +from typing import Any, Optional, Tuple + +import numpy as np +import torch +import torch.nn.functional as F +from torch import nn + + +@dataclass +class ModelArgs: + # 自定义超参数 + dim: int = 288 # 模型维度 + n_layers: int = 6 # Transformer层数 + n_heads: int = 6 # 注意力机制的头数 + n_kv_heads: Optional[int] = 6 # 键/值头数,如果未指定,则默认为n_heads + vocab_size: int = 32000 # 词汇表大小 + hidden_dim: Optional[int] = None # 隐藏层维度,如果未指定,则使用其他规则确定 + multiple_of: int = 32 # MLP隐藏层大小是这个数的倍数 + norm_eps: float = 1e-5 # 归一化层的epsilon值 + max_seq_len: int = 256 # 最大序列长度 + dropout: float = 0.0 # 丢弃率 + + +class LLaMA2RMSNorm(nn.Module): + def __init__(self, dim: int, eps: float): + super().__init__() + # eps是为了防止除以0的情况 + self.eps = eps + # weight是一个可学习的参数,全部初始化为1 + self.weight = nn.Parameter(torch.ones(dim)) + + def _norm(self, x): + # 计算RMSNorm的核心部分 + # x.pow(2).mean(-1, keepdim=True)计算了输入x的平方的均值 + # torch.rsqrt是平方根的倒数,这样就得到了RMSNorm的分母部分,再加上eps防止分母为0 + # 最后乘以x,得到RMSNorm的结果 + return x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps) + + def forward(self, x): + # forward函数是模型的前向传播 + # 首先将输入x转为float类型,然后进行RMSNorm,最后再转回原来的数据类型 + # 最后乘以weight,这是RMSNorm的一个可学习的缩放因子 + output = self._norm(x.float()).type_as(x) + return output * self.weight + +# 获得旋转嵌入的实部和虚部 +# 注意:此处的dim应为 dim//n_head,因为我们是对每个head进行旋转嵌入 +def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0): + # torch.arange(0, dim, 2)[: (dim // 2)].float()生成了一个从0开始,步长为2的序列,长度为dim的一半 + # 然后每个元素除以dim,再取theta的倒数,得到频率 + freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim)) + # 生成一个从0到end的序列,长度为end + t = torch.arange(end, device=freqs.device) + # 计算外积,得到一个二维矩阵,每一行是t的元素乘以freqs的元素 + freqs = torch.outer(t, freqs).float() + # 计算频率的余弦值,得到实部 + freqs_cos = torch.cos(freqs) + # 计算频率的正弦值,得到虚部 + freqs_sin = torch.sin(freqs) + return freqs_cos, freqs_sin + +# 此函数的作用是将freqs_cis调整为与x的形状相同,以便能够与x进行广播操作 +def reshape_for_broadcast(freqs_cis: torch.Tensor, x: torch.Tensor): + # 获取x的维度数 + ndim = x.ndim + # 断言,确保1在x的维度范围内 + assert 0 <= 1 < ndim + # 断言,确保freqs_cis的形状与x的第二维和最后一维相同 + assert freqs_cis.shape == (x.shape[1], x.shape[-1]) + # 构造一个新的形状,除了第二维和最后一维,其他维度都为1,这样做是为了能够将freqs_cis与x进行广播操作 + shape = [d if i == 1 or i == ndim - 1 else 1 for i, d in enumerate(x.shape)] + # 将freqs_cis调整为新的形状,并返回 + return freqs_cis.view(shape) + +def apply_rotary_emb( + xq: torch.Tensor, + xk: torch.Tensor, + freqs_cos: torch.Tensor, + freqs_sin: torch.Tensor +) -> Tuple[torch.Tensor, torch.Tensor]: + + # 将查询和键张量转换为浮点数,并重塑形状以分离实部和虚部 + xq_r, xq_i = xq.float().reshape(xq.shape[:-1] + (-1, 2)).unbind(-1) + xk_r, xk_i = xk.float().reshape(xk.shape[:-1] + (-1, 2)).unbind(-1) + + # 重新塑形频率张量以进行广播 + freqs_cos = reshape_for_broadcast(freqs_cos, xq_r) + freqs_sin = reshape_for_broadcast(freqs_sin, xq_r) + + # 应用旋转,分别计算旋转后的实部和虚部 + xq_out_r = xq_r * freqs_cos - xq_i * freqs_sin + xq_out_i = xq_r * freqs_sin + xq_i * freqs_cos + xk_out_r = xk_r * freqs_cos - xk_i * freqs_sin + xk_out_i = xk_r * freqs_sin + xk_i * freqs_cos + + # 将最后两个维度合并,并还原为原始张量的形状 + xq_out = torch.stack([xq_out_r, xq_out_i], dim=-1).flatten(3) + xk_out = torch.stack([xk_out_r, xk_out_i], dim=-1).flatten(3) + + return xq_out.type_as(xq), xk_out.type_as(xk) + +def repeat_kv(x: torch.Tensor, n_rep: int) -> torch.Tensor: + # 获取输入张量的形状:批量大小、序列长度、键/值对头的数量、每个头的维度大小 + bs, slen, n_kv_heads, head_dim = x.shape + + # 如果重复次数为1,则不需要重复,直接返回原始张量 + if n_rep == 1: + return x + + # 对张量进行扩展和重塑操作以重复键值对 + return ( + x[:, :, :, None, :] # 在第四个维度(头的维度前)添加一个新的维度 + .expand(bs, slen, n_kv_heads, n_rep, head_dim) # 将新添加的维度扩展到n_rep大小,实现重复的效果 + .reshape(bs, slen, n_kv_heads * n_rep, head_dim) # 重新塑形,合并键/值对头的数量和重复次数的维度 + ) + +class LLaMA2Attention(nn.Module): + def __init__(self, args: ModelArgs): + super().__init__() + # 根据是否指定n_kv_heads,确定用于键(key)和值(value)的头的数量。 + self.n_kv_heads = args.n_heads if args.n_kv_heads is None else args.n_kv_heads + # 确保总头数可以被键值头数整除。 + assert args.n_heads % self.n_kv_heads == 0 + + # 模型并行处理大小,默认为1。 + model_parallel_size = 1 + # 本地计算头数,等于总头数除以模型并行处理大小。 + self.n_local_heads = args.n_heads // model_parallel_size + # 本地键值头数,等于键值头数除以模型并行处理大小。 + self.n_local_kv_heads = self.n_kv_heads // model_parallel_size + # 重复次数,用于扩展键和值的尺寸。 + self.n_rep = self.n_local_heads // self.n_local_kv_heads + # 每个头的维度,等于模型维度除以头的总数。 + self.head_dim = args.dim // args.n_heads + + # 定义权重矩阵。 + self.wq = nn.Linear(args.dim, args.n_heads * self.head_dim, bias=False) + self.wk = nn.Linear(args.dim, self.n_kv_heads * self.head_dim, bias=False) + self.wv = nn.Linear(args.dim, self.n_kv_heads * self.head_dim, bias=False) + # 输出权重矩阵。 + self.wo = nn.Linear(args.n_heads * self.head_dim, args.dim, bias=False) + + # 定义dropout。 + self.attn_dropout = nn.Dropout(args.dropout) + self.resid_dropout = nn.Dropout(args.dropout) + # 保存dropout概率。 + self.dropout = args.dropout + + # 检查是否使用Flash Attention(需要PyTorch >= 2.0)。 + self.flash = hasattr(torch.nn.functional, 'scaled_dot_product_attention') + if not self.flash: + # 若不支持Flash Attention,则使用手动实现的注意力机制,并设置mask。 + print("WARNING: using slow attention. Flash Attention requires PyTorch >= 2.0") + # 创建一个上三角矩阵,用于遮蔽未来信息。 + mask = torch.full((1, 1, args.max_seq_len, args.max_seq_len), float("-inf")) + mask = torch.triu(mask, diagonal=1) + # 注册为模型的缓冲区 + self.register_buffer("mask", mask) + + def forward(self, x: torch.Tensor, freqs_cos: torch.Tensor, freqs_sin: torch.Tensor): + # 获取批次大小和序列长度,[batch_size, seq_len, dim] + bsz, seqlen, _ = x.shape + + # 计算查询(Q)、键(K)、值(V)。 + xq, xk, xv = self.wq(x), self.wk(x), self.wv(x) + # 调整形状以适应头的维度。 + xq = xq.view(bsz, seqlen, self.n_local_heads, self.head_dim) + xk = xk.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim) + xv = xv.view(bsz, seqlen, self.n_local_kv_heads, self.head_dim) + + # 应用旋转位置嵌入(RoPE)。 + xq, xk = apply_rotary_emb(xq, xk, freqs_cos, freqs_sin) + + # 对键和值进行扩展以适应重复次数。 + xk = repeat_kv(xk, self.n_rep) + xv = repeat_kv(xv, self.n_rep) + + # 将头作为批次维度处理。 + xq = xq.transpose(1, 2) + xk = xk.transpose(1, 2) + xv = xv.transpose(1, 2) + + # 根据是否支持Flash Attention,选择实现方式。 + if self.flash: + # 使用Flash Attention。 + output = torch.nn.functional.scaled_dot_product_attention(xq, xk, xv, attn_mask=None, dropout_p=self.dropout if self.training else 0.0, is_causal=True) + else: + # 使用手动实现的注意力机制。 + scores = torch.matmul(xq, xk.transpose(2, 3)) / math.sqrt(self.head_dim) + assert hasattr(self, 'mask') + scores = scores + self.mask[:, :, :seqlen, :seqlen] + scores = F.softmax(scores.float(), dim=-1).type_as(xq) + scores = self.attn_dropout(scores) + output = torch.matmul(scores, xv) + + # 恢复时间维度并合并头。 + output = output.transpose(1, 2).contiguous().view(bsz, seqlen, -1) + + # 最终投影回残差流。 + output = self.wo(output) + output = self.resid_dropout(output) + return output + +class LLaMA2MLP(nn.Module): + def __init__(self, dim: int, hidden_dim: int, multiple_of: int, dropout: float): + super().__init__() + # 如果没有指定隐藏层的维度,我们将其设置为输入维度的4倍 + # 然后将其减少到2/3,最后确保它是multiple_of的倍数 + if hidden_dim is None: + hidden_dim = 4 * dim + hidden_dim = int(2 * hidden_dim / 3) + hidden_dim = multiple_of * ((hidden_dim + multiple_of - 1) // multiple_of) + # 定义第一层线性变换,从输入维度到隐藏维度 + self.w1 = nn.Linear(dim, hidden_dim, bias=False) + # 定义第二层线性变换,从隐藏维度到输入维度 + self.w2 = nn.Linear(hidden_dim, dim, bias=False) + # 定义第三层线性变换,从输入维度到隐藏维度 + self.w3 = nn.Linear(dim, hidden_dim, bias=False) + # 定义dropout层,用于防止过拟合 + self.dropout = nn.Dropout(dropout) + + def forward(self, x): + # 前向传播函数 + # 首先,输入x通过第一层线性变换和SILU激活函数 + # 然后,结果乘以输入x通过第三层线性变换的结果 + # 最后,通过第二层线性变换和dropout层 + return self.dropout(self.w2(F.silu(self.w1(x)) * self.w3(x))) + + +class LLaMA2DecoderLayer(nn.Module): + def __init__(self, layer_id: int, args: ModelArgs): + super().__init__() + # 定义多头注意力的头数 + self.n_heads = args.n_heads + # 定义输入维度 + self.dim = args.dim + # 定义每个头的维度,等于输入维度除以头数 + self.head_dim = args.dim // args.n_heads + # 定义LLaMA2Attention对象,用于进行多头注意力计算 + self.attention = LLaMA2Attention(args) + # 定义LLaMAMLP对象,用于进行前馈神经网络计算 + self.feed_forward = LLaMA2MLP( + dim=args.dim, + hidden_dim=args.hidden_dim, + multiple_of=args.multiple_of, + dropout=args.dropout, + ) + # 定义层的ID + self.layer_id = layer_id + # 定义注意力计算的归一化层 + self.attention_norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps) + # 定义前馈神经网络计算的归一化层 + self.ffn_norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps) + + def forward(self, x, freqs_cos, freqs_sin): + # 前向传播函数 + # 首先,输入x经过注意力归一化层,然后进行注意力计算,结果与输入x相加得到h + # 然后,h经过前馈神经网络归一化层,然后进行前馈神经网络计算,结果与h相加得到输出 + h = x + self.attention.forward(self.attention_norm(x), freqs_cos, freqs_sin) + out = h + self.feed_forward.forward(self.ffn_norm(h)) + return out + +class LLaMA2Model(nn.Module): + last_loss: Optional[torch.Tensor] + + def __init__(self, args: ModelArgs): + super().