The Role and Application of Matrices in Artificial Intelligence: Foundations, Methods, and Advancements

Raviraju Balappa D; Dr. Gautam Kumar Rajput1

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Publication Date: 2024/11/29

Abstract: Matrices are foundational to artificial intelligence (AI), serving as critical tools for data representation, manipulation, and transformation across various applications. From machine learning algorithms to neural network architectures, matrix theory supports essential computational processes, enabling AI systems to manage vast datasets, detect intricate patterns, and execute complex transformations. This paper examines the integral role of matrices in AI, highlighting basic matrix operations in linear and logistic regression, as well as their applications in more advanced models like convolutional neural networks (CNNs) and recurrent neural networks (RNNs). Key mathematical operations, including matrix decomposition and eigenvalue computations, are explored for their significance in data reduction and feature extraction, which enhance computational efficiency in fields like computer vision, natural language processing (NLP), and robotics. The paper also addresses the computational challenges associated with large-scale matrix operations, such as high-dimensional data processing, scalability, and numerical stability. To overcome these limitations, advancements in distributed matrix computation frameworks, GPU and TPU hardware acceleration, and sparse matrix techniques are discussed, showing how these innovations enhance the efficiency and scalability of AI models. Additionally, recent progress in quantum computing and matrix-specific hardware solutions offers promising directions for future research, with potential to revolutionize AI by achieving exponential speed-ups in matrix computations. Overall, matrices remain at the heart of AI’s computational power, providing a versatile and efficient framework that supports both current applications and emerging capabilities in artificial intelligence.

Keywords: Matrix theory, linear algebra, machine learning, artificial intelligence, singular value decomposition (SVD).

DOI: https://doi.org/10.38124/ijisrt/IJISRT24NOV378

PDF: https://ijirst.demo4.arinfotech.co/assets/upload/files/IJISRT24NOV378.pdf

REFERENCES

  1. Ahmad, K., & Kamal, R. (2021). Matrix decomposition techniques in high-dimensional data processing. Journal of Machine Learning Research, 22(1), 456–469.
  2. Chen, M., & Li, F. (2020). The role of sparse matrices in transformer architectures for NLP. ACM Transactions on Information Systems, 38(3), 15–30.
  3. Das, T., & Malhotra, S. (2019). Collaborative filtering and matrix factorization in recommendation systems. ACM Transactions on Information Systems, 37(2), 10–25.
  4. Ebrahimi, A., & Zhao, H. (2021). Efficient data representation through matrix transformations in computer vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(7), 1453–1467.
  5. Fang, Z., & Wang, L. (2021). Quantum matrix algorithms for artificial intelligence: Potential and limitations. Nature Quantum Information, 7(12), 34–48.
  6. Gomez, R., & Lee, D. (2019). The impact of SVD in NLP for semantic understanding. Journal of Machine Learning Research, 20(4), 345–359.
  7. Hall, P. A., & Kearney, J. (2020). Matrix operations for convolutional neural networks in image processing. Neural Networks, 126(1), 57–70.
  8. Irwin, T. M., & Zheng, Y. (2020). Applications of eigenvalues in reinforcement learning policy optimization. IEEE Transactions on Neural Networks and Learning Systems, 31(10), 3451–3465.
  9. Jones, L., & Li, P. (2019). GPU acceleration of large-scale matrix operations in neural networks. Journal of Computational Science, 36(1), 89–103.
  10. Kim, J., & Park, Y. (2021). Exploring matrix-based representations for path planning and control in robotics. AI and Robotics Journal, 42(2), 101–116.
  11. Liu, W., & Thompson, K. (2020). Matrix fundamentals for linear and logistic regression in machine learning. Journal of Artificial Intelligence Research, 69, 1085–1102.
  12. Morgan, S. M., & Zhao, R. (2021). Scaling matrix computations in distributed AI systems. Journal of Parallel and Distributed Computing, 155, 87–101.
  13. Nguyen, V., & Chen, M. (2020). The role of matrix operations in CNNs for object detection. Neural Networks, 123, 99–113.
  14. Patel, R., & Mehta, S. (2021). Dimensionality reduction with PCA and its applications in image compression. International Journal of Computer Vision, 129(5), 1156–1172.
  15. Qian, J., & Sun, Y. (2020). Numerical stability in matrix-based neural network training. Journal of Computational Science, 39(4), 129–141.
  16. Raviraju Balappa D, & Gautam Kumar Rajput. (2024). Efficient Error Reduction Techniques by Hamming Code In Transmission Channel. Journal of Computational Analysis and Applications (JoCAAA), 33(06), 505–515. Retrieved from https://www.eudoxuspress.com/index.php/pub/article/view/827
  17. Singh, K., & Wu, H. (2019). Real-time matrix-based sensor fusion in robotics. AI and Robotics Journal, 39(3), 211–223.
  18. Tanaka, R., & Yoon, J. (2020). Advances in distributed matrix computation frameworks for machine learning. Journal of Parallel and Distributed Computing, 150, 78–91.
  19. Wang, Z., & Lin, Q. (2021). Applications of matrix theory in transformer models for NLP. Journal of Artificial Intelligence Research, 71, 672–685.
  20. Xu, D., & Chen, J. (2021). Optimizing matrix factorization for scalability in recommendation systems. ACM Transactions on Information Systems, 39(1), 45–60.
  21. Zhang, L., & Wei, Y. (2020). Leveraging TPUs for efficient matrix calculations in deep learning. Journal of Computational Science, 41, 312–325.