AI 基础知识十三 Transformer注意力机制(Attention)

指掀涛澜天下惊2026-04-03 10:52

注意力机制

Transformer 的核心是自注意力 与多头注意力，让序列每个位置都能动态关注全局相关信息，并行捕捉长程依赖。

自注意力公式

多头注意力公式

计算步骤

参照论文说明

  1. Q、 K矩阵相乘

  2. 缩放处理

  3. 加掩码处理 是可选项

  4. Softmax 归一化指数函数

  5. 与V矩阵相乘

本着简单的原则，用一个实例来说明Q,K,V计算过程

实例

自注意力

实现代码

例子 "Welcome to Machine Learning Pad Pad" 经过 词嵌入 和**位置编码，**得到6X4矩阵,为了方便计算对这个矩阵手动设置特定的数据

cpp 复制代码 
/*

	{"Pad",      0},
	{"Welcome",  1},
	{"to",       2},
	{"Machine",  3},
	{"Learning", 4}

	1. Welcome to Machine Learning Pad Pad -- > [1,2,3,4,0,0]

	2. Embedding + PositionalEncoding        ->  x

	3. x: [6 ,4]  

*/

	auto x = torch::tensor({
				{{1.0, 0.0, 0.0, 0.0}, // Welcome
				 {2.0, 0.0, 0.0, 0.0}, // to
				 {3.0, 0.0, 0.0, 0.0}, // Machine
				 {4.0, 0.0, 0.0, 0.0}, // Learning
				 {0.0, 0.0, 0.0, 0.0}, // Pad
				 {0.0, 0.0, 0.0, 0.0}  // Pad
				} }, torch::kFloat);

Q,K,V是一组权重 它的词嵌入的 维度**，**为了方便计算都它们设定单位矩阵

cpp 复制代码 
class SelfAttention : public torch::nn::Module
{
public:
	SelfAttention()
	{


	}
	void InitQKV(int64_t dim)
	{
		auto linear = torch::nn::LinearOptions(dim, dim).bias(false);

		Q = register_module("q", torch::nn::Linear(linear));
		K = register_module("k", torch::nn::Linear(linear));
		V = register_module("v", torch::nn::Linear(linear));

		norm_fact = 1.0 / sqrt(dim); // 缩放

		auto onesw = torch::eye(dim);  //单位矩阵

		Q->weight.set_data(onesw);
		K->weight.set_data(onesw);
		V->weight.set_data(onesw);
	}

	
	torch::nn::Linear Q{ nullptr };
	torch::nn::Linear K{ nullptr };
	torch::nn::Linear V{ nullptr };
	double norm_fact = 0 ;
};

torch::nn::Transformer 要求输入张量形状**seq, batch, dim,** 这里简单化为**seq,dim**

参照论文实现计算步骤

cpp 复制代码 
	auto forward(torch::Tensor x,torch::Tensor mask = {})
	{
		torch::Tensor q ;
		torch::Tensor k ;
		torch::Tensor v;
		torch::Tensor kt;
		torch::Tensor out;

		auto dim = x.dim();
	
	
		// x: [seq, dim]
		InitQKV(x.size(1));
		
		/// 1.输入x 与 q k v 运算  q k v是 单位矩阵所以 q k v = x
		 q = Q->forward(x);
		 k = K->forward(x);
		 v = V->forward(x);

		 cout << "q k v \n" << q << endl;

		
		kt = k.transpose(0, 1);// kt 是 k 的置换矩阵  kt: [dim,seq]
		

		cout << "kt \n" << kt << endl;

		auto attn_score = torch::matmul(q, kt); //2.  q:[seq, dim] X kt: [dim,seq] -> [seq, seq]
		cout << "q X kt \n" << attn_score << endl;

		attn_score = attn_score * norm_fact;     //3. 矩阵缩放
		cout << "scale q.X.kt  \n" << attn_score << endl;

		if (mask.defined())
		{
			attn_score += mask;
		}


		attn_score = torch::softmax(attn_score, -1);//4. Softmax 归一化指数函数
		cout << "torch::softmax q.X.kt  \n" << attn_score << endl;

