  Large Language Models (LLMs) have the ability to solve a variety of tasks,
such as text summarization and mathematical questions, just out of the box, but
they are often trained with a single task in mind. Due to high computational
costs, the current trend is to use prompt instruction tuning to better adjust
monolithic, pretrained LLMs for new -- but often individual -- downstream
tasks. Thus, how one would expand prompt tuning to handle -- concomitantly --
heterogeneous tasks and data distributions is a widely open question. To
address this gap, we suggest the use of \emph{Mixture of Prompts}, or MoPs,
associated with smart gating functionality: the latter -- whose design is one
of the contributions of this paper -- can identify relevant skills embedded in
different groups of prompts and dynamically assign combined experts (i.e.,
collection of prompts), based on the target task. Additionally, MoPs are
empirically agnostic to any model compression technique applied -- for
efficiency reasons -- as well as instruction data source and task composition.
In practice, MoPs can simultaneously mitigate prompt training "interference" in
multi-task, multi-source scenarios (e.g., task and data heterogeneity across
sources), as well as possible implications from model approximations. As a
highlight, MoPs manage to decrease final perplexity from $\sim20\%$ up to
$\sim70\%$, as compared to baselines, in the federated scenario, and from $\sim
3\%$ up to $\sim30\%$ in the centralized scenario.
