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Dimensionality Reduction in Sentence Transformer Vector Databases with Fast Fourier Transform

Vitaly Bulgakov, Alec Segal

TL;DR

This paper introduces a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context, and advocates for the broader adoption of FFT in vector database management.

Abstract

Dimensionality reduction in vector databases is pivotal for streamlining AI data management, enabling efficient storage, faster computation, and improved model performance. This paper explores the benefits of reducing vector database dimensions, with a focus on computational efficiency and overcoming the curse of dimensionality. We introduce a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context. By demonstrating its utility across various AI domains, including Retrieval-Augmented Generation (RAG) models and image processing, this FFT-based approach promises to improve data retrieval processes and enhance the efficiency and scalability of AI solutions. The incorporation of FFT may not only optimize operations in real-time processing and recommendation systems but also extend to advanced image processing techniques, where dimensionality reduction can significantly improve performance and analysis efficiency. This paper advocates for the broader adoption of FFT in vector database management, marking a significant stride towards addressing the challenges of data volume and complexity in AI research and applications. Unlike many existing approaches, we directly handle the embedding vectors produced by the model after processing a test input.

Dimensionality Reduction in Sentence Transformer Vector Databases with Fast Fourier Transform

TL;DR

This paper introduces a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context, and advocates for the broader adoption of FFT in vector database management.

Abstract

Dimensionality reduction in vector databases is pivotal for streamlining AI data management, enabling efficient storage, faster computation, and improved model performance. This paper explores the benefits of reducing vector database dimensions, with a focus on computational efficiency and overcoming the curse of dimensionality. We introduce a novel application of Fast Fourier Transform (FFT) to dimensionality reduction, a method previously underexploited in this context. By demonstrating its utility across various AI domains, including Retrieval-Augmented Generation (RAG) models and image processing, this FFT-based approach promises to improve data retrieval processes and enhance the efficiency and scalability of AI solutions. The incorporation of FFT may not only optimize operations in real-time processing and recommendation systems but also extend to advanced image processing techniques, where dimensionality reduction can significantly improve performance and analysis efficiency. This paper advocates for the broader adoption of FFT in vector database management, marking a significant stride towards addressing the challenges of data volume and complexity in AI research and applications. Unlike many existing approaches, we directly handle the embedding vectors produced by the model after processing a test input.
Paper Structure (10 sections, 6 equations, 5 figures)

This paper contains 10 sections, 6 equations, 5 figures.

Table of Contents

  1. 1. Introduction
  2. 2. Fourier Transform
  3. 3. Method description
  4. 4. Implementation
  5. 5. Numerical examples
  6. Conclusion

Figures (5)

  • Figure 1: Two sentences are processed through the transformer and pooling layers
  • Figure 2: After retrieval vectors have been grouped into 2 clusters, "machine learning" and "wine tasting"
  • Figure 3: Reduction by order of 5 rounded to the closest integer. All first 4 retrieved vectors are related to "machine learning" topic
  • Figure 4: Reduction by order of 8. All first 4 retrieved vectors are related to "machine learning" topic
  • Figure 5: First documents retrieved from "The General Laws of Massachusetts" on "Q: Tell me about environmental protection in Massachusetts"