		out = torch::matmul(attn_score, v); /// 5.与V矩阵相乘  [seq, seq] X v:[seq, dim] -> [seq, dim]

		cout << "torch::matmul V  \n" << out << endl;
	
		return out;
	}

重点解析

  1. = =

实际意义是

矩阵相乘结果

每个字符都能其他字符产生运算，也就是它能根据上下文来确定语意，字符序列长度N，Transformer时间复杂度为

  1. Softmax 归一化指数函数

数学公: 式 输入向量

=

第 i 个元素的 Softmax 输出为

每行内所有数据相加等于1, 原数据按一定比例缩小

  1. 与V矩阵相乘

qkv现在全部建立关系了

当要求输入张量形状**seq, batch, dim**时，其流程都一样，要变换处理张量

高维张量矩阵相乘

公式： a..,..., M,N * b...,...,N, K = ..,...,M, K 看到最后两维和两维矩阵相乘一样

整理之的代码，支持两三维输入张量

cpp 复制代码 
	auto forward(torch::Tensor x,torch::Tensor mask = {})
	{
		torch::Tensor q ;
		torch::Tensor k ;
		torch::Tensor v;
		torch::Tensor kt;
		torch::Tensor out;

		auto dim = x.dim();
	

		if (dim == 3)
		{
			//x:  [batch, seq, dim]  --->  [seq, batch, dim]
			x = x.permute({1,0,2});
			InitQKV(x.size(2));
		}
		else
		{
			// x: [seq, dim]
			InitQKV(x.size(1));
		}
		/// 1.输入x 与 q k v 运算  q k v是 单位矩阵所以 q k v = x
		 q = Q->forward(x);
		 k = K->forward(x);
		 v = V->forward(x);

		 cout << "q k v \n" << q << endl;

		if (dim == 3)
		{
			kt = k.permute({ 1,2,0 });
		 	v = v.permute({ 1,0,2 });
		}
		else
		{
			kt = k.transpose(0, 1);// kt 是 k 的置换矩阵  kt: [dim,seq]
		}

	
		cout << "kt \n" << kt << endl;

		auto attn_score = torch::matmul(q, kt); //2.  
		cout << "q X kt \n" << attn_score << endl;

		attn_score = attn_score * norm_fact;     //3. 矩阵缩放
		cout << "scale q.X.kt  \n" << attn_score << endl;

		if (mask.defined())
		{
			attn_score += mask;
		}


		attn_score = torch::softmax(attn_score, -1);//4. Softmax 归一化指数函数
		cout << "torch::softmax q.X.kt  \n" << attn_score << endl;

		out = torch::matmul(attn_score, v); /// 5. qKt * V

		cout << "torch::matmul V  \n" << out << endl;
	
		return out;
	}

多头注意力

在"自注意力"的基础上增加

  1. 维度被为多份 分别用于Q K V 计算

2.将多份重新拼接

3.最后加输出投影

输入两维张量时，写一个函数forward

  1. 输入张量x 形状**seq, dim， q、k、v** 形状 seq, dim

  2. 将q、k、v 拆分成 H, S, Dk ， seq简写S, H：头数量, Dk = dim/ H

cpp 复制代码 
q = q.view({ seq,H,Dk }); //q: [seq, dim] ->   [S, H, Dk] 
k = k.view({ seq,H,Dk });
v = v.view({ seq,H,Dk });

q = q.permute({ 1,0,2 }); //[S, H, Dk] --->[H, S, Dk]
k = k.permute({ 1,0,2 });
v = v.permute({ 1,0,2 });
  1. 调 形状 H, Dk, S
cpp 复制代码 
auto kt = k.permute({ 0,2,1 }); //kt:  [H, S, Dk] --> [H, Dk, S]
  1. 与V矩阵相乘之后 输出形状 H, S, Dk， 要转换成 S, H, Dk
cpp 复制代码 
auto out = torch::matmul(attn_score, v); // [H, S, S] * [H, S, Dk]  ->  out: [H, S, Dk]
  1. S, H, Dk 拼接成 **seq, dim，**最后输出投影
cpp 复制代码 
out = out.transpose(1, 0).contiguous().view({ seq, dim }); //  [H, S, Dk] --> [S, H, Dk] -> [seq, dim]

cout << "torch::matmul QK * V  \n" << out.squeeze() << endl;

out = Wo->forward(out);

