Donors and Recipients: On Asymmetric Transfer Across Tasks and Languages with Parameter-Efficient Fine-Tuning

Large language models (LLMs) perform strongly across tasks and languages, yet how improvements in one task or language affect other tasks and languages remains poorly understood. We conduct a controlled LoRA fine-tuning study across multiple open-weight LLM families and scales, using a standardised grid of 11 languages and four benchmarks. We fine-tune each model on a single task-language source and measure transfer when evaluated on all other task-language target pairs. We decompose transfer into three regimes: (i) Matched-Task (Cross-Language), (ii) Matched-Language (Cross-Task), and (iii) Cross-Task (Cross-Language). Single-source fine-tuning yields a net positive uplift across regimes, but the gains are strongly asymmetric. Matched-Task (Cross-Language) transfer emerges as the most effective and predictable regime, driven principally by the identity of the target language rather than model architecture. We identify a stable hierarchy where high-resource languages and broad semantic tasks act as efficient recipients that absorb gains from diverse sources, while specialised tasks and lower-resource languages are more isolated. These results imply that effective fine-tuning requires navigating donor-recipient roles to maximise downstream gains.