# Post-Training Language Models for Crosslingual Consistency

Source: [Post-Training Language Models for Crosslingual Consistency](<https://www.sota2.com/research/paper/69aa5f652d603e6de3e41703>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-30T05:00:11.986Z

Authors: Tianyu Liu, Jirui Qi, Mrinmaya Sachan, Ryan Cotterell, Raquel Fern\\'andez, Arianna Bisazza

Published: 2026-03-04T23:36:55.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Multilingual Language Understanding on MMMLU](<https://www.sota2.com/research/sota/multilingual-language-understanding-on-mmmlu.md>): Multilingual Language Understanding; MMMLU; CLCall: 13.8.

- [Commonsense Reasoning on XCSQA](<https://www.sota2.com/research/sota/commonsense-reasoning-on-xcsqa.md>): Commonsense Reasoning; XCSQA; CLCall Score: 9.1.

- [Factual Association on BMLAMA](<https://www.sota2.com/research/sota/factual-association-on-bmlama.md>): Factual association; BMLAMA; CLCall: 16.7.

- [General Knowledge on MMLU (CLCall, AEN, A¬EN)](<https://www.sota2.com/research/sota/general-knowledge-on-mmlu-clcall-aen-a-en.md>): General Knowledge; MMMLU; CLCall Score: 12.6.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.04678>)

[PDF](<https://arxiv.org/pdf/2603.04678.pdf>)