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Vector Embeddings: The Mathematical Foundation of Modern AI Systems

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  • Vijay Vaibhav Singh

Abstract

This comprehensive article examines vector embeddings as a fundamental component of modern artificial intelligence systems, detailing their mathematical foundations, key properties, implementation techniques, and practical applications. The article traces the evolution from basic word embeddings to sophisticated transformer-based architectures, highlighting how these representations enable machines to capture and process semantic relationships in human language and visual data. The article encompasses both theoretical frameworks and practical implementations, from the groundbreaking Word2Vec and GloVe models to contemporary developments in multimodal embeddings and dynamic learning systems. The article demonstrates how vector embeddings have revolutionized various domains, including natural language processing, computer vision, and information retrieval, while addressing crucial considerations in computational efficiency and scalability.

Suggested Citation

  • Vijay Vaibhav Singh, 2025. "Vector Embeddings: The Mathematical Foundation of Modern AI Systems," International Journal of Scientific Research in Computer Science, Engineering and Information Technology, International Journal of Scientific Research in Computer Science, Engineering and Information Technology, vol. 11(1), pages 2408-2417, February.
    • Handle: RePEc:jbh:ijsrcs:v11:y2025:i1:id:910
    DOI: 10.32628/CSEIT251112257
    Note: Article URL: https://ijsrcseit.com/home/article/view/CSEIT251112257
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