  As an effective alternative to the direct fine-tuning on target tasks in
specific languages, cross-lingual transfer addresses the challenges of limited
training data by decoupling ''task ability'' and ''language ability'' by
fine-tuning on the target task in the source language and another selected task
in the target language, respectively. However, they fail to fully separate the
task ability from the source language or the language ability from the chosen
task. In this paper, we acknowledge the mutual reliance between task ability
and language ability and direct our attention toward the gap between the target
language and the source language on tasks. As the gap removes the impact of
tasks, we assume that it remains consistent across tasks. Based on this
assumption, we propose a new cross-lingual transfer method called
$\texttt{AdaMergeX}$ that utilizes adaptive adapter merging. By introducing a
reference task, we can determine that the divergence of adapters fine-tuned on
the reference task in both languages follows the same distribution as the
divergence of adapters fine-tuned on the target task in both languages. Hence,
we can obtain target adapters by combining the other three adapters.
Furthermore, we propose a structure-adaptive adapter merging method. Our
empirical results demonstrate that our approach yields new and effective
cross-lingual transfer, outperforming existing methods across all settings.
