Text embeddings are a powerful tool for representing meaning in a way that machines can understand. They bridge the gap between human language and mathematical representations, enabling a wide range of NLP applications.

1. Linguistic Aspects: Representing Meaning as Vectors

• Core Idea:
  • Embeddings aim to capture the semantic meaning of words, phrases, or even entire documents as dense vectors in a high-dimensional space.
  • Instead of treating words as discrete symbols (like in one-hot encoding), embeddings represent them as continuous vectors, where similar words have vectors that are close to each other in the vector space (Linear Space).
• Semantic Relationships:
  • The key advantage is that embeddings encode semantic relationships. For example, the vectors for “king” and “queen” will be closer than the vectors for “king” and “kind.”
  • This allows models to understand analogies (“king - man + woman = queen”) and other complex linguistic relationships.
• Contextual Embeddings:
  • Modern embeddings, like those from BERT or GPT, are contextual. This means that the embedding of a word depends on the surrounding words in the sentence.
  • For example, “bank” in “river bank” and “bank account” will have different embeddings.
  • This addresses the issue of polysemy (words with multiple meanings).
• Beyond Words:
  • Embeddings are not limited to words. They can represent:
    • Phrases
    • Sentences
    • Documents
    • Even concepts or entities in a knowledge graph.
  • This allows for many kinds of natural language processing tasks.

2. Mathematical Aspects: Vector Spaces and Distance Metrics

• Vector Spaces:
  • Embeddings live in a high-dimensional vector space (e.g., 300 dimensions).
  • Each dimension represents a latent feature of the word or concept. These features are not easily interpretable by humans, but they capture subtle aspects of meaning.
• Distance Metrics:
  • To measure the similarity between embeddings, we use distance metrics:
    • Cosine Similarity: Measures the angle between two vectors. It’s often preferred for embeddings because it focuses on the direction of the vectors, rather than their magnitude.
    • Euclidean Distance: Measures the straight-line distance between two vectors.
    • These metrics allow us to quantify how semantically similar two pieces of text are.
• Dimensionality Reduction:
  • Techniques like [[PCA]], t-SNE, UMAP, MDS can be used to visualize embeddings in 2D or 3D, making it easier to see how words are clustered based on their meaning.
• Mathematical Operations:
  • Vector arithmetic can be performed on word embeddings to produce interesting results. For example:
    • vector("king") - vector("man") + vector("woman") ≈ vector("queen")

3. Programming Aspects: Implementation and Usage

• Libraries:
  • Popular libraries for working with embeddings:
    • TensorFlow/Keras: For training and using custom embeddings.
    • PyTorch: Another powerful deep learning framework with extensive embedding support.
    • spaCy: Provides pre-trained word and document embeddings.
    • Transformers (Hugging Face): Offers easy access to state-of-the-art pre-trained models like BERT, GPT, and their embeddings.
    • Gensim: A library for topic modeling and word embeddings (including Word2Vec).
• Pre-trained Embeddings:
  • Often, we use pre-trained embeddings (e.g., Word2Vec, GloVe, FastText, BERT embeddings) rather than training them from scratch.
  • These embeddings have been trained on massive text corpora and capture rich semantic information.
• Embedding Layers:
  • In neural networks, an embedding layer is used to convert input tokens (words or other discrete units) into dense vectors.
  • This layer can be trained as part of the network or initialized with pre-trained embeddings.
• Workflow:
  1. [[tokenization]]: Convert text into tokens (words, subwords, etc.) then to integer indices within the vocabulary.
  2. Embedding Lookup: Look up the embedding vector for each token.
  3. Vector Processing: Use the embeddings as input to a neural network or other machine learning model.
  4. Similarity Calculations: Use cosine similarity or other metrics to compare embeddings.
• Example python code using hugging face transformers:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21

from transformers import BertTokenizer, BertModel
import torch
from sklearn.metrics.pairwise import cosine_similarity

tokenizer = BertTokenizer.from_pretrained('bert-base-uncased')
model = BertModel.from_pretrained('bert-base-uncased')

def get_embedding(text):
    inputs = tokenizer(text, return_tensors='pt')
    with torch.no_grad():
        outputs = model(**inputs)
    return outputs.last_hidden_state.mean(dim=1) # Mean pooling to get sentence embedding

text1 = "The cat sat on the mat."
text2 = "A feline rested on the rug."

embedding1 = get_embedding(text1)
embedding2 = get_embedding(text2)

similarity = cosine_similarity(embedding1, embedding2)
print(f"Cosine similarity: {similarity[0][0]}")

Embedding storage

1. Vector Databases:

• Purpose:
  • Specifically designed for efficient storage and retrieval of vector embeddings.
  • Optimized for similarity search, which is crucial for applications using embeddings.
• Examples:
  • Chroma: An open-source embedding database that simplifies LLM application development.
  • Pinecone: A popular vector database service.
  • Weaviate: An open-source vector database.
  • Milvus: Another open-source vector database built for AI applications.
• Key Features:
  • Efficient similarity search algorithms (e.g., approximate nearest neighbor).
  • Scalability to handle large volumes of embeddings.
  • [[metadata]] storage alongside vectors.

2. Traditional Databases with Vector Extensions:

• Purpose:
  • Leveraging existing database infrastructure to store and query embeddings.
  • Adding vector search capabilities to traditional databases.
• Examples:
  • PostgreSQL with pgvector: The pgvector extension enables PostgreSQL to store and query vector embeddings efficiently.
  • BigQuery: Google BigQuery now offers vector search capabilities.
• Advantages:
  • Integration with existing database systems.
  • Combining vector search with other database operations.

3. Cloud-Based Vector Search Services:

• Purpose:
  • Cloud providers offer managed services for vector search.
  • Simplifying the deployment and management of vector search infrastructure.
• Examples:
  • Google Vertex AI Vector Search: A managed service for efficient similarity search.
  • Amazon OpenSearch Service: Offers k-NN (k-nearest neighbors) search for vector embeddings.
• Benefits:
  • Scalability and reliability provided by cloud infrastructure.
  • Reduced operational overhead.

4. Simple File Storage:

• Purpose:
  • For smaller-scale applications or development purposes, embeddings can be stored in files.
  • Examples of file types that can be used are pickle files, or CSV files.
• Limitations:
  • Not suitable for large-scale applications due to performance limitations.
  • Lack of efficient similarity search capabilities.