Authors seemed to have missed the history. They should at least cite Binary Connect or Straight Through Estimators (not my work).
Helpful hint to authors: you can get down to 0.68 bits / weight using a similar technique, good chance this will work for LLMs too.
https://arxiv.org/abs/1606.01981
This was a passion project of mine in my last few months at IBM research :).
I am convinced there is a deep connection to understanding why backprop is unreasonably effective, and the result that you can train low precision DNNs; for those note familiar, the technique is to compute the loss wrt to the low precision parameters (eg project to ternary) but apply the gradient to high precision copy of parameters (known as the straight through estimator). This is a biased estimator and there is no theoretical underpinning for why this should work, but in practice it works well.
My best guess is that it is encouraging the network to choose good underlying subnetworks to solve the problem, similar to Lottery Ticket Hypothesis. With ternary weights it is just about who connects to who (ie a graph), and not about the individual weight values anymore.