  Mainstream LLM research has primarily focused on enhancing their generative
capabilities. However, even the most advanced LLMs experience uncertainty in
their outputs, often producing varied results on different runs or when faced
with minor changes in input, despite no substantial change in content. Given
multiple responses from the same LLM to the same input, we advocate leveraging
the LLMs' discriminative capability to reduce this generative uncertainty,
aiding in identifying the correct answers. Specifically, we propose and analyze
three discriminative prompts: direct, inverse, and hybrid, to explore the
potential of both closed-source and open-source LLMs in self-improving their
generative performance on two benchmark datasets. Our insights reveal which
discriminative prompt is most promising and when to use it. To our knowledge,
this is the first work to systematically analyze LLMs' discriminative capacity
to address generative uncertainty.
