Linear Transformers are Versatile In-Context Learners
Authors: name: Max Vladymyrov, name: Johannes von Oswald, name: Mark Sandler, name: Rong Ge

Recent research has demonstrated that transformers, particularly linear
attention models, implicitly execute gradient-descent-like algorithms on data
provided in-context during their forward inference step. However, their
capability in handling more complex problems remains unexplored. In this paper,
we prove that any linear transformer maintains an implicit linear model and can
be interpreted as performing a variant of preconditioned gradient descent. We
also investigate the use of linear transformers in a challenging scenario where
the training data is corrupted with different levels of noise. Remarkably, we
demonstrate that for this problem linear transformers discover an intricate and
highly effective optimization algorithm, surpassing or matching in performance
many reasonable baselines. We reverse-engineer this algorithm and show that it
is a novel approach incorporating momentum and adaptive rescaling based on
noise levels. Our findings show that even linear transformers possess the
surprising ability to discover sophisticated optimization strategies.