Tensor Search and Vector Databases: Memory and Search for Generative AI

One of the most interesting aspects of generative AI is the underlying databases and search techniques that are opening up new worlds, including giving memory to tools like ChatGPT. (ChatGPT has a form of amnesia, and if the conversation gets too long, it may forget directions or items from the beginning of the conversation).

Having more memory to understand context can make generative AI very powerful, as you can witness in reviewing very new tools such as AutoGPT or BabyAGI - instead of just having a chat conversation, these tools can provide a form of autonomy, to remember what they are working on, come up with ideas and refiniements, and keep on going with a project - courtesy of the underlying database. (AutoGPT/BabyAGI may require installation, but AgentGPT is a hosted way to try this technology out.)

Companies like Marqo, Weaviate, QDrant and others are leading the charge, opening up new worlds for AI, and rapidly evolving. In order to help you keep up with developments, this article discusses vector databases and tensor search, and helps you to understand where each shines.

Vector databases and tensor search are both techniques used for efficient storage, search, and retrieval of high-dimensional data. While they share some similarities, they also have differences that set them apart.?

Let's take a closer look at both:

Vector databases

Vector databases are designed to store and search through large collections of high-dimensional vectors. These vectors can represent various data types, such as images, text, or audio. The primary goal of a vector database is to enable efficient similarity search or nearest neighbor search, which involves finding vectors in the database that are closest or most similar to a given query vector. Some popular vector databases include Faiss, Annoy, and HNSW.

Advantages of vector databases:

• Efficient search and retrieval of similar items in high-dimensional spaces.
• Scalability to handle large datasets and high-dimensional data.
• Support for various similarity metrics, such as Euclidean distance, cosine similarity, and others. In data science, the similarity measure is a way of measuring how data samples are related or closed to each other.

Tensor search

Tensor search, on the other hand, is a technique that focuses on the efficient search and retrieval of high-dimensional tensors. Tensors are multi-dimensional arrays or generalizations of vectors and matrices. While vector databases are focused on vectors, tensor search is designed to handle more complex data structures with multiple dimensions.?

Tensor search can be applied in various fields, such as machine learning, computer vision, and natural language processing, where multi-dimensional data is common.

Advantages of tensor search:

• Support for searching and retrieving multi-dimensional data (beyond vectors).
• Capability to handle complex data structures and relationships.
• Potential to leverage tensor-specific operations and properties for efficient search and retrieval.

In summary, both vector databases and tensor search aim to provide efficient search and retrieval of high-dimensional data, but they differ in the types of data structures they focus on. Vector databases are designed for handling high-dimensional vectors, while tensor search focuses on multi-dimensional tensors. Depending on the nature of your data and use case, you may choose to use one approach over the other.

Applications where vector shines

Text-based information retrieval and similarity search. In this case, high-dimensional vectors can be used to represent text data, such as documents, sentences, or words, by converting them into fixed-size embeddings using techniques like Word2Vec, GloVe, or BERT.

For example, consider a large collection of articles, and you want to find the most similar articles to a given query article. The articles can be transformed into high-dimensional vectors using text embedding techniques. Vector databases can efficiently handle the nearest neighbor search in this high-dimensional space to retrieve the most similar articles based on their embeddings.

In this particular scenario, the data is well-represented by vectors, and there might not be a need for the added complexity of multi-dimensional tensors. The use of tensors could increase the computational and memory requirements without providing additional benefits in this specific context.

Vector databases like Faiss, Annoy, and HNSW are optimized for handling high-dimensional vectors and can perform similarity search very efficiently, making them well-suited for text-based information retrieval and similarity search applications.

Other examples:

• Recommender systems: Vector search can be used in collaborative filtering-based recommender systems, where user preferences and item features are represented as high-dimensional vectors. By finding similar users or items, the system can provide personalized recommendations.
• Anomaly detection: In many domains, such as cybersecurity or fraud detection, data points can be represented as high-dimensional vectors. Vector search can help to identify unusual or anomalous data points by comparing them to the normal data distribution.
• Bioinformatics: In applications like gene expression analysis or protein sequence comparison, biological data can be represented as high-dimensional vectors. Vector search can enable efficient similarity searches, helping to identify related genes or proteins and uncovering potential functional relationships.
• Speech and audio analysis: Audio signals can be represented as high-dimensional vectors using feature extraction techniques like MFCC or deep learning-based methods. Vector search can be used for tasks like speaker identification, speech recognition, or audio similarity search.

Applications where tensor shines

Tensor search shines in applications that involve complex, multi-dimensional data structures or require preserving relationships between different dimensions of the data.

Here are some examples of applications where tensor search can be particularly useful:

• Video content analysis: Videos can be represented as multi-dimensional tensors (frames x height x width x channels), and tensor search can enable efficient similarity searches based on visual and temporal features, such as scene changes, object movements, and activity recognition.
• Multi-modal data fusion: In many applications, data comes from multiple sources, such as images, text, audio, and sensor readings. Tensor search can handle the fusion of these heterogeneous data types, enabling joint analysis and similarity searches based on multi-modal information.
• Recommender systems: Tensor search can be used in recommender systems that consider multiple dimensions of user preferences, item features, and contextual information. By leveraging tensor factorization techniques, these systems can provide more accurate and personalized recommendations.
• Medical imaging: Tensor search can be useful for searching through large collections of medical images, such as MRIs or CT scans, which can be represented as multi-dimensional tensors. It can enable efficient similarity searches based on spatial and volumetric features, aiding in tasks like diagnosis, treatment planning, and research.
• Spatial-temporal data analysis: In applications involving spatial-temporal data, such as climate data, traffic data, or social network data, tensor search can help to capture the complex relationships between spatial, temporal, and other dimensions, enabling efficient similarity searches and pattern discovery.
• Cheminformatics and material science: Tensors can be used to represent molecular structures, crystal lattices, or other complex structures, and tensor search techniques can help in identifying similar compounds or materials based on their structural properties and features.

These are just a few examples of the many applications where tensor search can excel. In general, tensor search is well-suited for scenarios where multi-dimensional data needs to be analyzed, and the relationships between dimensions play a crucial role in the analysis.

High Dimensional Data = Features = Vectors

Multidimensional Data = Structure = Tensors

High-dimensional data and multi-dimensional data are related concepts but not exactly the same.?

High-dimensional data refers to data points with a large number of features or attributes. In this case, the focus is on the number of dimensions (features). These data points are often represented as vectors in high-dimensional spaces.

Multi-dimensional data, on the other hand, refers to the structure and organization of data across multiple dimensions or axes. The emphasis here is on the data's organization and structure rather than the number of features or dimensions. Multi-dimensional data can be represented using tensors, which are generalizations of vectors (1D) and matrices (2D) to higher dimensions (3D and beyond).

In some cases, high-dimensional data can also be considered multi-dimensional, especially when the data's organization and structure are crucial for processing and analysis. However, not all multi-dimensional data is high-dimensional. For example, a 3D tensor representing an RGB image (height x width x channels) is multi-dimensional but not necessarily high-dimensional, as the number of dimensions (or features) is relatively small compared to high-dimensional data like text embeddings or image feature vectors.

So, while high-dimensional data and multi-dimensional data are related, they are not the same and focus on different aspects of data representation and organization.

High-dimensional data focuses on the large number of features or dimensions, while multi-dimensional data emphasizes the structure and organization of data across multiple dimensions or axes.

To review:

High Dimensional Data = Features = Vectors

Multidimensional Data = Structure = Tensors

Woohoo!