  Embedding tables are used by machine learning systems to work with
categorical features. In modern Recommendation Systems, these tables can be
very large, necessitating the development of new methods for fitting them in
memory, even during training. We suggest Clustered Compositional Embeddings
(CCE) which combines clustering-based compression like quantization to
codebooks with dynamic methods like The Hashing Trick and Compositional
Embeddings (Shi et al., 2020). Experimentally CCE achieves the best of both
worlds: The high compression rate of codebook-based quantization, but
*dynamically* like hashing-based methods, so it can be used during training.
Theoretically, we prove that CCE is guaranteed to converge to the optimal
codebook and give a tight bound for the number of iterations required.
