Optimizing Language Models for Crosslingual Knowledge Consistency

Large language models are known to often exhibit inconsistent knowledge. This is particularly problematic in multilingual scenarios, where models are likely to be asked similar questions in different languages, and inconsistent responses can undermine their reliability. In this work, we show that this issue can be mitigated using reinforcement learning with a structured reward function, which leads to an optimal policy with consistent crosslingual responses. We introduce Direct Consistency Optimization (DCO), a DPO-inspired method that requires no explicit reward model and is derived directly from the LLM itself. Comprehensive experiments show that DCO significantly improves crosslingual consistency across diverse LLMs and outperforms existing methods when training with samples of multiple languages, while complementing DPO when gold labels are available. Extra experiments demonstrate the effectiveness of DCO in bilingual settings, significant out-of-domain generalizability, and controllable alignment via direction hyperparameters. Taken together, these results establish DCO as a robust and efficient solution for improving knowledge consistency across languages in multilingual LLMs. All code, training scripts, and evaluation benchmarks will be released at https://anonymous.