  While large language models exhibit certain cross-lingual generalization
capabilities, they suffer from performance degradation (PD) on unseen
closely-related languages (CRLs) and dialects relative to their high-resource
language neighbour (HRLN). However, we currently lack a fundamental
understanding of what kinds of linguistic distances contribute to PD, and to
what extent. Furthermore, studies of cross-lingual generalization are
confounded by unknown quantities of CRL language traces in the training data,
and by the frequent lack of availability of evaluation data in lower-resource
related languages and dialects. To address these issues, we model phonological,
morphological, and lexical distance as Bayesian noise processes to synthesize
artificial languages that are controllably distant from the HRLN. We analyse PD
as a function of underlying noise parameters, offering insights on model
robustness to isolated and composed linguistic phenomena, and the impact of
task and HRL characteristics on PD. We calculate parameter posteriors on real
CRL-HRLN pair data and show that they follow computed trends of artificial
languages, demonstrating the viability of our noisers. Our framework offers a
cheap solution to estimating task performance on an unseen CRL given HRLN
performance using its posteriors, as well as for diagnosing observed PD on a
CRL in terms of its linguistic distances from its HRLN, and opens doors to
principled methods of mitigating performance degradation.
