The Hug of Death seems to have killed the page so I can't really tell what it's about, but here's an example of inserting new trainable layers in BERT: https://arxiv.org/abs/1902.00751
I don't think it's Hug of Death even since it's not actually that much traffic and it's not down for me. Cloudflare + Github Pages just seems to be a much less reliable combination than I believed before I moved to it a year ago (it sometimes goes down even with almost no traffic, and then is up a second later).
This paper is definitely relevant though!