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Embedding methods such as word embedding have become pillars for manyapplications containing discrete structures. Conventional embedding methodsdirectly associate each symbol with a continuous embedding vector, which isequivalent to applying linear transformation based on "one-hot" encoding of thediscrete symbols. Despite its simplicity, such approach yields number ofparameters that grows linearly with the vocabulary size and can lead tooverfitting. In this work we propose a much more compact K-way D-dimensionaldiscrete encoding scheme to replace the "one-hot" encoding. In "KD encoding",each symbol is represented by a $D$-dimensional code, and each of its dimensionhas a cardinality of $K$. The final symbol embedding vector can be generated bycomposing the code embedding vectors. To learn the semantically meaningfulcode, we derive a relaxed discrete optimization technique based on stochasticgradient descent. By adopting the new coding system, the efficiency ofparameterization can be significantly improved (from linear to logarithmic),and this can also mitigate the over-fitting problem. In our experiments withlanguage modeling, the number of embedding parameters can be reduced by 97\%while achieving similar or better performance.

Learning K-way D-dimensional Discrete Code For Compact Embedding Representations