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Recent research has reported that standard fine-tuning approaches can be unstable due to being prone to various sources of randomness, including but not limited to weight initialization, training data order, and hardware. Such brittleness can lead to different evaluation results, prediction confidences, and generalization inconsistency of the same models independently fine-tuned under the same experimental setup. Our paper explores this problem in natural language inference, a common task in benchmarking practices, and extends the ongoing research to the multilingual setting. We propose six novel textual entailment and broad-coverage diagnostic datasets for French, German, and Swedish. Our key findings are that the mBERT model demonstrates fine-tuning instability for categories that involve lexical semantics, logic, and predicate-argument structure and struggles to learn monotonicity, negation, numeracy, and symmetry. We also observe that using extra training data only in English can enhance the generalization performance and fine-tuning stability, which we attribute to the cross-lingual transfer capabilities. However, the ratio of particular features in the additional training data might rather hurt the performance for model instances. We are publicly releasing the datasets, hoping to foster the diagnostic investigation of language models (LMs) in a cross-lingual scenario, particularly in terms of benchmarking, which might promote a more holistic understanding of multilingualism in LMs and cross-lingual knowledge transfer. [ABSTRACT FROM AUTHOR]