When Transfer Breaks Fairness: A Group-Conditional Perspective on Fair and Robust Adaptation of Large Language Models

Large language models (LLMs) reach users only after a chain of transfer steps: full or parameter-efficient fine-tuning, preference alignment, prompting, and changes to the decoding procedure. Each step alters the model, the distribution it faces, or both. Yet fairness and robustness are usually assessed once, on a single fixed test set. This paper presents a unified group-conditional framework to analyze how transfer affects the fairness and robustness of LLMs, and how existing methods try to preserve these properties. To characterize these trade-offs, we introduce a analytical framework that views fair and robust transfer as constrained distributionally robust optimization. We view fair and robust transfer as constrained distributionally robust optimization whose feasible set is determined by the transfer interface, and we split any change in a fairness gap into an update term, caused by changing the model, and shift term, caused by changing the data. Building on existing fairness-transfer bounds, we record two elementary consequences that the LLM literature has not made explicit: the group-conditional bound on the shift term is tight, and when only one group shifts, the marginal shift equals exactly a \( \pi_{\min} \) fraction of the fairness-relevant shift, where \( \pi_{\min} \) is that group's proportion. We use these observations to classify mitigation methods by interface and by the term they target, to offer a reading under which conflicting findings on low-rank adaptation are compatible, and to derive reporting recommendations. We close with open problems, including per-group certificates, fairness of approximate decoding, and cumulative drift under continual transfer.