What is $ \nabla_{\theta_{k-1}} \theta_{k}$ in the context of MAML? I am attempting to fully understand the explicit derivation and computation of the Hessian and how it is used in MAML.  I came across this blog: https://lilianweng.github.io/lil-log/2018/11/30/meta-learning.html.
Specifically, could someone help to clarify this for me: is this term in the red box literally interpreted as the gradient at $\theta_{k-1}$ multiplied by the $\theta_k$?
$\nabla_{\theta_{k-1}} \theta_k$ is gradient of $\theta_k$ with respect to $\theta_{k-1}$, it follows chain rule as noted in the side comment in the image. $\nabla_{\theta} \mathcal L(\theta_k)$ is also not a Hessian but a gradient vector.