输入三维张量时，写一个函数forward2去实现，除了张量形状调整不同外其他都一样，实现细节只能看代码

cpp 复制代码 
	auto forward(torch::Tensor x, int64_t head = 2, torch::Tensor mask = {})
	{
		x.squeeze_(); //x: [batch, seq ,dim]  -->   [seq, dim]
		assert(x.dim() == 2);
		//x: [seq, dim]
		  
		InitQKV(x.size(1), head);

		auto seq = x.size(0);
		auto dim = x.size(1);

		auto q = Q->forward(x);
		auto k = K->forward(x);
		auto v = V->forward(x);
		q = q.view({ seq,H,Dk }); //q: [seq, dim] ->   [S, H, Dk] 
		k = k.view({ seq,H,Dk });
		v = v.view({ seq,H,Dk });

		q = q.permute({ 1,0,2 }); //[S, H, Dk] --->[H, S, Dk]
		k = k.permute({ 1,0,2 });
		v = v.permute({ 1,0,2 });

		cout << "q k v \n" << q << endl;

		auto kt = k.permute({ 0,2,1 }); //kt:  [H, S, Dk] --> [H, Dk, S]

		cout << "kt \n" << kt << endl;

		auto attn_score = torch::matmul(q, kt);  // [H, S, Dk] *  [H, Dk, S]
		cout << "q X kt \n" << attn_score << endl;


		attn_score = attn_score * norm_fact;
		cout << "scale q.X.kt  \n" << attn_score << endl;

		if (mask.defined())
		{
			attn_score += mask;
		}

		attn_score = torch::softmax(attn_score, -1); /// attn_score: [H, S, S]
		cout << "torch::softmax q.X.kt  \n" << attn_score.squeeze() << endl;

		auto out = torch::matmul(attn_score, v); // [H, S, S] * [H, S, Dk]  ->  out: [H, S, Dk]
		out = out.transpose(1, 0).contiguous().view({ seq, dim }); //  [H, S, Dk] --> [S, H, Dk] -> [seq, dim]

		cout << "torch::matmul QK * V  \n" << out.squeeze() << endl;
		
		out = Wo->forward(out);

		return out;
	}


	auto forward2(torch::Tensor x, int64_t head = 2,torch::Tensor mask = {})
	{
		assert(x.dim() == 3);
	  
		x = x.permute({ 1,0,2 });  //   x: x: [batch, seq, dim]-->  [seq, batch, dim]

		InitQKV(x.size(2), head);

		auto seq = x.size(0);
		auto batch = x.size(1);
		auto dim = x.size(2);

		auto q = Q->forward(x);
		auto k = K->forward(x);
		auto v = V->forward(x);
		q = q.view({ seq,batch,H,Dk}); //q: [seq, batch, dim] ->   [S, B, H, Dk] 
		k = k.view({ seq,batch,H,Dk });
		v = v.view({ seq,batch,H,Dk });
		
		q = q.permute({1,2,0,3}); //[S, B, H, Dk] --->[B, H, S, Dk]
		k = k.permute({ 1,2,0,3 });
		v = v.permute({ 1,2,0,3 });
		
		cout << "q k v \n" << q << endl;

		auto kt = k.permute({ 0,1,3,2}); //kt:  [B, H, S, Dk] --> [B, H, Dk, S]

		cout << "kt \n" << kt.squeeze() << endl;

		auto attn_score = torch::matmul(q, kt);
		cout << "q X kt \n" << attn_score << endl;


		attn_score = attn_score * norm_fact;
		cout << "scale q.X.kt  \n" << attn_score << endl;

		if (mask.defined())
		{
			attn_score += mask;
		}

		attn_score = torch::softmax(attn_score, -1); /// attn_score: [B, H, S, S]
		cout << "torch::softmax q.X.kt  \n" << attn_score << endl;

