Do you think a peer-reviewd publication is formal enough to warrant precise language? These publications are not only read by specialists in the field. I use automatic differentiation in my daily work, but I'm not familiar with machine learning. Thus I am very confused when "backpropagation" is used to mean an optimization algorithm.

EDIT: It is as if physicists used the term "special relativity" to talk about "quantum mechanics" because, after all, quantum mechanics happens in Lorentzian spacetime. Now for specialists of quantum physics it may make sense, since they are using "special relativity" to distinguish it from fancier quantum theories that combine field theory with GR. But for normal people it would be certainly misleading. Using "backpropagation" to include optimization has the same feeling.