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 $\theta_k$?

enter image description here

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

1 Answer 1


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


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