# Cross-Lingual Representation Alignment by Token-Level Optimal Transport in a Language-Agnostic Space

arXiv: https://arxiv.org/abs/2609.06381 · HTML: https://mlsanity.com/paper/2609.06381/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 40 references that are in the map.
- First posted on arXiv 6 Sep 2026.

## Builds on (most cited first, 26 of 26)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [On the Cross-lingual Transferability of Monolingual Representations](https://mlsanity.com/paper/1910.11856/) (2019)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [The Belebele Benchmark: a Parallel Reading Comprehension Dataset in 122 Language Variants](https://mlsanity.com/paper/2308.16884/) (2023)
- [MEGA: Multilingual Evaluation of Generative AI](https://mlsanity.com/paper/2303.12528/) (2023)
- [Do Llamas Work in English? On the Latent Language of Multilingual Transformers](https://mlsanity.com/paper/2402.10588/) (2024)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [SGPT: GPT Sentence Embeddings for Semantic Search](https://mlsanity.com/paper/2202.08904/) (2022)
- [Global MMLU: Understanding and Addressing Cultural and Linguistic Biases in Multilingual Evaluation](https://mlsanity.com/paper/2412.03304/) (2024)
- [Word Alignment by Fine-tuning Embeddings on Parallel Corpora](https://mlsanity.com/paper/2101.08231/) (2021)
- [Aya Dataset: An Open-Access Collection for Multilingual Instruction Tuning](https://mlsanity.com/paper/2402.06619/) (2024)
- [The Geometry of Multilingual Language Model Representations](https://mlsanity.com/paper/2205.10964/) (2022)
- [On the Language Neutrality of Pre-trained Multilingual Representations](https://mlsanity.com/paper/2004.05160/) (2020)
- [WMT24++: Expanding the Language Coverage of WMT24 to 55 Languages & Dialects](https://mlsanity.com/paper/2502.12404/) (2025)
- [The Semantic Hub Hypothesis: Language Models Share Semantic Representations Across Languages and Modalities](https://mlsanity.com/paper/2411.04986/) (2024)
- [Inducing Language-Agnostic Multilingual Representations](https://mlsanity.com/paper/2008.09112/) (2020)
- [Lost in Multilinguality: Dissecting Cross-lingual Factual Inconsistency in Transformer Language Models](https://mlsanity.com/paper/2504.04264/) (2025)
- [Language Ranker: A Metric for Quantifying LLM Performance Across High and Low-Resource Languages](https://mlsanity.com/paper/2404.11553/) (2024)
- [Improving In-context Learning of Multilingual Generative Language Models with Cross-lingual Alignment](https://mlsanity.com/paper/2311.08089/) (2023)
- [Middle-Layer Representation Alignment for Cross-Lingual Transfer in Fine-Tuned LLMs](https://mlsanity.com/paper/2502.14830/) (2025)
- [MEXA: Multilingual Evaluation of English-Centric LLMs via Cross-Lingual Alignment](https://mlsanity.com/paper/2410.05873/) (2024)
- [Language-Specific Latent Process Hinders Cross-Lingual Performance](https://mlsanity.com/paper/2505.13141/) (2025)
- [Discovering Low-rank Subspaces for Language-agnostic Multilingual Representations](https://mlsanity.com/paper/2401.05792/) (2024)
- [When Less Language is More: Language-Reasoning Disentanglement Makes LLMs Better Multilingual Reasoners](https://mlsanity.com/paper/2505.15257/) (2025)
- [Unlocking Multilingual Reasoning Capability of LLMs and LVLMs through Representation Engineering](https://mlsanity.com/paper/2511.23231/) (2025)
- [Rethinking Cross-lingual Alignment: Balancing Transfer and Cultural Erasure in Multilingual LLMs](https://mlsanity.com/paper/2510.26024/) (2025)

## Abstract (arXiv)

Cross-lingual alignment (CLA) aims to align the representations of large language models (LLMs) across languages, enabling cross-lingual transfer to improve multilingual capabilities. Previous CLA methods often ignore language-specific information encoded in representations and only consider sentence-level alignment, which may lead to suboptimal performance and input-output language mismatch. We propose CAROT (Cross-Lingual Alignment of Representations in a Language-Agnostic Space via Optimal Transport), which consists of two steps: identifying language-specific representations in LLMs' internal states and aligning language-agnostic representations across languages at the token level by optimal transport, while explicitly preserving language-specific representations. Inference-time steering experiments show that the representations computed by CAROT are effective alignment targets, improving multilingual performance by up to 11.2 points in accuracy while maintaining input-output language consistency. We further use the representations obtained by CAROT as training targets, internalizing the aligned representations. The trained models outperform existing CLA methods in 11 of 18 evaluation settings (3 models × 3 tasks × ID/OOD languages). Our work provides insights into what constitutes effective alignment targets for CLA in LLMs. Code is available at https://github.com/ynklab/CAROT