		auto out = torch::matmul(attn_score, v); // [B, H, S, S] * [B, H, S, Dk]  ->  out: [B, H, S, Dk]
		out = out.transpose(1, 2).contiguous().view({ seq,batch, dim }); //  [B, H, S, Dk] --> [B, S, H, Dk] -> [seq,batch, dim]
		
		cout << "torch::matmul QK * V  \n" << out << endl;
		
		out = Wo->forward(out);

		return out;
	}

完整代码

cpp 复制代码 
#include <torch/torch.h>
#include <iostream>
#include <torch/serialize.h>
#include <regex>
//#include <iostream>
#include <fstream>
using namespace std;


class FeedForwardNet : public torch::nn::Module
{
	//Q = register_module("q", torch::nn::Linear(linear));
};



class SelfAttention : public torch::nn::Module
{
public:
	SelfAttention()
	{


	}
	void InitQKV(int64_t dim)
	{
		auto linear = torch::nn::LinearOptions(dim, dim).bias(false);

		Q = register_module("q", torch::nn::Linear(linear));
		K = register_module("k", torch::nn::Linear(linear));
		V = register_module("v", torch::nn::Linear(linear));

		norm_fact = 1.0 / sqrt(dim); // 缩放

		auto onesw = torch::eye(dim); //单位矩阵

		Q->weight.set_data(onesw);
		K->weight.set_data(onesw);
		V->weight.set_data(onesw);
	}

	
	auto forward(torch::Tensor x,torch::Tensor mask = {})
	{
		torch::Tensor q ;
		torch::Tensor k ;
		torch::Tensor v;
		torch::Tensor kt;
		torch::Tensor out;

		auto dim = x.dim();
	

		if (dim == 3)
		{
			//x:  [batch, seq, dim]  --->  [seq, batch, dim]
			x = x.permute({1,0,2});
			InitQKV(x.size(2));
		}
		else
		{
			// x: [seq, dim]
			InitQKV(x.size(1));
		}
		/// 1.输入x 与 q k v 运算  q k v是 单位矩阵所以 q k v = x
		 q = Q->forward(x);
		 k = K->forward(x);
		 v = V->forward(x);

		 cout << "q k v \n" << q << endl;

		if (dim == 3)
		{
			kt = k.permute({ 1,2,0 });
		 	v = v.permute({ 1,0,2 });
		}
		else
		{
			kt = k.transpose(0, 1);// kt 是 k 的置换矩阵  kt: [dim,seq]
		}

	
		cout << "kt \n" << kt << endl;

		auto attn_score = torch::matmul(q, kt); //2.  
		cout << "q X kt \n" << attn_score << endl;

		attn_score = attn_score * norm_fact;     //3. 矩阵缩放
		cout << "scale q.X.kt  \n" << attn_score << endl;

		if (mask.defined())
		{
			attn_score += mask;
		}


		attn_score = torch::softmax(attn_score, -1);//4. Softmax 归一化指数函数
		cout << "torch::softmax q.X.kt  \n" << attn_score << endl;

		out = torch::matmul(attn_score, v); /// 5. qKt * V

		cout << "torch::matmul V  \n" << out << endl;
	
		return out;
	}

	torch::nn::Linear Q{ nullptr };
	torch::nn::Linear K{ nullptr };
	torch::nn::Linear V{ nullptr };
	double norm_fact = 0 ;
};

class MultiHeadAttention: public torch::nn::Module
{
public:
	void InitQKV(int64_t dim, int64_t head=2)
	{
		assert(dim % head == 0);

		auto linear = torch::nn::LinearOptions(dim, dim).bias(false);

		Q = register_module("q", torch::nn::Linear(linear));
		K = register_module("k", torch::nn::Linear(linear));
		V = register_module("v", torch::nn::Linear(linear));
		Wo = register_module("Wo", torch::nn::Linear(linear)); // 输出投影

		norm_fact = 1.0 / sqrt(dim);
		
