Vector embeddings

Introduction

Vector embeddings are numerical representations of data that encapsulate particular features of the data, enabling the effective execution of semantic search by capturing the semantic similarity between different data objects. They play a central role in numerous natural language processing (NLP), recommendation, and search algorithms. These embeddings enable systems such as recommendation engines, voice assistants, and language translators to function effectively. Machine learning algorithms, like other software algorithms, require numerical data to operate. Vector embeddings are lists of numbers that represent more abstract data types, such as text documents or other non-numeric objects, facilitating various operations. The use of vector embeddings allows for the translation of human-perceived semantic similarity into proximity within a vector space.

Understanding Vector Embeddings

In the context of text data, words with similar meanings, such as "cat" and "kitty", must be represented in a manner that captures their semantic similarity. Vector representations achieve this by transforming data objects into arrays of real numbers with a fixed length, typically ranging from hundreds to thousands of elements. These arrays are generated by machine learning models through a process called vectorization.

For instance, the words "cat" and "kitty" may be vectorized as follows:

cat = [1.5, -0.4, 7.2, 19.6, 3.1, ..., 20.2] kitty = [1.5, -0.4, 7.2, 19.5, 3.2, ..., 20.8]

These vectors exhibit a high similarity, while vectors for words like "banjo" or "comedy" would not be similar to either of these. In this way, vector embeddings capture the semantic similarity of words. The specific meaning of each number in a vector depends on the machine learning model that generated the vectors, and is not always clear in terms of human understanding of language and meaning.

Vector-based representation of meaning has gained attention due to its ability to perform mathematical operations between words, revealing semantic relationships. A famous example is:

"king − man + woman ≈ queen"

This result suggests that the difference between "king" and "man" represents some sort of "royalty", which is analogously applicable to "queen" minus "woman". Various concepts, such as "woman", "girl", "boy", etc., can be vectorized into arrays of numbers, often referred to as dimensions. These arrays can be visualized and correlated to familiar words, giving insight into their meaning.

Vector embeddings can represent more than just word meanings. They can effectively be generated from any data object, including text, images, audio, time series data, 3D models, video, and molecules. Embeddings are constructed such that two objects with similar semantics have vectors that are "close" to each other in vector space, with a "small" distance between them.

Generating Vector Embeddings

The primary aspect of vector search's effectiveness lies in generating embeddings for each entity and query. The secondary aspect is efficiently searching within very large datasets.

Vector embeddings can be generated for various media types, such as text, images, audio, and others. For text, vectorization techniques have significantly evolved over the last decade, from word2vec (2013) to the state-of-the-art transformer models era, which began with the release of BERT in 2018.

Word-level Dense Vector Models (word2vec, GloVe, etc.)

word2vec is a group of model architectures that introduced the concept of "dense" vectors in language processing, in which all values are non-zero. It uses a neural network model to learn word associations from a large text corpus. The model first creates a vocabulary fromthe corpus and then learns vector representations for the words, usually with 300 dimensions. Words found in similar contexts have vector representations that are close in vector space.

However, word2vec suffers from limitations, including its inability to address words with multiple meanings (polysemantic) and words with ambiguous meanings.

Transformer Models (BERT, ELMo, and others)

The current state-of-the-art models are based on the transformer architecture. Models like BERT and its successors improve search accuracy, precision, and recall by examining the context of each word to create full contextual embeddings. Unlike word2vec embeddings, which are context-agnostic, transformer-generated embeddings consider the entire input text. Each occurrence of a word has its own embedding that is influenced by the surrounding text, better reflecting the polysemantic nature of words, which can only be disambiguated when considered in context.

Some potential downsides of transformer models include:

Increased compute requirements: Fine-tuning transformer models is much slower (taking hours instead of minutes). Increased memory requirements: Context-sensitivity greatly increases memory requirements, often leading to limitations on possible input lengths. Despite these drawbacks, transformer models have been incredibly successful, leading to a proliferation of text vectorizer models for various data types such as audio, video, and images. Some models, like CLIP, can vectorize multiple data types (e.g., images and text) into a single vector space, enabling content-based image searches using only text.

Creating Vector Embeddings for Other Media Types

In addition to text, vector embeddings can be created for various types of data, such as images and audio recordings. Images can be embedded using convolutional neural networks (CNNs) like VGG and Inception, while audio recordings can be converted into vectors using image embedding transformations over their visual representations, such as spectrograms.

Example: Image Embedding with a Convolutional Neural Network

In this example, raw images are represented as greyscale pixels, which correspond to a matrix of integer values ranging from 0 to 255, where 0 signifies black and 255 represents white. The matrix values define a vector embedding, with the first coordinate being the matrix's upper-left cell and the last coordinate corresponding to the lower-right matrix cell.

While such embeddings effectively maintain the semantic information of a pixel's neighborhood in an image, they are highly sensitive to transformations like shifts, scaling, cropping, and other image manipulation operations. Consequently, they are often used as raw inputs to learn more robust embeddings.

A Convolutional Neural Network (CNN or ConvNet) is a class of deep learning architectures typically applied to visual data, transforming images into embeddings. CNNs process input through hierarchical small local sub-inputs known as receptive fields. Each neuron in each network layer processes a specific receptive field from the previous layer. Each layer either applies a convolution on the receptive field or reduces the input size through a process called subsampling.

A typical CNN structure includes receptive fields as sub-squares in each layer, serving as input to a single neuron within the preceding layer. Subsampling operations reduce layer size, while convolution operations expand layer size. The resulting vector embedding is obtained through a fully connected layer.

Learning the network weights (i.e., the embedding model) requires a large set of labeled images. The weights are optimized to ensure that images with the same labels have closer embeddings compared to those with different labels. Once the CNN embedding model is learned, images can be transformed into vectors and stored with a K-Nearest-Neighbor index. For a new unseen image, it can be transformed using the CNN model, its k-most similar vectors can be retrieved, and the corresponding similar images can be identified.