  Large language models (LLM) have emerged as a powerful tool for AI, with the
key ability of in-context learning (ICL), where they can perform well on unseen
tasks based on a brief series of task examples without necessitating any
adjustments to the model parameters. One recent interesting mysterious
observation is that models of different scales may have different ICL
behaviors: larger models tend to be more sensitive to noise in the test
context. This work studies this observation theoretically aiming to improve the
understanding of LLM and ICL. We analyze two stylized settings: (1) linear
regression with one-layer single-head linear transformers and (2) parity
classification with two-layer multiple attention heads transformers (non-linear
data and non-linear model). In both settings, we give closed-form optimal
solutions and find that smaller models emphasize important hidden features
while larger ones cover more hidden features; thus, smaller models are more
robust to noise while larger ones are more easily distracted, leading to
different ICL behaviors. This sheds light on where transformers pay attention
to and how that affects ICL. Preliminary experimental results on large base and
chat models provide positive support for our analysis.
