  Sparse mixture of experts provides larger model capacity while requiring a
constant computational overhead. It employs the routing mechanism to distribute
input tokens to the best-matched experts according to their hidden
representations. However, learning such a routing mechanism encourages token
clustering around expert centroids, implying a trend toward representation
collapse. In this work, we propose to estimate the routing scores between
tokens and experts on a low-dimensional hypersphere. We conduct extensive
experiments on cross-lingual language model pre-training and fine-tuning on
downstream tasks. Experimental results across seven multilingual benchmarks
show that our method achieves consistent gains. We also present a comprehensive
analysis on the representation and routing behaviors of our models. Our method
alleviates the representation collapse issue and achieves more consistent
routing than the baseline mixture-of-experts methods.
