  Cross-lingual natural language understanding (NLU) is a critical task in
natural language processing (NLP). Recent advancements have seen multilingual
pre-trained language models (mPLMs) significantly enhance the performance of
these tasks. However, mPLMs necessitate substantial resources and incur high
computational costs during inference, posing challenges for deployment in
real-world and real-time systems. Existing model cascade methods seek to
enhance inference efficiency by greedily selecting the lightest model capable
of processing the current input from a variety of models, based on model
confidence scores. Nonetheless, deep models tend to exhibit overconfidence, and
confidence distributions vary across languages. This leads to the emission of
confident but incorrect predictions by smaller models, hindering their ability
to generalize effectively across test languages. In this study, we introduce a
confidence calibration model cascade ($C^3$) method. This approach, simple yet
effective, involves calibration prior to cascade inference, thereby enhancing
cascade accuracy through more reliable predictions. Extensive experiments
conducted on three cross-lingual benchmarks demonstrate that $C^3$
significantly outperforms all state-of-the-art baselines.
