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 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.