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

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