Transformers learn through gradual rank increase
Authors: name: Enric Boix-Adsera, name: Etai Littwin, name: Emmanuel Abbe, name: Samy Bengio, name: Joshua Susskind

We identify incremental learning dynamics in transformers, where the
difference between trained and initial weights progressively increases in rank.
We rigorously prove this occurs under the simplifying assumptions of diagonal
weight matrices and small initialization. Our experiments support the theory
and also show that phenomenon can occur in practice without the simplifying
assumptions.