Introduction to Embeddings

Introduction

Embeddings are a representation technique in machine learning that transforms high-dimensional data, such as text or images, into a lower-dimensional vector space while retaining some information. The goal is to represent these quantities as vectors of numbers where the semantic distance is captured.

In machine learning, we sometimes work with data unsuitable for numerical computation, such as text, images or categorical variables. Embeddings provide a way to represent this data, enabling neural networks and other machine learning models to process and learn from it effectively.

Consider building a recommendation system for movies. The available information consists of user data and the movies they have watched. However, this data is represented as movie titles and user IDs, which a machine learning model cannot directly utilize. To address this issue, embeddings can be created for both movies and users, allowing them to be represented as dense vectors that capture their similarities and relationships. In this vector space, movies with similar characteristics or users with similar preferences will have embeddings close to each other. By leveraging this representation, the recommendation system can learn patterns and make personalized movie suggestions for each user based on their embedding's proximity to other users and movies in the vector space. This approach enables the recommendation system to effectively utilize the available data and provide users with accurate and tailored movie recommendations.

This transformation allows for more efficient processing and analysis of complex data. Embeddings are widely used in various domains, including natural language processing (NLP) and recommender systems.

Definition

An embedding maps discrete or categorical variables to a continuous vector space. In other words, it represents each entity (e.g., a word, a movie, or a user) as a dense vector of fixed dimensionality. The key idea behind embeddings is that similar entities should have similar vector representations.

Learning embeddings involves training a neural network or a matrix factorization model on a large dataset. The model learns to assign vectors to each entity by optimizing an objective function that captures the relationships and similarities between entities.

For example, commonly used, pre-trained word embedding models, such as Word2Vec (opens in a new tab) or GloVe (opens in a new tab), the objective is to predict the probability of a word given its context or the probability of the context given a word. The resulting embeddings capture semantic and syntactic relationships between words, such that words with similar meanings or grammatical properties have similar representations.

The embedding matrix, denoted as $E$, is a lookup table where each row corresponds to the embedding vector of an entity. For a given entity $i$, its embedding vector $e_i$ can be obtained by indexing the embedding matrix:

Where $E[i,:]$ denotes the $i$-th row of the embedding matrix.

The dimensionality of the embedding vectors denoted as $d$, is a hyperparameter that determines the capacity and expressiveness of the embeddings. Higher-dimensional embeddings can capture more fine-grained relationships but also require more computational resources and may be prone to overfitting.

Once the embeddings are learned, they can be used as input features for downstream tasks, such as classification, clustering, or similarity search. The embeddings provide a dense and informative representation of the entities, allowing machine learning models to leverage the captured relationships and patterns.

Applications

• Profiling On-chain Users: Given a set of transactions and addresses, and their past transaction history, embedding models can be trained to develop representation of on-chain users. These representation would ask as Sybil profiles, or credit worthiness etc.

• Natural Language Processing: Word embeddings, such as Word2Vec and GloVe, have transformed the field of NLP. They enable models to understand and reason about the meaning of words and their relationships. Embeddings have been successfully applied to sentiment analysis, named entity recognition, and machine translation tasks.

• Recommendation Systems: Embeddings are widely used in recommendation systems to represent users and items (e.g., movies, products) in a shared vector space. By learning embeddings based on user-item interactions, recommendation models can capture user preferences and item similarities, enabling personalized recommendations.

Conclusion

Embeddings are a powerful technique for representing data in a shared vector space. By learning dense vector representations that capture the relationships and similarities between entities, embeddings enable machine learning models to process and learn from non-numerical data effectively.

As a machine learning practitioner, understanding embeddings is crucial for working with text, categorical variables, and recommendation systems. By leveraging the expressiveness of embeddings, one can build models that understand and reason about complex relationships in data.

Resources

• Embeddings for Everything by Dan Gillick (opens in a new tab)
• Word Vector Representations by Christopher Manning (opens in a new tab)
• Getting Started with Embeddings - Hugging Face (opens in a new tab)