# Post-Training Language Models for Crosslingual Consistency

arXiv: https://arxiv.org/abs/2603.04678 · HTML: https://mlsanity.com/paper/2603.04678/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Aya Model: An Instruction Finetuned Open-Access Multilingual Language Model](https://mlsanity.com/paper/2402.07827/) (2024)
- [Direct Language Model Alignment from Online AI Feedback](https://mlsanity.com/paper/2402.04792/) (2024)
- [Cross-Lingual Consistency of Factual Knowledge in Multilingual Language Models](https://mlsanity.com/paper/2310.10378/) (2023)
- [X-FACTR: Multilingual Factual Knowledge Retrieval from Pretrained Language Models](https://mlsanity.com/paper/2010.06189/) (2020)
- [Lost in Multilinguality: Dissecting Cross-lingual Factual Inconsistency in Transformer Language Models](https://mlsanity.com/paper/2504.04264/) (2025)
- [Middle-Layer Representation Alignment for Cross-Lingual Transfer in Fine-Tuned LLMs](https://mlsanity.com/paper/2502.14830/) (2025)
- [Paths Not Taken: Understanding and Mending the Multilingual Factual Recall Pipeline](https://mlsanity.com/paper/2505.20546/) (2025)
- [Causal Estimation of Tokenisation Bias](https://mlsanity.com/paper/2506.03149/) (2025)
- [CALM: Unleashing the Cross-Lingual Self-Aligning Ability of Language Model Question Answering](https://mlsanity.com/paper/2501.18457/) (2025)
- [Are Knowledge and Reference in Multilingual Language Models Cross-Lingually Consistent?](https://mlsanity.com/paper/2507.12838/) (2025)
- [Evaluating Knowledge-based Cross-lingual Inconsistency in Large Language Models](https://mlsanity.com/paper/2407.01358/) (2024)

## Built on by (most cited first, 3 of 3)

- [PolyFact: Comparing Consistency-Driven Post-training Methods for Cross-Lingual Factual Recall](https://mlsanity.com/paper/2606.06586/) (2026)
- [A Systematic Evaluation of Cross-Lingual Consistency Enhancement Methods in Multilingual Language Models](https://mlsanity.com/paper/2609.04409/) (2026)
- [Why Pretraining Fails to Share Cross-Lingual Knowledge](https://mlsanity.com/paper/2609.19291/) (2026)

## Abstract (arXiv)

Language models often respond inconsistently to translation-equivalent prompts across languages, undermining the reliability of multilingual systems. To quantify this, we give an information-theoretic definition of crosslingual consistency as a divergence bound between a model's response distribution and its round-trip pushforward across languages. We then introduce penalized consistency optimization (PCO), a post-training procedure that couples this divergence with a Kullback-Leibler penalty to a fixed reference language model. Because direct optimization of PCO requires expensive on-policy roll-outs, we propose a tractable surrogate, direct consistency optimization (DCO), which can be optimized off-policy. Across diverse language models and 26 languages, DCO significantly improves crosslingual consistency, outperforms existing methods, and enables targeted alignment of low-resource languages.