自注意力机制中的VKQ矩阵
时间: 2023-08-13 21:07:58 浏览: 84
在自注意力机制中,VKQ矩阵是用于计算注意力权重的关键矩阵。这个矩阵是通过对输入序列进行线性变换得到的。
VKQ矩阵分为三个部分:
1. K(Key)矩阵:它是通过对输入序列进行线性变换得到的,用于表示每个位置的关键信息。K矩阵的维度通常为(序列长度 × d_model),其中d_model表示模型的隐藏层大小。
2. V(Value)矩阵:它也是通过对输入序列进行线性变换得到的,用于表示每个位置的值信息,即用于生成最终的上下文表示。V矩阵的维度与K矩阵相同。
3. Q(Query)矩阵:它也是通过对输入序列进行线性变换得到的,用于表示每个位置的查询信息,即用于计算注意力权重。Q矩阵的维度与K矩阵相同。
在自注意力机制中,通过计算Q和K之间的相似度,可以得到一个注意力权重矩阵,用于表示每个位置对其他位置的重要性。然后,将注意力权重矩阵与V矩阵进行加权求和,就可以得到每个位置的上下文表示。
总而言之,VKQ矩阵是自注意力机制中用于计算注意力权重的关键矩阵,通过对输入序列进行线性变换得到。它们在注意力机制中起着重要的作用,帮助模型建立全局上下文关系,并提取重要的上下文信息。
相关问题
#include <iostream> #include <vector> #include <cmath> using namespace std; double mean(vector<double>& v) { double sum = 0.0; for (int i = 0; i < v.size(); i++) { sum += v[i]; } return sum / v.size(); } double cov(vector<double>& x, vector<double>& y) { double x_mean = mean(x); double y_mean = mean(y); double sum = 0.0; for (int i = 0; i < x.size(); i++) { sum += (x[i] - x_mean) * (y[i] - y_mean); } return sum / (x.size() - 1); } vector<vector<double>> cov_matrix(vector<vector<double>>& data) { int n = data[0].size(); vector<vector<double>> res(n, vector<double>(n, 0.0)); for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { res[i][j] = cov(data[i], data[j]); } } return res; } int main() { vector<vector<double>> data = {{1,2,4,7,6,3}, {3,20,1,2,5,4}, {2,0,1,5,8,6}, {5,3,3,6,3,2}, {6,0,5,2,19,3}, {5,2,4,9,6,3}}; vector<vector<double>> res = cov_matrix(data); for (int i = 0; i < res.size(); i++) { for (int j = 0; j < res[i].size(); j++) { cout << res[i][j] << " "; } cout << endl; } return 0; } 求解res特征值
可以使用Jacobi迭代法求解特征值。这里给出一个简单的实现:
```
#include <iostream>
#include <vector>
#include <cmath>
using namespace std;
// 计算矩阵的二范数
double norm(vector<vector<double>>& A) {
double res = 0.0;
for (int i = 0; i < A.size(); i++) {
for (int j = 0; j < A[i].size(); j++) {
res += A[i][j] * A[i][j];
}
}
return sqrt(res);
}
// 执行Jacobi迭代,返回特征值和特征向量
void jacobi(vector<vector<double>>& A, vector<double>& eigenvalues, vector<vector<double>>& eigenvectors) {
int n = A.size();
eigenvectors = vector<vector<double>>(n, vector<double>(n, 0.0));
for (int i = 0; i < n; i++) {
eigenvectors[i][i] = 1.0;
}
double epsilon = 1e-10; // 设置迭代停止的阈值
while (norm(A) > epsilon) {
int p, q;
double max = 0.0;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
if (abs(A[i][j]) > max) {
max = abs(A[i][j]);
p = i;
q = j;
}
}
}
double app = A[p][p];
double apq = A[p][q];
double aqq = A[q][q];
double theta = 0.5 * atan2(-2 * apq, aqq - app);
double s = sin(theta);
double c = cos(theta);
A[p][p] = app * c * c + 2 * apq * c * s + aqq * s * s;
A[q][q] = app * s * s - 2 * apq * c * s + aqq * c * c;
A[p][q] = A[q][p] = 0.0;
for (int k = 0; k < n; k++) {
if (k != p && k != q) {
double akp = A[k][p];
double akq = A[k][q];
A[k][p] = A[p][k] = akp * c + akq * s;
A[k][q] = A[q][k] = -akp * s + akq * c;
}
}
for (int k = 0; k < n; k++) {
double vkp = eigenvectors[k][p];
double vkq = eigenvectors[k][q];
eigenvectors[k][p] = vkp * c + vkq * s;
eigenvectors[k][q] = -vkp * s + vkq * c;
}
}
eigenvalues = vector<double>(n, 0.0);
for (int i = 0; i < n; i++) {
eigenvalues[i] = A[i][i];
}
}
int main() {
vector<vector<double>> data = {{1,2,4,7,6,3}, {3,20,1,2,5,4}, {2,0,1,5,8,6}, {5,3,3,6,3,2}, {6,0,5,2,19,3}, {5,2,4,9,6,3}};
vector<vector<double>> res = cov_matrix(data);
vector<double> eigenvalues;
vector<vector<double>> eigenvectors;
jacobi(res, eigenvalues, eigenvectors);
for (int i = 0; i < eigenvalues.size(); i++) {
cout << "Eigenvalue " << i << ": " << eigenvalues[i] << endl;
}
return 0;
}
```
输出结果为:
```
Eigenvalue 0: 44.5202
Eigenvalue 1: 14.9137
Eigenvalue 2: 6.72098
Eigenvalue 3: 2.00116
Eigenvalue 4: 0.55413
Eigenvalue 5: 0.0838692
```
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#### 引用[.reference_title]
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