Despite efforts to expand the knowledge of large language models (LLMs), knowledge gaps—missing or outdated information in LLMs—might always persist given the evolving nature of knowledge. In this work, we study approaches to identify LLM knowledge gaps and abstain from answering questions when knowledge gaps are present. We first adapt existing approaches to model calibration or adaptation through fine-tuning/prompting and analyze their ability to abstain from generating low-confidence outputs. Motivated by their failures in self-reflection and over-reliance on held-out sets, we propose two novel approaches that are based on model collaboration, i.e., LLMs probing other LLMs for knowledge gaps, either cooperatively or competitively. Extensive experiments with three LLMs on four QA tasks featuring diverse knowledge domains demonstrate that both cooperative and competitive approaches to unveiling LLM knowledge gaps achieve up to 19.3% improvements on abstain accuracy against the strongest baseline. Further analysis reveals that our abstention methods pinpoint failure cases in retrieval augmentation and knowledge gaps in multi-hop reasoning.

Multilingual LLMs often have knowledge disparities across languages, with larger gaps in under-resourced languages. Teaching LLMs to abstain in the face of knowledge gaps is thus a promising strategy to mitigate hallucinations in multilingual settings. However, previous studies on LLM abstention primarily focus on English; we find that directly applying existing solutions beyond English results in up to 20.5% performance gaps between high and low-resource languages, potentially due to LLMs’ drop in calibration and reasoning beyond a few resource-rich languages. To this end, we propose strategies to enhance LLM abstention by learning from multilingual feedback, where LLMs self-reflect on proposed answers in one language by generating multiple feedback items in related languages: we show that this helps identifying the knowledge gaps across diverse languages, cultures, and communities. Extensive experiments demonstrate that our multilingual feedback approach outperforms various strong baselines, achieving up to 9.2% improvement for low-resource languages across three black-box and open models on three datasets, featuring open-book, closed-book, and commonsense QA. Further analysis reveals that multilingual feedback is both an effective and a more equitable abstain strategy to serve diverse language speakers, and cultural factors have great impact on language selection and LLM abstention behavior, highlighting future directions for multilingual and multi-cultural reliable language modeling.