__init__() + # 初始化模型参数 + self.args = args + # 词汇表大小 + self.vocab_size = args.vocab_size + # 层数 + self.n_layers = args.n_layers + + # 词嵌入层 + self.tok_embeddings = nn.Embedding(args.vocab_size, args.dim) + # Dropout层 + self.dropout = nn.Dropout(args.dropout) + # Decoder层 + self.layers = torch.nn.ModuleList() + for layer_id in range(args.n_layers): + self.layers.append(LLaMA2DecoderLayer(layer_id, args)) + # 归一化层 + self.norm = LLaMA2RMSNorm(args.dim, eps=args.norm_eps) + # 输出层 + self.output = nn.Linear(args.dim, args.vocab_size, bias=False) + + # 将词嵌入层的权重与输出层的权重共享 + self.tok_embeddings.weight = self.output.weight + + # 预计算相对位置嵌入的频率 + freqs_cos, freqs_sin = precompute_freqs_cis(self.args.dim // self.args.n_heads, self.args.max_seq_len) + self.register_buffer("freqs_cos", freqs_cos, persistent=False) + self.register_buffer("freqs_sin", freqs_sin, persistent=False) + + # 初始化所有权重 + self.apply(self._init_weights) + # 对残差投影进行特殊的缩放初始化 + for pn, p in self.named_parameters(): + if pn.endswith('w3.weight') or pn.endswith('wo.weight'): + torch.nn.init.normal_(p, mean=0.0, std=0.02/math.sqrt(2 * args.n_layers)) + + # 初始化最后一次前向传播的损失属性 + self.last_loss = None + + def _init_weights(self, module): + # 初始化权重的函数 + if isinstance(module, nn.Linear): + torch.nn.init.normal_(module.weight, mean=0.0, std=0.02) + if module.bias is not None: + torch.nn.init.zeros_(module.bias) + elif isinstance(module, nn.Embedding): + torch.nn.init.normal_(module.weight, mean=0.0, std=0.02) + + def forward(self, tokens: torch.Tensor, targets: Optional[torch.Tensor] = None) -> torch.Tensor: + # 前向传播函数 + _bsz, seqlen = tokens.shape + # 通过词嵌入层和Dropout层 + h = self.tok_embeddings(tokens) + h = self.dropout(h) + # 获取相对位置嵌入的频率 + freqs_cos = self.freqs_cos[:seqlen] + freqs_sin = self.freqs_sin[:seqlen] + + # 通过Decoder层 + for layer in self.layers: + h = layer(h, freqs_cos, freqs_sin) + # 通过归一化层 + h = self.norm(h) + + if targets is not None: + # 如果给定了目标,计算损失 + logits = self.output(h) + self.last_loss = F.cross_entropy(logits.view(-1, logits.size(-1)), targets.view(-1), ignore_index=-1) + else: + # 推理时的小优化:只对最后一个位置的输出进行前向传播 + logits = self.output(h[:, [-1], :]) + self.last_loss = None + + return logits + +if __name__ == '__main__': + args = ModelArgs() + # LLaMA2Model.forward 接受两个参数,tokens和targets,其中tokens是输入的张量, 应为int类型 + x = torch.randint(0, 32000, (1, 50)) # [bs, seq_len] + # 实例化LLaMA2Model + model = LLaMA2Model(args=args) + # 计算model的全部参数 + num_params = sum(p.numel() for p in model.parameters()) + print('Number of parameters:', num_params) + + out = model(x) + print(out.shape) # [batch_size, 1, vocab_size] \ No newline at end of file diff --git a/参考资料.md b/参考资料.md new file mode 100644 index 0000000..14eefec --- /dev/null +++ b/参考资料.md @@ -0,0 +1,5 @@ +1. https://github.com/karpathy/llama2.c +2. https://jalammar.github.io/illustrated-gpt2/ +3. https://www.cipsc.org.cn/uploadfiles/2023/02/20230207154741181.pdf +4. https://www.zhihu.com/people/4338c2384a026f9c1f430d81771f0e0a +5. https://github.com/Tongjilibo/build_MiniLLM_from_scratch

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