SPELL-OUT: Preserving Semantic Progression in Cross-Lingual Alignment

Cross-Lingual Alignment (CLA) of LLMs has sought to improve multilingual consistency by aligning representations across languages while preserving general capabilities. However, it remains underexplored how to preserve shared semantic progression without collapsing language-specific realization or undermining general capabilities. In this work, we hypothesize that cross-lingual trajectories are better characterized as language-specific realizations of a shared semantic progression, and that CLA should preserve this structure rather than collapse it. We introduce SPELL-OUT, a relational representation alignment objective that uses the source-side trajectory to anchor semantic progression while adapting the target-side realization trajectory. We evaluate SPELL-OUT across diverse multilingual settings and general-capability evaluations. Representation-level analyses further characterize how shared semantic progress is preserved while language-specific trajectory structure remains differentiated. Further analyses show that SPELL-OUT supports diverse target languages under high-resource-language anchors, suggesting broader applicability beyond individual language pairs.