Below are the abstract, introduction, and conclusion of a computer science research paper. Please summarize the main contribution of the work in a single sentence. Your response should include the summary and no additional text.

Paper text:

Computations for the softmax function in neural network models are expensive when the number of output classes is large.
This can become a significant issue in both training and inference for such models.
In this paper, we present Doubly Sparse Softmax (DS-Softmax), Sparse Mixture of Sparse of Sparse Experts, to improve the efficiency for softmax inference.
During training, our method learns a two-level class hierarchy by dividing entire output class space into several partially overlapping experts.
Each expert is responsible for a learned subset of the output class space and each output class only belongs to a small number of those experts.
During inference, our method quickly locates the most probable expert to compute small-scale softmax.
Our method is learning-based and requires no knowledge of the output class partition space a priori.
We empirically evaluate our method on several real-world tasks and demonstrate that we can achieve significant computation reductions without loss of
We present doubly sparse softmax, the sparse mixture of sparse of sparse experts, to improve the efficiency for softmax inference through exploiting the two-level overlapping hierarchy.