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 $$\theta_k$$?

• Here is a related question.
– nbro
Jan 14, 2021 at 0:26

$$\nabla_{\theta_{k-1}} \theta_k$$ 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.