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

Abstract: LLMs perform strongly across tasks and languages, yet how improvements in one task or language affect other tasks and languages and their combinations remains poorly understood. We conduct a controlled PEFT/LoRA study across multiple open-weight LLM families and sizes, treating task and language as transfer axes while conditioning on model family and size; we fine-tune each model on a single task-language source and measure transfer as the percentage-point change versus its baseline score when evaluated on all other task-language target pairs. We decompose transfer into (i) Matched-Task (Cross-Language), (ii) Matched-Language (Cross-Task), and (iii) Cross-Task (Cross-Language) regimes. We uncover two consistent general patterns. First, a pronounced on-task vs. off-task asymmetry: Matched-Task (Cross-Language) transfer is reliably positive, whereas off-task transfer often incurs collateral degradation. Second, a stable donor-recipient structure across languages and tasks (hub donors vs. brittle recipients). We outline implications for risk-aware fine-tuning and model specialisation.