  Pretrained language models have achieved state-of-the-art performance when
adapted to a downstream NLP task. However, theoretical analysis of these models
is scarce and challenging since the pretraining and downstream tasks can be
very different. We propose an analysis framework that links the pretraining and
downstream tasks with an underlying latent variable generative model of text --
the downstream classifier must recover a function of the posterior distribution
over the latent variables. We analyze head tuning (learning a classifier on top
of the frozen pretrained model) and prompt tuning in this setting. The
generative model in our analysis is either a Hidden Markov Model (HMM) or an
HMM augmented with a latent memory component, motivated by long-term
dependencies in natural language. We show that 1) under certain non-degeneracy
conditions on the HMM, simple classification heads can solve the downstream
task, 2) prompt tuning obtains downstream guarantees with weaker non-degeneracy
conditions, and 3) our recovery guarantees for the memory-augmented HMM are
stronger than for the vanilla HMM because task-relevant information is easier
to recover from the long-term memory. Experiments on synthetically generated
data from HMMs back our theoretical findings.
