A Systematic Evaluation of Cross-Lingual Consistency Enhancement Methods in Multilingual Language Models

Multilingual language models often produce inconsistent answers to semantically equivalent questions across languages, motivating methods to improve cross-lingual consistency (CLC). However, existing methods are typically evaluated using different models, tasks, and protocols, leaving their relative strengths unclear. In this work, we present a unified evaluation of representative CLC-enhancement methods for question answering, spanning inference-time interventions and post-training approaches across three model families and three closed-form benchmarks. The results show that post-training methods are generally more reliable, with direct distribution alignment consistently improving CLC across all model-dataset combinations, while other methods are more sensitive to answer format and the breadth of language coverage. Notably, cross-domain transfer is limited unless source and target tasks share similar output formats. We further investigate whether CLC enhancement hurts models' ability to respond differently *when needed*, that is, when asked culture-dependent questions. Across two benchmarks of culturally diverse question answering, we find no systematic degradation in controlled closed-form evaluation, whereas open-ended generation reveals occasional accuracy reductions, particularly for non-English responses. Our work highlights the need to evaluate CLC enhancement for both cross-domain robustness and culturally appropriate variation, informing future work in post-training and benchmark development.