It's a research paper targeted at other researchers; you do need to understand some of the field for it to make sense. It's not written to be MechInterp 101.
But it's not bad writing. It's actually very clear. I'm not an professional AI researcher, I just read papers for fun, but I found everything in Nick's article clearly articulated and easy to understand. It's actually one of the more digestable papers I've come across this year.
Here's a translation to easier language:
> "a network’s own mechanisms are its legible building blocks"
To understand this you have to know that up until now attempts to figure out what's going on inside neural networks have relied on indirect techniques, in particular by training another neural network to "unpack" what's happening in the first. This was driven by the belief that a deep neural network isn't directly readable (legible) because the neurons do so many unrelated things simultaneously.
Nick is saying that actually, you don't need a second neural net. You can just read out what's happening directly from the first's own "mechanisms" (arrangements of neurons and weights between them).
> "The canonical evidence of polysemanticity and superposition that convinced much of the field, including me, that networks pack concepts arbitrarily was misread."
In simpler English: we thought individual neurons did lots of unrelated things, but that's because the standard evidence we had for that belief was misunderstood.
"Concepts do not overlap arbitrarily" and "Concepts overlap in a recurring pattern" don't mean the same thing as what he's saying.