However, categorical features present a unique challenge as they require embedding a typically vast vocabulary into a smaller vector space for further calculations.

A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function (the hashing trick). In hash embeddings each token is represented by $k$ $d$-dimensional embeddings vectors and one $k$ dimensional weight vector. The final $d$ dimensional representation of the token is the product of the two. Rather than fitting the embedding vectors for each token these are selected by the hashing trick from a shared pool of $B$ embedding vectors. Our experiments show that hash embeddings can easily deal with huge vocabularies consisting of millions tokens. When using a hash embedding there is no need to create a dictionary before training nor to perform any kind of vocabulary pruning after training. We show that models trained using hash embeddings exhibit at least the same level of performance as models trained using regular embeddings across a wide range of tasks. Furthermore, the number of parameters needed by such an embedding is only a fraction of what is required by a regular embedding. Since standard embeddings and embeddings constructed using the hashing trick are actually just special cases of a hash embedding, hash embeddings can be considered an extension and improvement over the existing regular embedding types.

Our experiments show that hash embeddings can easily deal with huge vocabularies consisting of millions of tokens.

This work describes an extension of the standard word hashing trick for embedding representation by using a weighted combination of several vectors indexed by different hash functions to represent each word. This can be done using a predefined dictionary or during online training. The approach has the benefit of being easy to understand and implement and greatly reduces the number of embedding parameters. The results are generally good and the approach is quite elegant. Additionally, the hash embeddings seem to act as an effective regularizer.

A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function (the hashing trick). In hash embeddings each token is represented by k d-dimensional embeddings vectors and one k dimensional weight vector. The final d dimensional representation of the token is the product of the two. Rather than fitting the embedding vectors for each token these are selected by the hashing trick from a shared pool of B embedding vectors. Our experiments show that hash embeddings can easily deal with huge vocabularies consisting of millions of tokens. When using a hash embedding there is no need to create a dictionary before training nor to perform any kind of vocabulary pruning after training. We show that models trained using hash embeddings exhibit at least the same level of performance as models trained using regular embeddings across a wide range of tasks. Furthermore, the number of parameters needed by such an embedding is only a fraction of what is required by a regular embedding. Since standard embeddings and embeddings constructed using the hashing trick are actually just special cases of a hash embedding, hash embeddings can be considered an extension and improvement over the existing regular embedding types.

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.

Nowadays, deep learning models are widely adopted in web-scale applications such as recommender systems, and online advertising. In these applications, embedding learning of categorical features is crucial to the success of deep learning models. In these models, a standard method is that each categorical feature value is assigned a unique embedding vector which can be learned and optimized. Although this method can well capture the characteristics of the categorical features and promise good performance, it can incur a huge memory cost to store the embedding table, especially for those web-scale applications. Such a huge memory cost significantly holds back the effectiveness and usability of EDRMs. In this paper, we propose a binary code based hash embedding method which allows the size of the embedding table to be reduced in arbitrary scale without compromising too much performance. Experimental evaluation results show that one can still achieve 99\% performance even if the embedding table size is reduced 1000$\times$ smaller than the original one with our proposed method.

A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function (the hashing trick). In hash embeddings each token is represented by $k$ $d$-dimensional embeddings vectors and one $k$ dimensional weight vector. The final $d$ dimensional representation of the token is the product of the two. Rather than fitting the embedding vectors for each token these are selected by the hashing trick from a shared pool of $B$ embedding vectors. Our experiments show that hash embeddings can easily deal with huge vocabularies consisting of millions tokens.

We present hash embeddings, an efficient method for representing words in a continuous vector form. A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function (the hashing trick). In hash embeddings each token is represented by $k$ $d$-dimensional embeddings vectors and one $k$ dimensional weight vector. The final $d$ dimensional representation of the token is the product of the two. Rather than fitting the embedding vectors for each token these are selected by the hashing trick from a shared pool of $B$ embedding vectors. Our experiments show that hash embeddings can easily deal with huge vocabularies consisting of millions tokens. When using a hash embedding there is no need to create a dictionary before training nor to perform any kind of vocabulary pruning after training. We show that models trained using hash embeddings exhibit at least the same level of performance as models trained using regular embeddings across a wide range of tasks. Furthermore, the number of parameters needed by such an embedding is only a fraction of what is required by a regular embedding. Since standard embeddings and embeddings constructed using the hashing trick are actually just special cases of a hash embedding, hash embeddings can be considered an extension and improvement over the existing regular embedding types.