  Despite substantial progress in multilingual extractive Question Answering
(QA), models with high and uniformly distributed performance across languages
remain challenging, especially for languages with limited resources. We study
cross-lingual transfer mainly focusing on the Generalized Cross-Lingual
Transfer (G-XLT) task, where the question language differs from the context
language - a challenge that has received limited attention thus far. Our
approach seeks to enhance cross-lingual QA transfer using a high-performing
multilingual model trained on a large-scale dataset, complemented by a few
thousand aligned QA examples across languages. Our proposed strategy combines
cross-lingual sampling and advanced self-distillation training in generations
to tackle the previous challenge. Notably, we introduce the novel mAP@k
coefficients to fine-tune self-knowledge distillation loss, dynamically
regulating the teacher's model knowledge to perform a balanced and effective
knowledge transfer. We extensively evaluate our approach to assess XLT and
G-XLT capabilities in extractive QA. Results reveal that our self-knowledge
distillation approach outperforms standard cross-entropy fine-tuning by a
significant margin. Importantly, when compared to a strong baseline that
leverages a sizeable volume of machine-translated data, our approach shows
competitive results despite the considerable challenge of operating within
resource-constrained settings, even in zero-shot scenarios. Beyond performance
improvements, we offer valuable insights through comprehensive analyses and an
ablation study, further substantiating the benefits and constraints of our
approach. In essence, we propose a practical solution to improve cross-lingual
QA transfer by leveraging a few data resources in an efficient way.
