  In the rapidly evolving landscape of large language models (LLMs) and mobile
edge computing for 6G, the need for efficient service delivery to mobile users
with constrained computational resources has become paramount. Addressing this,
our paper delves into a collaborative framework for model training where user
data and model adapters are shared with servers to optimize performance. Within
this framework, users initially update the first several layers of the adapters
while freezing the other layers of them, leveraging their local datasets. Once
this step is complete, these partially trained parameters are transmitted to
servers. The servers, equipped with more robust computational capabilities,
then update the subsequent layers. After this training, they send the enhanced
parameters back to the users. This collaborative training approach ensures that
mobile users with limited computational capacities can still benefit from
advanced LLM services without being burdened by exhaustive computations.
Central to our methodology is the DASHF algorithm, which encapsulates the
Dinkelbach algorithm, alternating optimization, semidefinite relaxation (SDR),
the Hungarian method, and a pioneering fractional programming technique from a
recent IEEE JSAC paper [1]. The crux of DASHF is its capability to reformulate
an optimization problem as Quadratically Constrained Quadratic Programming
(QCQP) via meticulously crafted transformations, making it solvable by SDR and
the Hungarian algorithm. Through extensive simulations, we demonstrate the
effectiveness of the DASHF algorithm, offering significant insights for the
advancement of collaborative LLM service deployments.
