Why Better Cross-Lingual Alignment Fails for Better Cross-Lingual Transfer: Case of Encoders

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 $\times$ 3 tasks $\times$ 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

Cross-lingual alignment in multilingual language models is typically attributed to joint training: shared parameters, mixed-language batches, or explicit alignment objectives. We ask whether monolingual models trained on non-parallel data learn alignable representations without joint training. By testing on strictly monolingual language models, such as the Goldfish model families and independently developed models from different research labs, we find three results. Correlation: these models develop alignable representational geometry across layers, with alignment strengthening as data scale, model scale, or linguistic proximity increases. Construction: a single Procrustes rotation fit on parallel sentences maps hidden states between models. Causation: the same rotation transfers functional content; patching a rotated English residual into a German model on a factual cloze flips the prediction to the donor's capital in most cases. We confirm that cross-lingual alignment can emerge from the structure of language and the information it carries rather than from joint training, and this points to practical future directions including model stitching, merging, and modular multilingual systems built from monolingual components.

Realignment is a promising approach for improving the cross-lingual transfer ability of multilingual language models, particularly for extremely low-resource languages (LRLs). However, existing realignment methods rely on uniform and random sampling of parallel sentences across languages, which may be suboptimal under limited batch sizes. In practice, models may benefit from seeing certain languages more frequently, especially those that are poorly aligned, and the optimal distribution can evolve throughout training. In this work, we propose a simple yet effective adaptive sampling strategy that assigns trainable sampling probabilities to each language. Languages that contribute more to the realignment loss are sampled more frequently in subsequent batches, and the optimal distribution can evolve throughout training. Our method employs an inner-outer optimization loop with a small overhead, leading to consistent performance improvements and, more importantly, distributing the gains across languages. We observed a $+0.67$ average performance increase on all tasks with XLM-R, and $+0.60$ with Gemma 2 9B compared with uniform realignment. Furthermore, our method is robust across different models. Code available at https://github.com/felixgaschi/multilingual-alignment-and-transfer.