diff --git a/docs/1.4/blitz/autograd_tutorial.md b/docs/1.4/blitz/autograd_tutorial.md index f1a66621b26da80d138e9fa30b7f8c4dafb2582e..2f410f21db4729b63a643a56436f56122078d925 100644 --- a/docs/1.4/blitz/autograd_tutorial.md +++ b/docs/1.4/blitz/autograd_tutorial.md @@ -138,10 +138,10 @@ tensor([[4.5000, 4.5000], $$ J=\left(\begin{array}{ccc} - \frac{\partial y_{1}}{\partial x_{1}} & \cdots & \frac{\partial y_{m}}{\partial x_{1}}\\ - \vdots & \ddots & \vdots\\ - \frac{\partial y_{1}}{\partial x_{n}} & \cdots & \frac{\partial y_{m}}{\partial x_{n}} - \end{array}\right) + \frac{\partial y_{1}}{\partial x_{1}} & \cdots & \frac{\partial y_{1}}{\partial x_{n}}\\ + \vdots & \ddots & \vdots\\ + \frac{\partial y_{m}}{\partial x_{1}} & \cdots & \frac{\partial y_{m}}{\partial x_{n}} + \end{array}\right) $$ 通常来说,`torch.autograd` 是计算雅可比向量积的一个“引擎”。也就是说,给定任意向量 $$v=\left(\begin{array}{cccc} v_{1} & v_{2} & \cdots & v_{m}\end{array}\right)^{T}$$,计算乘积 $$v^{T}\cdot J$$。如果 $$v$$ 恰好是一个标量函数 $$l=g\left(\vec{y}\right)$$ 的导数,即 $$v=\left(\begin{array}{ccc}\frac{\partial l}{\partial y_{1}} & \cdots & \frac{\partial l}{\partial y_{m}}\end{array}\right)^{T}$$,那么根据链式法则,雅可比向量积应该是 $$l$$ 对 $$\vec{x}$$ 的导数: