  Understanding transformer-based language models is becoming increasingly
crucial, particularly as they play pivotal roles in advancing towards
artificial general intelligence. However, language model research faces
significant challenges, especially for academic research groups with
constrained resources. These challenges include complex data structures,
unknown target functions, high computational costs and memory requirements, and
a lack of interpretability in the inference process, etc. Drawing a parallel to
the use of simple models in scientific research, we propose the concept of an
anchor function. This is a type of benchmark function designed for studying
language models in learning tasks that follow an "anchor-key" pattern. By
utilizing the concept of an anchor function, we can construct a series of
functions to simulate various language tasks. The anchor function plays a role
analogous to that of mice in diabetes research, particularly suitable for
academic research. We demonstrate the utility of the anchor function with an
example, revealing two basic operations by attention structures in language
models: shifting tokens and broadcasting one token from one position to many
positions. These operations are also commonly observed in large language
models. The anchor function framework, therefore, opens up a series of valuable
and accessible research questions for further exploration, especially for
theoretical study.