		Dk = dim / head;
		H = head;

		auto onesw = torch::eye(dim);   
		Q->weight.set_data(onesw);
		K->weight.set_data(onesw);
		V->weight.set_data(onesw);
		Wo->weight.set_data(onesw);
	}

	auto forward(torch::Tensor x, int64_t head = 2, torch::Tensor mask = {})
	{
		x.squeeze_(); //x: [batch, seq ,dim]  -->   [seq, dim]
		assert(x.dim() == 2);
		//x: [seq, dim]
		  
		InitQKV(x.size(1), head);

		auto seq = x.size(0);
		auto dim = x.size(1);

		auto q = Q->forward(x);
		auto k = K->forward(x);
		auto v = V->forward(x);
		q = q.view({ seq,H,Dk }); //q: [seq, dim] ->   [S, H, Dk] 
		k = k.view({ seq,H,Dk });
		v = v.view({ seq,H,Dk });

		q = q.permute({ 1,0,2 }); //[S, H, Dk] --->[H, S, Dk]
		k = k.permute({ 1,0,2 });
		v = v.permute({ 1,0,2 });

		cout << "q k v \n" << q << endl;

		auto kt = k.permute({ 0,2,1 }); //kt:  [H, S, Dk] --> [H, Dk, S]

		cout << "kt \n" << kt << endl;

		auto attn_score = torch::matmul(q, kt);  // [H, S, Dk] *  [H, Dk, S]
		cout << "q X kt \n" << attn_score << endl;


		attn_score = attn_score * norm_fact;
		cout << "scale q.X.kt  \n" << attn_score << endl;

		if (mask.defined())
		{
			attn_score += mask;
		}

		attn_score = torch::softmax(attn_score, -1); /// attn_score: [H, S, S]
		cout << "torch::softmax q.X.kt  \n" << attn_score.squeeze() << endl;

		auto out = torch::matmul(attn_score, v); // [H, S, S] * [H, S, Dk]  ->  out: [H, S, Dk]
		out = out.transpose(1, 0).contiguous().view({ seq, dim }); //  [H, S, Dk] --> [S, H, Dk] -> [seq, dim]

		cout << "torch::matmul QK * V  \n" << out.squeeze() << endl;
		
		out = Wo->forward(out);

		return out;
	}


	auto forward2(torch::Tensor x, int64_t head = 2,torch::Tensor mask = {})
	{
		assert(x.dim() == 3);
	  
		x = x.permute({ 1,0,2 });  //   x: x: [batch, seq, dim]-->  [seq, batch, dim]

		InitQKV(x.size(2), head);

		auto seq = x.size(0);
		auto batch = x.size(1);
		auto dim = x.size(2);

		auto q = Q->forward(x);
		auto k = K->forward(x);
		auto v = V->forward(x);
		q = q.view({ seq,batch,H,Dk}); //q: [seq, batch, dim] ->   [S, B, H, Dk] 
		k = k.view({ seq,batch,H,Dk });
		v = v.view({ seq,batch,H,Dk });
		
		q = q.permute({1,2,0,3}); //[S, B, H, Dk] --->[B, H, S, Dk]
		k = k.permute({ 1,2,0,3 });
		v = v.permute({ 1,2,0,3 });
		
		cout << "q k v \n" << q << endl;

		auto kt = k.permute({ 0,1,3,2}); //kt:  [B, H, S, Dk] --> [B, H, Dk, S]

		cout << "kt \n" << kt.squeeze() << endl;

		auto attn_score = torch::matmul(q, kt);
		cout << "q X kt \n" << attn_score << endl;


		attn_score = attn_score * norm_fact;
		cout << "scale q.X.kt  \n" << attn_score << endl;

		if (mask.defined())
		{
			attn_score += mask;
		}

		attn_score = torch::softmax(attn_score, -1); /// attn_score: [B, H, S, S]
		cout << "torch::softmax q.X.kt  \n" << attn_score << endl;

		auto out = torch::matmul(attn_score, v); // [B, H, S, S] * [B, H, S, Dk]  ->  out: [B, H, S, Dk]
		out = out.transpose(1, 2).contiguous().view({ seq,batch, dim }); //  [B, H, S, Dk] --> [B, S, H, Dk] -> [seq,batch, dim]
		
		cout << "torch::matmul QK * V  \n" << out << endl;
		
		out = Wo->forward(out);

