  Recent empirical evidence indicates that transformer based in-context
learning performs better when using a prefix language model (prefixLM), in
which in-context samples can all attend to each other, compared to causal
language models (causalLM), which use auto-regressive attention that prohibits
in-context samples to attend to future samples. While this result is intuitive,
it is not understood from a theoretical perspective. In this paper we take a
theoretical approach and analyze the convergence behavior of prefixLM and
causalLM under a certain parameter construction. Our analysis shows that both
LM types converge to their stationary points at a linear rate, but that while
prefixLM converges to the optimal solution of linear regression, causalLM
convergence dynamics follows that of an online gradient descent algorithm,
which is not guaranteed to be optimal even as the number of samples grows
infinitely. We supplement our theoretical claims with empirical experiments
over synthetic and real tasks and using various types of transformers. Our
experiments verify that causalLM consistently underperforms prefixLM in all
settings.
