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.