backward函数中gradient参数的一些理解

当标量对向量求导时不需要该参数，但当向量对向量求导时，若不加上该参数则会报错，显示“grad can be implicitly created only for scalar outputs”，对该gradient参数解释如下。

当\(\mathbf y\)对\(\mathbf x\)求导时，结果为梯度矩阵，数学表达如下：

\[\frac{\partial \mathbf{y}}{\partial \mathbf{x}}=\left(\begin{array}{cccc}
\frac{\partial y_{1}}{\partial x_{1}} & \frac{\partial y_{2}}{\partial x_{1}} & \cdots & \frac{\partial y_{m}}{\partial x_{1}} \\
\frac{\partial y_{1}}{\partial x_{2}} & \frac{\partial y_{2}}{\partial x_{2}} & \cdots & \frac{\partial y_{m}}{\partial x_{2}} \\
\vdots & \vdots & \ddots & \vdots \\
\frac{\partial y_{1}}{\partial x_{n}} & \frac{\partial y_{2}}{\partial x_{n}} & \cdots & \frac{\partial y_{m}}{\partial x_{n}}
\end{array}\right)
\]

当获取\(x\)的梯度时，x.grad = \(\frac{\partial \mathbf{y}}{\partial \mathbf{x}}gradient\)

具体例子可见该博客中的例子 https://blog.csdn.net/kuan__/article/details/108828003