  The lottery ticket hypothesis posits the existence of ``winning tickets''
within a randomly initialized neural network. Do winning tickets exist for LLMs
in fine-tuning scenarios? How can we find such winning tickets? In this paper,
we propose KS-Lottery, a method to identify a small subset of LLM parameters
highly effective in multilingual fine-tuning. Our key idea is to use
Kolmogorov-Smirnov Test to analyze the distribution shift of parameters before
and after fine-tuning. We further theoretically prove that KS-Lottery can find
the certified winning tickets in the embedding layer, fine-tuning on the found
parameters is guaranteed to perform as well as full fine-tuning. Comparing
KS-Lottery with other parameter-efficient tuning algorithms on translation
tasks, the experimental results show that KS-Lottery finds a much smaller set
of parameters for fine-tuning while achieving the comparable performance as
full fine-tuning LLM. Surprisingly, we find that fine-tuning 18 tokens'
embedding of LLaMA suffices to reach the fine-tuning translation
performance~\footnote{https://github.com/CONE-MT/KS-Lottery.}.
