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.

Self-consistency with chain-of-thought prompting (CoT) has demonstrated remarkable performance gains on various challenging tasks, by utilizing multiple reasoning paths sampled from large language models (LLMs). However, self-consistency relies on the answer extraction process to aggregate multiple solutions, which is not applicable to free-form answers. In this work, we propose Universal Self-Consistency (USC), which leverages LLMs themselves to select the most consistent answer among multiple candidates. We evaluate USC on a variety of benchmarks, including mathematical reasoning, code generation, long-context summarization, and open-ended question answering. On open-ended generation tasks where the original self-consistency method is not applicable, USC effectively utilizes multiple samples and improves the performance. For mathematical reasoning, USC matches the standard self-consistency performance without requiring the answer formats to be similar. Finally, without access to execution results, USC also matches the execution-based voting performance on code generation.