		return out;
	}


	torch::nn::Linear Q{ nullptr };
	torch::nn::Linear K{ nullptr };
	torch::nn::Linear V{ nullptr };
	torch::nn::Linear Wo{ nullptr };

	double norm_fact = 0;
	int64_t Dk;
	int64_t H;
};


void TransformerAttentionMain()
{


	auto x = torch::tensor({
				{{1.0, 0.0, 0.0, 0.0}, // Welcome
				 {2.0, 0.0, 0.0, 0.0}, // to
				 {3.0, 0.0, 0.0, 0.0}, // Machine
				 {4.0, 0.0, 0.0, 0.0}, // Learning
				 {0.0, 0.0, 0.0, 0.0}, // Pad
				 {0.0, 0.0, 0.0, 0.0}  // Pad
				} }, torch::kFloat);



	
	auto w = torch::tensor({
			{
				{0.0, 1.0, 0.0, 0.0},
				{0.0, 2.0, 0.0, 0.0},
				{0.0, 3.0, 0.0, 0.0},
				{0.0, 4.0, 0.0, 0.0}
			}
		}, torch::kFloat);

	cout << "input\n" << x << endl;
	
	cout << "-------------SelfAttention--------------------\n"  << endl;
	auto x1 = x.squeeze();
	auto atten= SelfAttention();
	auto y = atten.forward(x1);
	cout << "-------------SelfAttention--------------------\n"  << endl;
	

	cout << "\n\n-------------MultiHeadAttention--------------------\n"  << endl;
	auto multiAtten = MultiHeadAttention();
	multiAtten.forward2(x,1);
	cout << "-------------MultiHeadAttention--------------------\n"  << endl;

}

感谢大家的支持，如要问题欢迎提问指正。

相关推荐
枫叶丹45 分钟前
Codex Hooks 实战：给 AI 工作流增加确定性门禁
人工智能·chatgpt·agent·codex
大鹏的NLP博客5 分钟前
CMAD：基于紧凑表征学习与马氏距离统计判别的工业异常检测架构
人工智能·深度学习
安逸sgr9 分钟前
Agent经典面试题：Agent 安全问题有哪些？如何防止工具误调用和 Prompt Injection？
人工智能·ai·agent·智能体
发量惊人的中年网工14 分钟前
AI服务器托管怎么选机房？GPU集群对机柜、电力和网络的硬要求
服务器·网络·人工智能
cn分享汇17 分钟前
2026 企业 AI 平台：低代码融合赛道
人工智能·低代码·rxjava
2501_9423895518 分钟前
为支撑持续攀升的AI资本开支
人工智能·oracle·hbase·database·storm
lkforce24 分钟前
Transformer架构下的详细计算流程模拟，精确到数字（单层单头）
人工智能·深度学习·ai·transformer
summer_du25 分钟前
Qdrant
人工智能·python
doiito（Do It Together）28 分钟前
【AI 应用】从“外国人味”到地道中文：kokoroi-rs v0.1.2 架构升级深度解析
人工智能
GuWenyue32 分钟前
AI对话打字机效果卡顿崩溃？1套Vue3流式代码搞定逐Token输出，彻底解决断包报错
人工智能
热门推荐
01GitHub 镜像站点02如何新建文件夹？ 电脑新建文件夹的4种方法032026年7月AI圈大地震：GPT-5.6被政府限制、Claude入驻Slack、Anthropic自研芯片04AI科技热点日报 | 2026年07月01日05国内可直接用、免费额度/永久免费的大模型API清单（含 SiliconFlow、火山、阿里、智谱、百度、Kimi、DeepSeek、DMXAPI 等）06幻兽帕鲁 - 服务器管理员权限与 GM 命令完全指南07AI 编程 IDE 全景解析 2026：Agent 全面接管开发链路08微信历史版本含下载地址（ Windows PC | 安卓 | MAC ）及设置微信不更新092026 国产 AI 大模型横评：DeepSeek、通义千问、Kimi、文心一言、星火、豆包谁更能打？10【解构】DeepSeek V4 发布：技术报告深度解读 + 横向对比六大开源模型，我们的判断是……